Comparison of the Role of Beamwidth in Biological andEngineered Sonar

Bryan D. Todd

Thesis submitted to the Faculty of theVirginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree

Master of Sciencein

Mechanical Engineering

Rolf Muller, ChairAlexander Leonessa

Pinhas Ben-Tzvi

September 29, 2017Blacksburg, Virginia

Keywords: Bat, Beamwidth, Bioinspired, SonarCopyright 2017, Bryan D. Todd

Comparison of the Role of Beamwidth in Biological and Engineered Sonar

Bryan D. Todd

(ABSTRACT)

Sonar is an important sensory modality for engineers as well as in nature. In engineer-ing, sonar is the dominating modality for underwater sensing. In biology, it is likely tohave been a central factor behind the unprecedented evolutionary success of bats, a highlydiverse group that accounts for over 20% of all mammal species. However, it remainsunclear to what extent engineered and biosonar follow similar design and operationalprinciples. In the current work, the key sonar design characteristic of beamwidth is ex-amined in technical and biosonar. To this end, beamwidth data has been obtained for 23engineered sonar systems and from numerical beampattern predictions for 151 emissionand reception elements (noseleaves and pinnae) from bat biosonar. Beamwidth data fromthese sources is compared to the beamwidth of a planar ellipsoidal transducer as a refer-ence. The results show that engineered and biological both obey the basic physical limiton beamwidth as a function of the ratio of aperture size and wavelength. However, be-yond that, the beamwidth data revealed very different behaviors between the engineeredand the biological sonar systems. Whereas the beamwidths of the technical sonar systemswere very close to the planar transducer limit, the biological samples showed a very widescatter away from this limit. This scatter was as large – if not wider – than what was seenin a small reference data set obtained with random aluminum cones. A possible interpre-tation of these differences in the variability could be that whereas sonar engineers try tominimize beamwidth subject to constraints on device size, the evolutionary optimizationof bat biosonar beampatterns has been directed at other factors that have left beamwidthas a byproduct. Alternatively, the biosonar systems may require beamwidth values thatare larger than the physical limit and differ between species and their sensory ecologicalniches.

This work was supported by grants from the National Science Foundation (NSF Grant No.ID 1362886) and the Naval Engineering Education Consortium (NEEC, contract numberN00174-16-C-0026).

Comparison of the Role of Beamwidth in Biological and Engineered Sonar

Bryan D. Todd

(GENERAL AUDIENCE ABSTRACT)

Sonar is an important method of sensing for engineers in undersea environments, but it isalso used by several species of animals for for everyday use. The most prominent speciesthat uses sonar, or echolocation, are bats, one of the most diverse groups of mammals. Thestudy of bat biosonar systems serves as a counterpoint to many of the concepts in technicalsonar. In technical sonar, arrays are made to be larger in size, with more elements, andoperate at higher frequencies in order to decrease their beamwidth which increases theirresolution. Unlike technical sonars bats must rely on smaller sized systems that they cancarry around and they operate in air which has worse qualities for propagating soundwaves. Even with these disadvantages, bats are able to operate in complex environments,such as dense vegetation, with ease. This work compared 151 emission and receptionelements of bat biosonar systems with 23 engineered sonars to find that the biosonar hadvery different behavior from the engineered sonars. The engineered sonars, as well as aset of experimental baffles, closely followed the curve for the beamwidth limit of planartransducers but the biosonar samples had a large scatter from the curve. These results couldbe interpreted to show that while the engineered sonars attempt to minimize the beamwidthin order to maximize the resolution, the biosonar did not place much importance on havinglow beamwidths and high resolutions during its evolution. Alternatively, the results couldindicate that it is preferable for biosonar to have larger beamwidths, a contrast to standardsonar design.

Acknowledgements

I would like to thank Dr. Rolf Muller for having provided me with the opportunity toperform this research and teaching me so much along the way. I would also like to thankmy committee members, Dr. Alexander Leonessa and Dr. Pinhas Ben-Tzvi. Addition-ally, I would like to thank Dr. Jason Gaudette from the Naval Undersea Warfare Centerfor the original idea of comparing technical and bat biosonar beamwidths and the NavalEngineering Education Consortium for sponsoring my research.

iv

Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Review of Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Bioinspiration and Biomimetics . . . . . . . . . . . . . . . . . . 3

1.2.2 Bats and Biosonar . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.3 Review of Technical Sonar Literature . . . . . . . . . . . . . . . 5

1.2.4 Sonar Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.5 Trends in Sonar Research . . . . . . . . . . . . . . . . . . . . . 6

1.2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Problem Statement and Research Objectives . . . . . . . . . . . . . . . . 8

1.3.1 The Case for Studying Biosonar . . . . . . . . . . . . . . . . . . 8

1.3.2 Research Objectives and Hypotheses . . . . . . . . . . . . . . . 8

2 Methods 11

2.1 Biosonar Apertures and Conversion to Engineering Analogues . . . . . . 11

2.1.1 Biosonar Aperture Data . . . . . . . . . . . . . . . . . . . . . . 11

2.1.2 Conversion from µCT Scans to Engineering Analogue . . . . . . 12

2.2 Beamwidth Determination for Biosonar Apertures . . . . . . . . . . . . . 14

2.2.1 Importance of Beamwidth . . . . . . . . . . . . . . . . . . . . . 14

v

2.2.2 Planar Array Reference Beamwidth . . . . . . . . . . . . . . . . 14

2.2.3 Generation of Numerically Derived Beampatterns . . . . . . . . . 15

2.2.4 Biosonar Beamwidth Evaluation . . . . . . . . . . . . . . . . . . 15

2.2.5 Half-Power vs Quarter-Power Beamwidths . . . . . . . . . . . . 16

2.3 Acquisition of Technical Sonar Data . . . . . . . . . . . . . . . . . . . . 17

2.3.1 Military Sonar vs Commercial Sonar . . . . . . . . . . . . . . . 17

2.3.2 Technical Sonars Used for Comparison . . . . . . . . . . . . . . 18

2.4 Aluminum Random Emission Baffle Experiment . . . . . . . . . . . . . 18

2.4.1 Equipment and Setup . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4.2 Creation of Random Emission Baffles . . . . . . . . . . . . . . . 19

3 Results 21

3.1 Half-Power Beamwidths and Quarter-Power Beamwidths . . . . . . . . . 21

3.2 Beamwidth Comparison of Engineered and Biosonar . . . . . . . . . . . 24

3.3 Noseleaf Simulate Experiment Results Compared to Biosonar . . . . . . 28

3.4 Comparison of Bat Families With and Without Active Biosonar . . . . . . 31

3.5 Emission vs Reception Elements . . . . . . . . . . . . . . . . . . . . . . 32

3.6 Additional Supporting Analysis . . . . . . . . . . . . . . . . . . . . . . 35

3.6.1 Maximum vs Minimum Beamwidth . . . . . . . . . . . . . . . . 35

3.6.2 Geometric Effects on Beamwidth . . . . . . . . . . . . . . . . . 37

3.6.3 Distance To Limit . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Discussion 43

4.1 Importance of Beamwidth in Biosonar . . . . . . . . . . . . . . . . . . . 43

4.2 Differences in Emission and Reception . . . . . . . . . . . . . . . . . . . 44

5 Conclusion 46

vi

5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3 Importance of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.4 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Bibliography 50

Appendix 54

Appendix A: Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Appendix A.1: Geometric Processing Code . . . . . . . . . . . . . . . . 54

Appendix A.2: Beampattern Processing Code . . . . . . . . . . . . . . . 65

Appendix A.3: Beampattern Post Processing Code . . . . . . . . . . . . 78

Appendix B: Raw Data Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

vii

List of Figures

1.1 A look at an engineered sonar system vs biosonar elements. A) An Ed-getech 4200 Side Scan sonar system that contains sensors along it’s 125cm length [5] (Picture Copyright Edgetech, reproduced with permission)and B) A bat from the Rhinolophidae family with its right pinnae (outerear) and noseleaf circled in purple. . . . . . . . . . . . . . . . . . . . . . 2

1.2 Visual representation of the first hypothesis tested in the current work: A)shows the first form of the hypothesis, that the engineered sonars, repre-sented by black triangles, and biosonars, grey dots, have similar scatter andcloseness to the reference limit represented by the black line. B) shows thealternative hypothesis that the biosonar has a larger scatter. . . . . . . . . 9

1.3 Visual representation of the second hypothesis to be tested in the currentwork: A) shows the first form of the hypothesis, that the aluminum baf-fles, represented by black triangles, and biosonars, grey dots, have sim-ilar scatter and closeness to the reference limit represented by the blackline. B) shows the alternative hypothesis that either the reference bafflesor biosonar has less scatter. . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 Approximation of the biological shape samples by a planar elliptical trans-ducer: A) µCT model of a noseleaf from a Sulawesi horseshoe bat (Rhi-nolophus celebensis), B) Point cloud resulting from detecting edge ver-tices in the mesh, C) Edge vertices projected into the fitting plane withlines along the minimum and maximum aperture lengths (dashed lines). . 13

viii

2.2 Conversion of two-dimensional, numerical beampattern estimates into one-dimensional beampattern functions: A) a numerical beampattern estimatederived from the Sulawesi horseshoe bat (Rhinolophus celebensis) shownin Figure 2.1. B) One of the beampattern slices obtained at different ro-tation angles, shown in polar coordinates. C) The same beampattern sliceshown in B) converted in to Cartesian coordinates. The horizontal linesindicate the -3dB and -6dB threshold levels . . . . . . . . . . . . . . . . 17

2.3 Setup for the experiment with the random aluminum baffles: A) Diagramof the experimental setup with dimensions of the loudspeaker, waveguide(shown in blue), and random aluminum foil baffles with the microphonein the far-field. B) Picture of the experiment set up. . . . . . . . . . . . . 20

3.1 Comparison of half-power (-3dB) beamwidth (A) and quarter-power (-6dB) beamwidth (B) for the bat biosonar elements. Theoretical minimumbeamwidth values are shown as solid black lines for both levels. D is thebat aperture diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Impact of sidelobes on the beamwidth of the biosonar beampattern sam-ples for noseleaves (gray circles) and pinnae (black x’s). Points on thediagonal line do not have sidelobes amplitudes that are large enough toeffect the beamwidth estimates. . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Half-power beamwidth values with respect to the aperture diameter (D)to wavelength (λ) ratio. A) The HP beamwidths calculated using the firstpoint where the beampattern amplitudes crossed the HP threshold and B)the HP beamwidths calculated using the furthest point where the beampat-tern crossed the HP threshold. . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Quarter-power beamwidth values with respect to the aperture diameter (D)to wavelength (λ) ratio. A) The QP beamwidths calculated using the firstpoint where the beampattern amplitudes crossed the QP threshold and B)the QP beamwidths calculated using the furthest point where the beampat-tern crossed the QP threshold. . . . . . . . . . . . . . . . . . . . . . . . 25

ix

3.5 Comparison of biosonar and engineered sonar half-power beamwidths tothe elliptical-transducer limit values (solid line) as a function of the ratiocharacteristic dimension (D) over wavelength (λ). Biosonar samples arerepresented by light gray circles and engineered sonars by black triangles.D is a characteristic dimension of the sonar, i.e., array-length for technicalsonar and noseleaf or pinna diameter for bat biosonar. . . . . . . . . . . . 26

3.6 Results of the analysis of variance test comparing the scatter of the engi-neered sonars and biosonars to the reference limit at half-power. For eachset of data, the red line inside of the blue box indicates the mean of thatset, with the upper and lower edges of the blue box indicating the first andthird quantiles. The red crosses represent data points considered outlierswithin the set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.7 Comparison of the beamwidths of the biological samples with randomlyshaped aluminum baffles as a function of the ratio aperture diameter overwavelength (D

λ). Biological samples are shown as gray circles, aluminum

baffles as black triangles. . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.8 Plot results of the analysis of variance test comparing the scatter of thenoseleaf simulates and biosonars to the reference limit at quarter-power.For each set of data, the red line inside of the blue box indicates the meanof that set, with the upper and lower edges of the blue box indicating thefirst and third quantiles. The red crosses represent data points consideredoutliers within the set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.9 Comparison of beamwidths in two bat families with heavy reliance on ac-tive biosonar (horseshoe bats, Rhinolophidae, and Old World roundleafbats, Hipposideridae, A) and a bat family where the use of active biosonaronly occurs as an exception in a few species (Old World fruit bats, Pteropo-didae, B). For both families, the QP beamwidth associated with the sam-ples as a function of the ratio of aperture diameter (D) to wavelength (λ)are shown along with the elliptical-transducer limit. . . . . . . . . . . . . 31

3.10 Results of the analysis of variance test comparing the scatter of the echolo-cating families (Rhinolophidae and Hipposideridae) and non-echolocatingfamily (Pteropodidae) to the reference limit at quarter-power. For each setof data, the red line inside of the blue box indicates the mean of that set,with the upper and lower edges of the blue box indicating the first andthird quantiles. The red crosses represent data points considered outlierswithin the set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

x

3.11 Comparison of the distributions for noseleaf (light gray) and pinna sam-ples (dark gray) with respect to the ratio aperture diameter (D) over wave-length (λ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.12 Distance between the beamwidth values of the biosonar samples and therespective lower beamwidth limit as a function of the ratio of character-istic dimension (D) over wavelength (λ). A) noseleaf samples, B) pinnasamples. D is a characteristic dimension, i.e., aperture diameter for the batbiosonar samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.13 Results of the analysis of variance test comparing the scatter of the recep-tion elements (pinnae) and emission elements (noseleaves) to the referencelimit at quarter-power. The comparison was performed only for values ofD/λ less than 4 to keep the comparison in the regime where noseleaveswere typically located. For each set of data, the red line inside of the bluebox indicates the mean of that set, with the upper and lower edges of theblue box indicating the first and third quantiles. The red crosses representdata points considered outliers within the set. . . . . . . . . . . . . . . . 36

3.14 Comparison of minimum and maximum beamwidths: A) Minimum beamwidthvalues matched with the maximum aperture diameters. B) Maximumbeamwidth values matched with the minimum aperture diameters. . . . . 38

3.15 The reference beamwidth values is plotted as the black line with respectto aperture diameter (D) to wavelength (λ). The scattered points are on agrey scale, where the darker a point is, the flatter the aperture is. . . . . . 39

3.16 The reference beamwidth value is plotted as the black line with respect toaperture diameter (D) to wavelength (λ). Eccentricity is measured by thegreyscale of the points on the graph, where the darker a point is, the lowerit’s eccentricity, i.e. the less circular the aperture is. . . . . . . . . . . . . 40

3.17 The eccentricity of the geometry is compared to the eccentricity of thebeampattern. The black line in the middle represents the expected be-haviour for elliptical-transducers. The grey o’s represent noseleaves whilethe black x’s are pinnae. Each of the points on the graphs is the aver-age eccentricity of the beamwidths for the aperture over its 10 measuredfrequencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

xi

3.18 Distance between the beamwidths of the biosonar samples and the respec-tive elliptical-transducer limit as a function of the diameter to wavelengthratio (D

λ). The beamwidth data has been arranged in bins of width 0.25 D

λ.

The averages for all data points in each bin are indicated by open circles;the error bars mark the standard deviations. . . . . . . . . . . . . . . . . 42

xii

List of Tables

3.1 Results of the analysis of variance test comparing the scatter from the limitof the biosonar apertures and the engineered sonars. All comparisons wereperformed on the half-power beamwidth data. SS is the sum of squares,df is the degrees of freedom, MS is the mean squared error and F is the fstatistic, which is the ratio of the mean squared error of the groups to themean squared error of the error. . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Results of the analysis of variance test comparing the scatter from the limitof the biosonar apertures and the noseleaf simulates. All comparisons wereperformed on the quarter-power beamwidth data. SS is the sum of squares,df is the degrees of freedom, MS is the mean squared error and F is the fstatistic, which is the ratio of the mean squared error of the groups to themean squared error of the error. . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Results of the analysis of variance test comparing the scatter from the limitof the echolocating families (Rhinolophidae and Hipposideridae) and thenon-echolocating family (Pteropodidae). All comparisons were performedon the quarter-power beamwidth data. SS is the sum of squares, df is thedegrees of freedom, MS is the mean squared error and F is the f statistic,which is the ratio of the mean squared error of the groups to the meansquared error of the error. . . . . . . . . . . . . . . . . . . . . . . . . . . 32

xiii

3.4 Results of the analysis of variance test comparing the scatter of the recep-tion elements (pinnae) and emission elements (noseleaves). All compar-isons were performed on the quarter-power beamwidth data. The compar-ison was performed only for values of D/λ less than 4 to keep the com-parison in the regime where noseleaves were typically located. SS is thesum of squares, df is the degrees of freedom, MS is the mean squared errorand F is the f statistic, which is the ratio of the mean squared error of thegroups to the mean squared error of the error. . . . . . . . . . . . . . . . 37

5.1 Table Containing Geometry and Beamwidth Data for Samples sorted byScientific Name. Species denoted as sp. represent an unknown specieswithin a genera. Beamwidths given as the half-power beamwidths for thataperture at a given frequency excluding sidelobes. The 10 frequencies areequally spaced between the minimum and maximum frequency. . . . . . 89

5.2 Table Containing Geometry and Beamwidth Data for Samples sorted byScientific Name. Species denoted as sp. represent an unknown specieswithin a genera. Beamwidths given as the quarter-power beamwidths forthat aperture at a given frequency excluding sidelobes. The 10 frequenciesare equally spaced between the minimum and maximum frequency. . . . 90

xiv

Chapter 1

Introduction

1.1 Background

Engineered sonar is of pivotal importance for sensing in underwater environments, wheresound waves are able to propagate over long distances at high speeds, whereas electro-magnetic waves such as visible light are severely limited in range [49].

In-air sonar follows the same basic principles as underwater sonar, but has to deal withhigher absorption and lower sound speed which result in less favorable conditions [49].Nevertheless, the capabilities of echolocating bat species show that sonar can support thesensory information needs of highly mobile mammals [29] - although at ranges that areshort compared to the operational ranges of underwater sonar.

A system characteristics frequently used to describe biosonar and technical sonar alikeis the beampattern [2, 29], i.e., the distribution of emitted signal energy or the receiversensitivity over direction angle and frequency [49].

In engineered sonar, the primary criterion for judging the utility of a given beampattern isthe concentration of pulse energy or receiver sensitivity over direction angle. The narrowerthe beam, i.e., the smaller the beamwidth, the higher the sonar’s resolution [49]. Theability of any given sonar emitter or receiver to produce a narrow beam is limited by howlarge or small its aperture is compared to the employed wavelengths. A lower limit on thebeamwidth can be derived from the ratio of wavelength to diameter of the sonar aperture[2]; the larger the aperture of a sonar is compared to the wavelengths it operates on, thenarrower a beam it is capable of creating.

1

2

A B

Figure 1.1: A look at an engineered sonar system vs biosonar elements. A) An Edgetech4200 Side Scan sonar system that contains sensors along it’s 125 cm length [5] (PictureCopyright Edgetech, reproduced with permission) and B) A bat from the Rhinolophidaefamily with its right pinnae (outer ear) and noseleaf circled in purple.

In order to create large apertures and the corresponding narrow beams, engineered sonarstend to consist of large numbers of emitting and receiving elements working together inan array. The incoming and outgoing signals are combined across all elements in the arrayto produce a narrow sonar beam that is used to scan the environment [2]. The downsidesof this approach are the large size of the array and the large number of elements that areneeded to cover it, as well was the computationally expensive operations that are neededto combine the signals from a large number of elements.

In contrast to engineered sonar, the biosonar of bats operates with only three elements[29]: one emitter, the nose or the mouth (depending on species), and two receivers, theouter ears (pinnae). Bat biosonar operates in air and the overall system size is much smallercompared to the wavelengths used than is typically the case for engineered sonar (s.Figure1.1). The technical sonars presented in this work range from operating frequencies of42kHz [21] to 1.8MHz [23], though a majority of the sonars discussed have operatingfrequencies between 200kHz and 900kHz [33, 17, 47, 45, 46, 40, 51, 5]. Bat biosonar hasa frequency range between 11kHz and 212kHz [13] but most bats call with frequenciesbetween 20kHz and 60kHz [13]. Due to their substantially lower frequencies combinedwith much smaller sizes, bats are in a much less favorable conditions than engineeredsonars when it comes to forming narrow beams.

The goal of the work presented here has been to compare beamwidth in biosonar andengineered sonar with each other and to the theoretical beamwidth limit for the respectiveratio of sonar aperture size and wavelength. Closeness to the theoretical limit could be

3

seen as an indication that a small beamwidth is an important parameter for the functionof the respective system. In addition, an experimental data set with noseleaf simulatebaffle shapes with random internal geometry and imperfections has been acquired to serveas a reference for how close random shapes of a given size will cluster around the limitthreshold. All these comparisons should shed light on the question whether beamwidth hasbeen as critical to the evolution of bat biosonar as it is has been to the design of engineeredsonar.

1.2 Review of Literature

1.2.1 Bioinspiration and Biomimetics

Bioinspiration is the study of materials, designs, structures and behaviors of biologicalspecimens with the goal of adapting these ideas into technical and synthetic designs. Sim-ilarly, biomimetics, or biomimicry, is the study of imitating, or mimicking, natural designsto solve complex problems [50]. Both of these ideas form from the same base concept:taking advantage of nature’s billions of years of evolution to gain insight into how naturalorganisms or systems have solved complex or difficult problems. While a search of theliterature reveals the keywords of bioinspiration and biomimetics didn’t start regularly ap-pearing in literature until the turn of the century, the concept of using nature as guidancefor design was not a new idea. A very widely used and well known example of this, Vel-cro, first came about due to the inventor noticing burdocks (seeds from the genus Arctium),sticking to his clothes [12].

Many contemporary researchers however actively look into natural and biological systemsfor inspiration. One of the largest fields currently benefiting from bioinspiration is thefield of robotics [36]. Bioinspiration has lead to new developments and ideas such as softrobotics which uses highly flexible materials, instead of rigid materials, to allow a largerand more natural set of motion [16] or the creation of new artificial polymers from study-ing artificial muscle [31]. Bioinspiration has been applied to more than just mechanicalproblems. It has been used heavily in chemistry as a basis for creating composite mate-rials [7] or materials with unusual properties such as superwettability [43]. It has alsobeen used to design new types of sensors and sensing paradigms, such as spider-inspiredflexible hair sensors [22] or, of important relevance to this work, bat biosonar inspiredsensing platforms [4].

Bioinspiration and biomimetics have been trending in engineering research. For the past

4

twenty years, the number of conference papers, journal papers, and patents using bioin-spired or biomimetic technology has continually increased each year as the importanceand relevance of looking at nature for inspiration in engineering designs has continuallyproven its worth. Bioinspiration and biomimetics have been applied to an incredibly largeand varied array of different engineering problems as engineers and scientists continue touse nature’s billions of years of evolution as a springboard for new ideas and concepts.

1.2.2 Bats and Biosonar

Bats have proven to be a highly diverse and successful group of mammals, accountingfor over 20% of all mammal species [29]. While they are not the only species to useecholocation to navigate, bats are the most researched species in terms of echolocationand biosonar. There has been significant research conducted into the echolocation behav-iors of bats, particularly the hunting of insectile prey, stretching back to the 1960s [10]and continuing throughout the twentieth century and into the twenty-first century withother researchers performing similar investigations and analysis of echolocation behav-iors except for differing families or genera of bat [38, 15, 37]. Much of this early workin biosonar [10, 38, 15, 37] has had an emphasis on collection of field data in order todescribe how the differing families of bat operate within their environments, focusing ontheir operating conditions, such as flight speed, distance needed to acquire targets, etc, andthe capabilities of the bats themselves rather than having a focus on what could be learnedand applied from how the biosonar performs.

In addition to the study of the natural environments, there was initial research done inthe early 1990s into using bat-like sonars on robots [19]. These robots were setup witha sonar system that mimicked the sensor configuration of bats [1]. The bat-like systemwas used in experimentation based on the context of prey capture [19] as well as obstaclelocalization [1] and the results of the experiments were that the bat-like sonar representedan efficient sensing system.

An article published in 2007 [28] is one of the first sources discussing the differencesbetween biosonar and technical sonars as well as the merits of incorporating biosonar-inspired approaches. This article brought up many important challenges facing the designof biosonar, such as dynamics in the sensors during emission and reception, challenges intransducer performance, the actuation and integration of beamforming baffle shapes, andthe miniaturization of the sonar system among others [28].

Since the publication of the 2007 article, there has been a significant amount of researchinvested into examining what can be learned from biosonar and applied to technical sonar.

5

One of the differences between technical and biosonar that has been observed and studiedin literature since has been the dynamics of the biosonar system [3, 26, 25, 9]. This hasbeen of particular interest due to the novelty of the idea: bending the biosonar apertures todynamically alter a sonar signal [3]. The apertures have been found to change their shapeby up to 20% of their total length within 100 miliseconds while emitting or receivingsound [25]. The effect of the dynamics on the emission signal has been studied and foundto produce strong time-dependent characteristics in elliptical sound outlets similar in sizeand shape to those used by horseshoe bats [9].

In addition to information on changes in the beampattern due to dynamics of the system,recent research has begun to show that these changes in beampattern can dynamicallyencode target information into the signal [44]. This branch of research has changed fromsimply showing differences to showing that the differences in signal is able to encodeadditional information, an exceedingly useful tool for technical sonars that is not usedor well understood and hasn’t been extensively studied. Sonar systems designed to usethese dynamics and outfitted with biomimetic apertures have been developed and show thepotential of the bioinspired system as a new paradigm in sonar sensing, though significantresearch is still required to be able to make full use of the biosonars unique characteristics[4].

Other research has been conducted into recreating biosonar beampatterns from the ge-ometry of the biosonar apertures [54]. Combined with analysis of the static biosonarbeamforming mechanism and strategies [24], there is now the ability to create acurate,numerically derived beampatterns and beam information for biosonar apertures that canbe used to gain new insights into how to incorporate bioinspired strategies to help solveproblems facing sonar today.

1.2.3 Review of Technical Sonar Literature

Research in sonar and the propagation of sound underwater is an old field of study, datingas far back in literature as the discovery and documentation of primitive passive sonarsby Leonardo da Vinci in 1490, but began to resemble its modern form of research startingin World War II, where quantitative and precise measurements of undersea environmentsbecame more and more important [49]. Since World War II there has been a large amountof research on sonar and sonar capabilities due to the important nature of the marine envi-ronment in warfare and navigation.

6

1.2.4 Sonar Concepts

As previously mentioned, the basis of sonar is the study of the propagation of acousticwaves in a medium, typically water [2]. Sonars can be split broadly into two categories,passive and active, where passive sonars only listen to incoming acoustic waves whileactive sonars emit their own acoustic waves and listen for the echoes of their signals toreturn [2]. This work and most of the following section will focus on discussions as theyrelate to active sonars, but that isn’t to dismiss the importance of passive sonar or to implythat the same physical principles and research does not also apply to passive sonar.

With an important goal of active sonar being to survey the surroundings of the craft,whether looking at the local topography or attempting to find and track other objects, suchas undersea mines or submersibles [8], there has been a large amount of focus placed oncontrolling the beams of the sonar systems. Beamforming is a signal processing techniquethat is utilized to increase the directivity of sonar arrays by controlling the phase and am-plitudes of the many transmitters in an array in order to create constructive and destructiveinterference in the acoustic wave [48]. As beamwidths, a measure of sonar resolution, aredependent on the size and frequencies at which a transmitter is operated at [49] and thereare physical constraints imposed in the creation and use of transmitters, beamforming hasan important role in the development of very high resolution sonars.

Beamwidths are primarily measured in the main lobe of a sonar signal, which is the lobeof the sonar signal that contains the maximum gain, and is typically sent in the directionthat the sonar is attempting to look at. However, many sonars have naturally occurring,or induced through beamforming, sidelobes in the signal that are lobes of the sonar signalwith local maxima that are not the main lobe. Sidelobes, especially larger sidelobes, havepotential to interfere with the sonar signal and research has been conducted on how toreduce them in arrays, such as by using older methods like nonuniform element spacing inthe array [11] or newer methods like flexible genetic algorithms for pattern synthesis [52].Whichever method is used, the end goal is to reduce the magnitude of the sidelobes so thatthey do not interfere with the signal detection of the main lobe. While still an importantsubject in undersea sonar, much of the contemporary research for sibelobe reduction is inthe area of antenna arrays and wireless communication.

1.2.5 Trends in Sonar Research

In recent years, research in sonar arrays has become very wide and varied to match themany innovations in the field. There has been an increasing amount of research into

7

miniaturization of submersible systems and the addition of sonar to unmanned underwa-ter vehicles (UUVs). Even narrowing down research to these areas results in researchwith drastically different aims, such as creating UUVs with small, economically efficientsonars [14], or creating miniaturized UUV’s able to operate in alien or non-terrestrial en-vironments like the beneath the frozen crust of Europa [30]. In these situations the largearrays in use by contemporary sonar engineers would be too expensive or too large forthe mission, so research continues into finding ways of making the sonar systems smallerwhile still retaining the resolution and capabilities of larger sonar.

Much of the current research increasing the capabilities of sonar is being focused on theprocessing of sonar signals rather than development of new hardware. Researchers areattempting to use methods such as matched filtering theory [53] or Bayesian localization[32] with simple sensors or sensor arrays in order to increase the performance of the sonarthat is typically reliant on the size and number of sensors, not processing. A quick searchof literature reveals that in the previous year, 2016, there were more than twice as manyarticles published relating to sonar software than sonar hardware.

These two trends in publications and research in sonar, miniaturization for UUV and in-creased sensing and processing capabilities, also point towards another emerging trend insonar research: the use of autonomous UUVs to perform dangerous or tedious tasks. Ofparticular interest in the rising study of autonomous sonar controlled systems are thoseused for clearing undersea mine fields [42] on the military side of research and usingautonomy in UUVs for marine archaelogy [27] and surveillance of natural resources andsites, such as coral reefs [20].

1.2.6 Conclusion

Throughout much of the contemporary research the bat biosonar system has been approx-imated or represented as an elliptical transducer or a baffled elliptical transducer. Therehasn’t been any direct comparisons between the expected performance of appropriatelysized transducers or sonar arrays and the biosonar arrays while several publications havesought to look into factors, such as dynamics, that could contribute to shortening a per-ceived performance gap between biosonar and technical sonar. Meanwhile, engineeredsonar is constantly seeking new methods of improving performance without increasingthe size or cost of the sonar. In the following work, biosonar apertures will be compared toengineered sonars, showing the performance gap in terms of sensing resolution betweenthe biosonar systems and contemporary engineered sonars.

8

1.3 Problem Statement and Research Objectives

1.3.1 The Case for Studying Biosonar

There are many works on biosonar that attempt to use measurements of bats in their naturalhabitat to make statements about broad capabilities of biosonar [38, 15, 37]. It is difficultto obtain precise numerical beampatterns directly from bats which would require havinga bat naturally emitting its sonar into a large microphone array. Difficulties with creatingexperimental beampatterns directly from bats led to development of numerical methodsthat can be used to simulate the beampatterns of biosonar apertures [54].

Much of the contemporary research on biosonar is focused on operational differences be-tween biosonar and technical sonar, such as the dynamic motion of the biosonar aperturewhile emitting or receiving sound [25]. Part of the reason for this research is that there areperceived, or known but not quantified, differences between biosonar and technical sonar.A quick inspection of sizes shows that there is indeed a significant size difference betweenbiosonar apertures and technical sonar arrays, lending merit to the concept that biosonarand technical sonar operate differently. However, to this point prior research has not quan-tified this difference to see if the perceived difference is as large as initial inspection wouldmake it out to be. Additionally, it is known that engineered sonars attempt to minimizetheir beamwidths as much as physically possible, but it is unknown whether bats attemptto have the same minimization.

By creating a method for comparing biosonar systems to equivocal engineered sonar sys-tems or reference baffles, the amount of difference between biological and technical sonarcan be quantified. Additionally, creation of a large data set of beampatterns and examina-tion in terms of their beamwidths allows examination in new areas to investigate biosonarand better understand how it works.

1.3.2 Research Objectives and Hypotheses

Prior to the research presented here, it was qualitatively obvious that bats operated inmuch smaller regimes of diameter over wavelength. This operational difference can beseen in the size of the biosonar apertures (5mm to 20mm typical, s. Table 5.1) com-pared to engineered sonars (300mm to 1.25m typical for sonars used in this research[33, 17, 34, 18, 51, 47, 41, 45, 46, 35, 40]) and the operating frequencies (20kHz and60kHz typical for bats [13] vs 200kHz to 900kHz typical for the sonar investigated in this

9

100 102

D/λ

0

50

100

150

Ha

lf-P

ow

er

Be

am

wid

th (

°)

100 102

D/λ

0

50

100

150

Ha

lf-P

ow

er

Be

am

wid

th (

°)

Figure 1.2: Visual representation of the first hypothesis tested in the current work: A)shows the first form of the hypothesis, that the engineered sonars, represented by blacktriangles, and biosonars, grey dots, have similar scatter and closeness to the referencelimit represented by the black line. B) shows the alternative hypothesis that the biosonarhas a larger scatter.

research [33, 17, 47, 45, 46, 40, 51, 5]). As beamwidth can be measured as a functionof diameter over wavelength, with larger values of diameter over wavelength leading tonarrower beamwidths [2], it can be surmised that the biosonar beamwidths will be largerthan the engineered beamwidths. Nevertheless, the following four main research questionsremain open when comparing bat biosonar and engineered sonar:

Engineered sonars follow reference equations for beamwidth as a function of diameterover wavelength and have very little scatter from these limits. The first hypothesis thatwas tested is that biosonar will have similar scatter from the limit as engineered sonar,with the alternative hypothesis being that the biosonar will have more scatter (s. Figure1.2).

The second hypothesis that was tested is that aluminum noseleaf simulates with randomimperfections and internal geometry will have the same scatter as the biosonar aperturesdo, with the alternative hypothesis being that either the biosonar or noseleaf simulates willhave less scatter (s. Figure 1.3).

The third hypothesis that was tested is that families of bats that use echolocation havebiosonar apertures that operate in the same regimes of diameter over wavelength andbeamwidth as families of bat that do not use echolocation, with the alternative hypoth-

10

2 4 6 8 10

D/λ

0

50

100

150

Ha

lf-P

ow

er

Be

am

wid

th (

°)

B

2 4 6 8 10

D/λ

0

50

100

150

Ha

lf-P

ow

er

Be

am

wid

th (

°)

A

Figure 1.3: Visual representation of the second hypothesis to be tested in the current work:A) shows the first form of the hypothesis, that the aluminum baffles, represented by blacktriangles, and biosonars, grey dots, have similar scatter and closeness to the reference limitrepresented by the black line. B) shows the alternative hypothesis that either the referencebaffles or biosonar has less scatter.

esis being that families that use echolocation and families that do not use echolocationoperate in different regimes of diameter over wavelength or beamwidth.

The final hypothesis that was tested is that noseleaf (emission) elements operate in thesame regimes and with the same beamwidths and scatter as pinnae (reception) elements,with the alternative hypothesis being that they operate in different regimes.

In order to test these hypotheses, several sets of research objectives were created. The firstwas the creation of a framework within which the biosonar apertures could be comparedto engineering sonars. This objective included selection of suitable engineering analoguesfor the biosonar apertures as well as the creation of a methodology for converting thebiosonar into the chosen analogue. The second objective of the research was to take nu-merically generated biosonar beampatterns and find the corresponding beamwidths. Thefinal objectives of the research were to use the large database created to test the hypothesesand look for additional insights or areas for future research.

Chapter 2

Methods

2.1 Biosonar Apertures and Conversion to EngineeringAnalogues

2.1.1 Biosonar Aperture Data

The biosonar apertures used in this work are all taken from computer micro-tomographic(µCT) scans of bat noseleaves and pinnae. The bats scanned were dead and had been pre-served in a low-concentration ethanol solution prior to scanning. There were over 500 dif-ferent µCT scans of bat apertures from over 300 different bats. After scanning a specimenthe relevant apertures were cut out from the rest of the mesh so they could be examined bythemselves.

After all of the apertures were scanned, it was necessary to check meshes manually in orderto verify that there were no problems with the scan. While there were some µCT meshesthat had easily identifiable problems, such as artifacts or other problems with the scan,a more time consuming aspect of filtering was making sure that the examined samplesthemselves appeared to be in good condition. In this context, good condition meant thatthe aperture was completely intact and in an upright neutral position. Pictures and videosof families of bats were used to identify whether pinnae or noseleafs were bent, damaged,or had other problems that would make them poor choices for comparison.

Additionally, all of the samples that were found by manual inspection to be in good con-dition had beampatterns generated using methods described later in Chapter 5. Some

11

12

meshes had problems not apparent to visual inspection that caused the numerically gen-erated beampatterns to fail to converge, resulting in meshes that geometry could be ob-tained from but not beampattern data. Since both geometry and beampattern data wouldbe required for full comparisons of the biosonar apertures, meshes that failed to producenumerical beampatterns were also discarded.

The final set of apertures were comprised of a total of 151 shape samples taken from137 different bats. There was only one sample where both pinnae and the noseleaf waswell preserved enough to use all three of its apertures for comparison, but there were 12different bats were both ears were preserved well enough to be used. Of the 151 aperturesamples there were 61 noseleaves and 90 pinnae. While it might be expected that therewould be twice as many pinnae compared to noseleaves, since bats have two pinnae andonly one noseleaf and there were more pinnae in the scans, the noseleaves appeared towithstand preservation and scanning better than the pinnae resulting in a higher percentageof them being usable for comparison.

The pinnae and noseleaves came from 8 different bat families, with the most prominentfamily being the horseshoe bats (family Rhinolophidae) from which 21 noseleaf sam-ples and 24 pinna samples were analyzed. The other bat families represented in the dataset were: Hipposideros (23 samples), Emballonuridae (5 samples), Molossidae (2 sam-ples), Megadermatidae (1 sample), Nycteridae (15 samples), Phyllostomidae (20 samples),Pteropodidae (4 samples), and Vespertilionidae (36 samples).

2.1.2 Conversion from µCT Scans to Engineering Analogue

In order to approximate the 3D mesh of the biological structures by a 2D transducer thepoint cloud mesh is taken through a series of simplifications and processing. The first stepis edge filtering the mesh, finding edges whose dihedral angle is greater than 15◦. Theresult of this is that only heavily curved edges, such as those along the outer edge of theaperture, are kept, discarding much of the internal geometry. A point along the outer edgeof the aperture was manually selected and the rest of the points along that edge are selectedby using a point clustering, nearest neighbor algorithm. The majority of the apertureswere able to use a hop-through distance in the point clustering algorithm of 0.1mm, but17 of the 151 samples required additional manual cleaning or different filtering in orderto select just the outer edges of the aperture. Once the outer edges of the structure weredetermined, a plane of best fit was found using least squared of normal distance. Finally,the points from the edge were projected onto the plane of best fit and then the minimumand maximum length of the aperture through the centroid were found (s. Figure 2.1). The

13

A B C

Figure 2.1: Approximation of the biological shape samples by a planar elliptical trans-ducer: A) µCT model of a noseleaf from a Sulawesi horseshoe bat (Rhinolophus celeben-sis), B) Point cloud resulting from detecting edge vertices in the mesh, C) Edge verticesprojected into the fitting plane with lines along the minimum and maximum aperturelengths (dashed lines).

code used to convert the µCT scans to the 2D engineering analogues is given in AppendixA.1: Geometric Processing Code. This code is provided so that other researchers canreplicate the results or use the code to generate additional data points for new apertures.

The minimum and maximum diameters were chosen to be found through the centroid foreasier comparison with technical sonars and transducers. As will be discussed in moredepth later, beamwidth for a sonar is typically measured through maximum gain of thesignal, which in transducers and other planar arrays aligns with the centroid of the trans-ducer or array. Consideration was given on whether to use the measured maximum andminimum or to use the length perpendicular to the maximum as the minimum, as wouldbe the case of a perfectly elliptical transducer, but the decision was made to calculate max-imum and minimum separately due to the non-uniformity of the shapes and beampatterns.This choice in calculating minimum and maxmimum seperately had a larger effect onnoseleaves than pinnae, as the pinnae have relatively uniform and consistent shape whilesome noseleafs, such as those of the trident bats (Aselliscus stoliczkanus), have peculiarand nonuniform shapes.

14

2.2 Beamwidth Determination for Biosonar Apertures

2.2.1 Importance of Beamwidth

Beamwidth is a widely used metric by sonar engineers for evaluating the performance ofsonars. Beamwidths represent the resolution with which a sonar can sense its environmentand is measured in degrees. Of the two categories of sonar, active and passive, this workis concerned primarily with active sonar, that is sonars that emit sound pulses and listenfor the echoes of those pulses [2]. Having a narrower beamwidth represents the ability tomore accurately and precisely direct energy, which in addition to the benefit of increasingyour sensing resolution can also help reduce interference between multiple sonar systemsand help reduce the signature of the sonar carrier. These advantages to having narrowbeamwidth has lead to beamwidth being a heavily discussed and documented metric forengineered sonars which makes it a valuable metric for being able to make quick perfor-mance comparisons to a wide array of sonar systems.

2.2.2 Planar Array Reference Beamwidth

For comparison with this reference, the noseleaves and pinnae were treated as unbaffled2D elliptical transducers. To compute the ratio of diameter (D) over wavelength (λ), themaximum diameter of the biosonar element was matched with the minimum beamwidthand the minimum diameter of the biosonar with the maximum beamwidth.

A reference lower beamwidth limit used for comparison to the data was derived from theequation for a continuous planar circular array in an infinite baffle (s. Equation 1, [49]).This equation also covers infinitely baffled circular planar arrays of diameter D or a singleelement of diameter D and a wavelength λ:

b(θ) =

[2J1[(πD/λ)sin(θ)](πD/λ)sin(θ)

]2(2.1)

where b(θ) is the beampattern response at angle θ and J1[] is the first-order Bessel function.

The choice to use an infinite baffled circular planar array as the reference instead of aspecifically baffled array or a conical horn was made to find common ground betweenbiosonar apertures and technical sonar. An infinitely baffled system was chosen so thatan arbitrary baffling would not be used. While some biosonar apertures do appear fromvisual inspection to bear resemblance to baffled transducers, the amount of baffling and

15

it’s arrangement varies from species to species. The choice to use a planar array ratherthan a conical horn was made for similar reasons. By using a planar array, the dimensionsthat need to be controlled for are decreased to just minimum and maximum diameters, sothere is no need to choose arbitrary dimensions for length, curvature, etc, that vary heavilyfrom one bat species to another.

2.2.3 Generation of Numerically Derived Beampatterns

Predictions of bat biosonar beampatterns were derived numerically from digital modelsof the geometries of bat noseleaves (emission baffles used by bats with nasal emissionof biosonar pulses) and pinnae (outer ears, i.e., the sound receivers in bat biosonar) [3].The digital models were taken from µCT scans and the geometries were treated as a cubicfinite-element mesh with a perfectly reflecting boundary condition to represent the bound-ary between the biological tissue and air [24]. Using these meshes and boundary condi-tions, the near field was solved for by using the wave equation which, given the stationaryand space-dependent nature of the beampattern, was expressed by the Helmholtz equation[54]. Using the complex field values from the finite-element model, the propagation of theacoustic wave into the far-field was handled using the Kirchoff integral formulation [24].

The ultrasonic beampatterns of each of the 151 pinnae and noseleaves samples were eval-uated at 10 frequencies evenly spaced throughout the operating frequency band that hasbeen documented for respective bat species in the literature.

2.2.4 Biosonar Beamwidth Evaluation

The minimum and maximum beamwidths of the biosonar samples were determined fromthe numerical beampattern estimates as follows: First the beampatterns were rotated sothat the angle associated with the maximum gain, i.e., the maximum response angle (MRA)was pointed in a known direction. This was done both to make the next steps of the processsimpler and so that the beampatterns could all be aligned in the same direction for visualinspection and comparison of size and shape. After this, the beampattern was cut by aseries of planes each of which contained the vector from the origin to the MRA. A fam-ily of planes was created by rotation around the vector of the MRA. A plane was placedevery 0.5◦ of rotation angle to sample the entire two-dimensional beampattern (gain as afunction of two angles, e.g., azimuth and elevation) with high resolution. Each slice ofthe beampattern produced a one-dimensional function (normalized beam gain as a func-tion of a single angle). A beamwidth was calculated for each of the slices, looking for

16

the minimum and maximum beamwidth across all slices. The maximum and minimumbeamwidths are found at two different levels: -3dB (half-power, HP) and -6dB (quarter-power, QP, or half-voltage, s. Figure 2.2).

In addition, some of the beampatterns had prominent sidelobes which contained valueshigher than HP or QP that are separate from the main lobe of the sonar signal. For thepurpose of the comparison in this work, beamwidths have been calculated in two differentways – with and without taking sidelobes into account. Beamwidth estimates not includingsidelobes were obtained by traversing the one-dimensional beampattern from the MRAoutward until the amplitude dropped below the respective threshold (-3 or -6dB) for thefirst time. In order to get beamwidth estimates including sidelobes, each beampatternwas traversed starting at angles 180 degree away from the MRA and the beamwidth wasdetermined by the first angles were the beampattern gain exceeded the threshold for thefirst time.

There were two primary pieces of code used in the beamwidth evaluation. The first pieceis given in Appendix A.2: Beampattern Processing Code and takes a beampattern, nu-merically or experimentally generated, in the form of gain as a function of azmiuth andelevation angles and performs the interpolation to create the 2D slices of the beampat-tern as well as solving for the HP beamwidth excluding sidelobes. An additional piece ofcode given in Appendix A.3: Beampattern Post Processing Code takes the 2D beampatternslices saved from the previous code and calculates several additional values, such as QPbeamwidth, beamwidths including sidelobes, locations and values of the nulls, etc. Thesetwo pieces of code are provided so that readers and future researchers can either replicatethe results seen in this research or use the code to generate additional data for beampatternsnot used in this research.

2.2.5 Half-Power vs Quarter-Power Beamwidths

In engineered sonar, it is standard to use the half-power beamwidth [2], however someof the comparisons for the biosonar in this paper were done using the quarter-powerbeamwidth. The reason for this was that some of the sampled biosonars have sidelobesnear the MRA that were included in the beamwidth at the -6dB level, but not for the -3dB level. Additionally, some biosonars have ripple in the signal thresholds where thereis noise in the signal that is too small to be accurately described as a sidelobe but canhave small impacts on the measurement values. The -6dB threshold is used for manycomparisons between biosonars due to the beamwidths being larger and having had moretime for ripple and noise in the signal around the MRA to have dispersed, resulting in a

17

A B C

Figure 2.2: Conversion of two-dimensional, numerical beampattern estimates into one-dimensional beampattern functions: A) a numerical beampattern estimate derived fromthe Sulawesi horseshoe bat (Rhinolophus celebensis) shown in Figure 2.1. B) One ofthe beampattern slices obtained at different rotation angles, shown in polar coordinates.C) The same beampattern slice shown in B) converted in to Cartesian coordinates. Thehorizontal lines indicate the -3dB and -6dB threshold levels

smaller impact on the beamwidth. Comparisons with technical sonar were performed us-ing the half-power value as many manufacturers do not have public information on theirquarter-power beamwidth.

2.3 Acquisition of Technical Sonar Data

2.3.1 Military Sonar vs Commercial Sonar

Engineered sonars additionally can be split into two categories: commercial and military.This work will use metrics solely from commercial sonars for comparison to biosonar dueto the difficulty in obtaining publishable specifications for military sonars. However, itshould be noted that military sonars tend to be of larger size and higher quality than theircommercial counterparts. Of the commercial sonars used in this thesis, the largest sonar isthe Sonardyne Solstice SSS, which is 1.25m long [5]. For comparison, the bow array ofa Seawolf SSN-21 submarine has a 24 foot (7.3 meter) diameter making it more than fivetimes as large. Due to the physics governing size and beamwidth, it is easy to understandeven without seeing any technical specifications and capabilities that these massive sonararrays would likely be an order of magnitude higher in terms of their resolution from the

18

discussed commercial sonars. Additionally, the technical sonars discussed in this paperare contemporary sonar, commercially available at the time of the comparison.

2.3.2 Technical Sonars Used for Comparison

The data set of engineered sonar was compiled from 23 different technical sonar devices.The beamwidths and sizes for the engineered sonar were taken directly from manufactur-ers’ specifications [33, 21, 17, 6, 34, 18, 51, 47, 41, 45, 46, 35, 40]. These sonars hadoperating frequencies ranging from 42kHz [21] to 1.8MHz [23]. Several of the sonarswere dual-beam or multi-beam, meaning that they had two or more operating frequencieswhich would produce two different sized beamwidths [33, 35, 34]. Most commonly forthese sonars the higher frequency would be double the lower, which resulted in the higherfrequency having half the beamwidth of the lower frequency [33, 34], which highlightsthe relative linearity of decreases in beamwidth with respect to array-length to wavelengthat high values of array-length to wavelength. The smallest of the sonars had a diameter of16.4mm [21], which is comparable to some of the larger biosonar apertures, and with it’slow frequency placed it at scale of diameter to wavelength ratio equivocal to the biosonarapertures. The largest of the engineered sonars was 1.25m long [5] which, combined withits high operating frequency, resulted in a diameter to wavelength two magnitudes largerthan the average biosonar.

2.4 Aluminum Random Emission Baffle Experiment

Having compared the biosonar apertures to technical sonar and found differences in per-formance, both in how close to the limit the apertures were and the area of operation, anexperiment was designed to test and see if the biosonar apertures performed better thanrandomly produced aluminum baffles, which would be operated in the same aperture di-ameter (D) to wavelength (λ) ratio as the biosonar apertures. If the biosonar was found tooperate similarly, or worse than, randomly generated baffles it would serve as additionalindication that beamwdith may not have been an important evolutionary consideration forbiosonar. Additionally, the aluminum baffles provide a reference point for how randomlygenerated baffles of the approximate size of bats compare to the reference equations foran unbaffled planar array used as the reference limit. The baffles being close to the limitwould indicate that the unbaffled planar array serves as an acceptable approximation ofshort, conical, baffled transducers.

19

2.4.1 Equipment and Setup

The chirp for the experiment was produced by two Senscomp 600 loudspeakers. The loud-speakers had a 100mm long waveguide attached to them that went from the two 42mmloudspeaker diameters to two separate 2mm diameter exits. The noseleaf simulate baffleswere attached to the ends of the waveguide. The acoustic properties of the noseleaf sim-ulates were tested using a linear-frequency modulated chirp ranging from 25 to 105kHz,a range which covered most operating frequencies of the bat species represented in theanalyzed data set. The chirps were recorded at a distance of 1 meter from the baffle witha measurement microphone (Bruel and Kjær, 1/8 inch). The microphone output was digi-tized at 16 bit resolution and 500 kHz sampling rate (National Instruments NI pci-e 6351).The signals emitted through the baffles were recorded over an azimuth angular range of176◦ in steps of 1◦ and an elevation angular range of 75◦ in steps of 1◦ to create a front-facing beam pattern for the baffle. At each location a set of 20 chirps was recorded. AFourier transform was applied to the chirps and the resulting frequency spectrum was con-verted to power. The resulting bin width of the power calculation was 500 Hz, and fiveevenly spaced bins throughout the chirp were chosen for calculating beampatterns. Ateach azimuth and elevation point, the power of the 20 chirps were averaged within eachfrequency bin to create a front-facing beampattern at the five different frequencies. Fromthe front-facing beampattern the beamwidth of the baffle was determined using the samemethod used to determine the beamwidth of the biosonar apertures.

2.4.2 Creation of Random Emission Baffles

There were five different emission baffles created from a piece of aluminum foil. The foilwas first cut to size and them crumpled into a ball. The foil was uncrumpled into an oblonghorn, similar in shape to biosonar apertures, before being mounted to the waveguide. Bycrumpling and uncrumpling the aluminum foil the interior geometry of the baffle was ableto have entirely randomized crevices and veins that changed each test. The simulates haddiameters ranging from 25mm to 55mm and were a mix of both elliptical baffles, with onediameter significantly larger than the other, and circular baffles with similar diameters. Thelength of the simulate, when measured from the waveguide to the edge of the simulate,ranged from 20mm to 35mm. In order to help randomize the geometry of the baffles,three of the five baffles were created by other individuals to decrease any bias in theirconstruction and shape.

20

A B

Figure 2.3: Setup for the experiment with the random aluminum baffles: A) Diagram ofthe experimental setup with dimensions of the loudspeaker, waveguide (shown in blue),and random aluminum foil baffles with the microphone in the far-field. B) Picture of theexperiment set up.

Chapter 3

Results

3.1 Half-Power Beamwidths and Quarter-Power Beamwidths

For bat biosonar, the half-power (HP) beamwidths tended to follow the theoretical limitcloser than the quarter-power (QP) beamwidths, with the HP beamwidths having an av-erage distance to the limit of 10◦ and the QP beamwidths having an average distance tolimit of 42◦ (s. Figure 3.1). The HP beamwidths, however, had more values fall belowthe limit with 14% of the values below the limit compared to 1% of the QP beamwidthsbelow the limit. The majority of the HP beamwidths below the limit were associated withcomparatively low diameter to wavelength ratios (e.g., less than 4, s. Figure 3.1). Manyof these biological baffle shapes created sidelobes in the beampatterns that extended up tothe -3dB level but not the -6dB level.

Another difference between the half-power and quarter-power beamwidths was that in theregion of lower array length to wavelength values the QP values increased compared tothe limit more rapidly than the HP values (s. Figure 3.1). Overall, the results obtainedwith both amplitude threshold levels showed that the biosonar beamwidths did follow atendency that matches the behavior of the theoretical beamwidth limit with the ratio ofdiameter to wavelength.

Comparing the beamwidth values obtained starting from the beam gain maximum (i.e.,sidelobes excluded) with those starting from the periphery (i.e., sidelobes included) pro-vided evidence for a role that sidelobes play in determining the beamwidth of the biosonarbeampatterns. 14% of the QP beamwidth values were affected by sidelobes with ampli-tudes that were large enough to effect either the maximum or the minimum beamwidth

21

22

2 4 6 8 10

D/λ

0

50

100

150

200

Quate

r-P

ow

er

Beam

wid

th (

°)

B

2 4 6 8 10

D/λ

0

50

100

150

200

Half

-Pow

er

Beam

wid

th (

°)A

Figure 3.1: Comparison of half-power (-3dB) beamwidth (A) and quarter-power (-6dB)beamwidth (B) for the bat biosonar elements. Theoretical minimum beamwidth values areshown as solid black lines for both levels. D is the bat aperture diameter.

when included (s. Figure 3.2).

When examining the effect of sidelobes, a threshold of 10 ◦ was used to determine whethera change in size was due to a sidelobe or ripple in the signal being unresolved. Sidelobeswere more common in noseleaf beampatterns, in which 22% had sidelobes compared to9% of the pinnae. The average increase in beamwidth due to sidelobes was 62◦ (± 52◦

standard deviation). The data has a large standard deviation in part due to 20% of thesidelobes being very large (>100◦).

The raw data for the half-power beamwidths excluding sidelobes is shown in Table 5.1while the raw data for the quarter-power beamwidths excluding sidelobes is shown inTable 5.2. Both of these tables are located in Appendix B: Raw Data Tables. The raw datais provided so that so the analyses performed in this work can be duplicated as well as sothat researchers interested in specific families, genera, or species can find information onthe samples of particular interest.

When comparing sidelobes in half-power to sidelobes in quarter-power it was found thatsidelobes had a larger impact in the QP region. 14% of the QP beampatterns had significantsidelobes (s. Figure 3.4) compared to only 8% of the HP beamwidths (s. Figure 3.3). In theHP beamwidths the average increase in sidelobe was also smaller at 44◦ (± 31◦ standarddeviation) and had a smaller standard deviation due to only 6% of the sidelobes being verylarge (>100◦). However, another distinction between the two beamwidths is that the QP

23

0 50 100 150 200 250 300 350

Beamwidth not including sidelobes (°)

0

50

100

150

200

250

300

350

Bea

mw

idth

counti

ng s

idel

obes

(°)

Figure 3.2: Impact of sidelobes on the beamwidth of the biosonar beampattern samples fornoseleaves (gray circles) and pinnae (black x’s). Points on the diagonal line do not havesidelobes amplitudes that are large enough to effect the beamwidth estimates.

24

2 4 6 8 10

D/λ

0

50

100

150

HP

Bea

mw

idth

(°)

A

2 4 6 8 10

D/λ

0

50

100

150

HP

Bea

mw

idth

(°)

, in

cludin

g L

obes B

Figure 3.3: Half-power beamwidth values with respect to the aperture diameter (D) towavelength (λ) ratio. A) The HP beamwidths calculated using the first point where thebeampattern amplitudes crossed the HP threshold and B) the HP beamwidths calculatedusing the furthest point where the beampattern crossed the HP threshold.

beamwidths had ripple in the signal around the threshold resulting in small changes to thebeamwidth in 6% of the samples while the HP beamwidths had similar ripple in 15% ofbeamwidths.

3.2 Beamwidth Comparison of Engineered and Biosonar

The HP beamwidths of the biosonar and engineered sonar samples both showed a tendencysimilar to the theoretical beamwidth limit, in that larger ratios of array-length to wave-length tended to produce smaller beamwidths. However, the majority of the engineeredsonars were located in a region of much higher array-length to wavelength ratios than thebiosonars. In the engineered sonars, the beamwidth stayed very close to the theoreticallimit, especially for systems with larger ratios of array-length to wavelength. In contrastto this, the biosonar samples showed a much larger scatter away from the theoretical limitcurve in the direction towards larger beamwidths (s. Figure 3.5).

While it can be seen from Figure 3.5 that the biosonar apertures appear to scatter furtherfrom the reference limit than the technical sonars do, an analysis of variance (ANOVA)test was conducted in order to determine if this difference was statistically significant. The

25

2 4 6 8 10

D/λ

0

50

100

150

200

QP

Bea

mw

idth

(°)

A

2 4 6 8 10

D/λ

0

50

100

150

200

QP

Bea

mw

idth

(°)

, in

cludin

g L

obes B

Figure 3.4: Quarter-power beamwidth values with respect to the aperture diameter (D) towavelength (λ) ratio. A) The QP beamwidths calculated using the first point where thebeampattern amplitudes crossed the QP threshold and B) the QP beamwidths calculatedusing the furthest point where the beampattern crossed the QP threshold.

null hypothesis for the ANOVA test was that the biosonar and engineered sonar had similarscatter from the limit, and the scatter from the distance was calculated using the half-powerbeamwidths. The p-value for the test was found to be significantly smaller than a 0.01significance level (s. Table 3.1), resulting in rejecting the null hypothesis. Additionally,the mean value of the scatter of the biosonar was significantly larger than the mean scatterof the engineered sonar (s. Figure 3.6). These results corroborate the inspection of thegraph, showing the increased scatter of the biosonar is statistically significant.

Table 3.1: Results of the analysis of variance test comparing the scatter from the limit ofthe biosonar apertures and the engineered sonars. All comparisons were performed on thehalf-power beamwidth data. SS is the sum of squares, df is the degrees of freedom, MS isthe mean squared error and F is the f statistic, which is the ratio of the mean squared errorof the groups to the mean squared error of the error.

Source SS df MS F Prob>FGroups 2419.1 1 2419.07 21.4 3.89× 10−6

Error 308102.8 2726 113.02Total 310521.8 2727

26

100 101 102 103

D/λ

0

20

40

60

80

100

120

140

160

180

Ha

lf-P

ow

er

Be

am

wid

th (

°)

Figure 3.5: Comparison of biosonar and engineered sonar half-power beamwidths to theelliptical-transducer limit values (solid line) as a function of the ratio characteristic dimen-sion (D) over wavelength (λ). Biosonar samples are represented by light gray circles andengineered sonars by black triangles. D is a characteristic dimension of the sonar, i.e.,array-length for technical sonar and noseleaf or pinna diameter for bat biosonar.

27

Engineered Sonars Biosonar

0

10

20

30

40

50

60

70

80

90

100

Dis

tance F

rom

Lim

it(°

)

Figure 3.6: Results of the analysis of variance test comparing the scatter of the engineeredsonars and biosonars to the reference limit at half-power. For each set of data, the red lineinside of the blue box indicates the mean of that set, with the upper and lower edges ofthe blue box indicating the first and third quantiles. The red crosses represent data pointsconsidered outliers within the set.

28

3.3 Noseleaf Simulate Experiment Results Compared toBiosonar

The experimental beamwidth results obtained from the noseleaf simulate baffles showed asimilar scatter away from the elliptical-transducer limit as the bat samples (s. Figure 3.7).The scatter associated with the biological samples appeared to be somewhat bigger thanthat associated with the aluminum baffles, especially towards lower values of the ratioaperture diameter (D) to wavelength (λ) where most of the experimental data points wereconcentrated. For ratios around the lower end of this region, the biological samples ap-peared to show a larger variability than the random shapes, but it is not clear if this is agenuine trend in the data or just an effect of the small sample size.

An ANOVA test was performed to determine if there were statistically significant differ-ences between the scatter of the biosonar and the scatter of the noseleaf simulates. The nullhypothesis to be tested was that the biosonar and noseleaf simulates had similar scatter.The scatter from the reference limit for both sets was calculated at quarter-power, wherethey were compared in Figure 3.7. The p-value of the ANOVA test results was found tobe significantly smaller than a significance value of 0.01, causing the null hypothesis tobe rejected (s. Table 3.2). By looking at the results of the ANOVA test it can be seen thatthe noseleaf simulates have a lower mean scatter (s. Figure 3.8). This indicates that thebiosonar have statistically significant additional scatter from the reference limit comparedto the noseleaf simulates.

Table 3.2: Results of the analysis of variance test comparing the scatter from the limit ofthe biosonar apertures and the noseleaf simulates. All comparisons were performed on thequarter-power beamwidth data. SS is the sum of squares, df is the degrees of freedom, MSis the mean squared error and F is the f statistic, which is the ratio of the mean squarederror of the groups to the mean squared error of the error.

Source SS df MS F Prob>FGroups 72981.7 1 72981.7 122.09 8.29× 10−28

Error 1662421 2781 597.8Total 1735402 2782

29

1 2 3 4 5 6 7 8 9 10

D/λ

0

50

100

150

200

Quate

r-P

ow

er

Beam

wid

th (

°)

Figure 3.7: Comparison of the beamwidths of the biological samples with randomlyshaped aluminum baffles as a function of the ratio aperture diameter over wavelength (D

λ).

Biological samples are shown as gray circles, aluminum baffles as black triangles.

30

Noseleaf Simulates Biosonar

0

20

40

60

80

100

120

140

Dis

tance F

rom

Lim

it(°

)

Figure 3.8: Plot results of the analysis of variance test comparing the scatter of the noseleafsimulates and biosonars to the reference limit at quarter-power. For each set of data, thered line inside of the blue box indicates the mean of that set, with the upper and loweredges of the blue box indicating the first and third quantiles. The red crosses representdata points considered outliers within the set.

31

2 4 6 8 10

D/λ

0

60

120

180

Quate

r-P

ow

er

Beam

wid

th (

°)

B

2 4 6 8 10

D/λ

0

60

120

180

Quate

r-P

ow

er

Beam

wid

th (

°)A

Figure 3.9: Comparison of beamwidths in two bat families with heavy reliance on activebiosonar (horseshoe bats, Rhinolophidae, and Old World roundleaf bats, Hipposideridae,A) and a bat family where the use of active biosonar only occurs as an exception in a fewspecies (Old World fruit bats, Pteropodidae, B). For both families, the QP beamwidth as-sociated with the samples as a function of the ratio of aperture diameter (D) to wavelength(λ) are shown along with the elliptical-transducer limit.

3.4 Comparison of Bat Families With and Without ActiveBiosonar

The families of horseshoe bats (Rhinolophidae) and the Old World roundleaf bats (Hip-posideridae) are known to rely on particularly sophisticated active sonar systems that en-able them to navigate and hunt in dense vegetation [13]. As these two families of bats areknown to use and rely on sonar systems, they can be used as a basis to compare to a familyof bats (Old World fruit bats, family Pteropodidae) that – with few exceptions – do notuse active biosonar [13]. These two families were compared, using only pinnae as the Oldworld fruit bats do not have noseleaves, to find that even though the horseshoe bats androundleaf bats use a very sophisticated active sonar system they still show the same trendsto beamwidth as a family that does not use active sonar (s. Figure 3.9).

To verify that were no statistically significant differences in the scatter from the referencelimit of the echolocating and non-echolocating families an ANOVA test was performed.The null hypothesis for the ANOVA test was set as the echolocating and non-echolocatingfamilies having equal scatter from the reference limit, measured in quarter-power. The p-

32

value was significantly larger than a significance value of 0.01, causing the null hypothesisto fail to be rejected (s. Table 3.3). Looking at the ANOVA plot it can be seen that themeans of the two sets are roughly equivilent though the non-echolocating families havea larger range of the first and third quantile (s. Figure 3.10). This difference in quantileposition could be due to having fewer samples from the non-echolocating families.

Table 3.3: Results of the analysis of variance test comparing the scatter from the limit ofthe echolocating families (Rhinolophidae and Hipposideridae) and the non-echolocatingfamily (Pteropodidae). All comparisons were performed on the quarter-power beamwidthdata. SS is the sum of squares, df is the degrees of freedom, MS is the mean squared errorand F is the f statistic, which is the ratio of the mean squared error of the groups to themean squared error of the error.

Source SS df MS F Prob>FGroups 30.8 1 30.79 0.36 0.5484Error 66457.5 778 85.421Total 66488.3 779

3.5 Emission vs Reception Elements

Comparing the beamwidths belonging to pinna samples to those obtained from noseleavesshowed two main differences. First, noseleaf samples tended to be smaller compared totheir respective operating wavelengths than the pinnae; for the noseleaves, 63% of thesamples had a diameter-to-wavelength ratio less than 2. For the pinnae, this was the casefor 40% of the samples (s. Figure 3.11). Second, the noseleaves tended to deviate furtherfrom the theoretical limit values. The noseleaf beamwidths deviated from the theoreticallimit by 15◦ on average (standard deviation 35◦) compared to 5◦ average distance (standarddeviation 23◦) for pinnae (s. Figure 3.12).

In Figure 3.12, and based on the above calculations of mean and standard deviation, itappears that there are significant differences between emission and reception elements inthe biosonar. In order to test whether these differences were statistically significant, anANOVA test was performed. The null hypothesis for the test was set that the emission andreception elements had similar scatter from the reference limit. The scatter was calculatedin quarter power and only for values of D/λ less than 4 where the majority of the nose-leafs were located. The p-value was significantly smaller than a significane value of 0.01,causing the null hypothesis to be rejected (s. Table 3.4). Upon inspection of the ANOVA

33

Echolocating Families Non-Echolocating Families

0

10

20

30

40

50

60

Dis

tance F

rom

Lim

it(°

)

Figure 3.10: Results of the analysis of variance test comparing the scatter of the echolocat-ing families (Rhinolophidae and Hipposideridae) and non-echolocating family (Pteropo-didae) to the reference limit at quarter-power. For each set of data, the red line inside ofthe blue box indicates the mean of that set, with the upper and lower edges of the blue boxindicating the first and third quantiles. The red crosses represent data points consideredoutliers within the set.

34

0 1 2 3 4 5 6 7 8 9 10

D/λ

0

5

10

15

Port

ion o

f S

ample

s [%

]

Figure 3.11: Comparison of the distributions for noseleaf (light gray) and pinna samples(dark gray) with respect to the ratio aperture diameter (D) over wavelength (λ).

35

2 4 6 8

D/λ

0

20

40

60

80

100

Dis

tance t

o L

imit

,(°)

A

2 4 6 8

D/λ

0

20

40

60

80

100

Dis

tance t

o L

imit

,(°)

B

Figure 3.12: Distance between the beamwidth values of the biosonar samples and therespective lower beamwidth limit as a function of the ratio of characteristic dimension(D) over wavelength (λ). A) noseleaf samples, B) pinna samples. D is a characteristicdimension, i.e., aperture diameter for the bat biosonar samples.

plot it is seen that the pinnae have a smaller mean scatter and smaller sizes of the quantiles(s. Figure 3.13).

3.6 Additional Supporting Analysis

The following sets of analysis did not have as strong results as those in previous sections,however the results still contain some insights into how biosonars operate and how theyare potentially different from engineered sonar.

3.6.1 Maximum vs Minimum Beamwidth

The minimum and maximum beamwidths, matched with the maximum and minimumaperture sizes respectively, can be compared to see that the minimum beamwidths bothoccupy a much larger range of D/λ values and over that range they tend to stay muchcloser to the limit. The maximum beamwidths were all found below a D/λ of 7 and 78%were found to have a D/λ of 3 or lower. In the half-power regime, it was found that thematched maximum beamwidths were on average 21◦ larger (±15◦ standard deviation),

36

Pinnae Noseleaves

0

50

100

150

200

250

Dis

tan

ce

Fro

m L

imit(°

)

Figure 3.13: Results of the analysis of variance test comparing the scatter of the receptionelements (pinnae) and emission elements (noseleaves) to the reference limit at quarter-power. The comparison was performed only for values of D/λ less than 4 to keep thecomparison in the regime where noseleaves were typically located. For each set of data,the red line inside of the blue box indicates the mean of that set, with the upper and loweredges of the blue box indicating the first and third quantiles. The red crosses representdata points considered outliers within the set.

37

Table 3.4: Results of the analysis of variance test comparing the scatter of the receptionelements (pinnae) and emission elements (noseleaves). All comparisons were performedon the quarter-power beamwidth data. The comparison was performed only for values ofD/λ less than 4 to keep the comparison in the regime where noseleaves were typicallylocated. SS is the sum of squares, df is the degrees of freedom, MS is the mean squarederror and F is the f statistic, which is the ratio of the mean squared error of the groups tothe mean squared error of the error.

Source SS df MS F Prob>FGroups 73494.9 1 73494.9 205.85 8.71× 10−45

Error 825440.8 2312 357Total 898935.7 2313

while in the quarter-power beamwidths the average difference was 47◦ (±47◦ standarddeviation). Pinnae in half-power had an average difference of 15◦ compared to noseleaveswith an average difference of 27◦.

3.6.2 Geometric Effects on Beamwidth

Two different methods were used to test the effect of geometric factors on the accuracyof the reference model to the calculated beamwidths. The first comparison checked howwell the apertures could be evaluated as 2 dimensional by calculating the root mean squaredistance traveled by the point clouds to the plane of best fit in order to determine the depthof the aperture (s. Figure 3.15). After comparison the depth of the aperture did not appearto have any noticeable affect or trend on the likelihood of the beamwidth falling closer tothe reference limit.

Another property examined was the eccentricity, i.e. roundness, of the 2D transducer.Many of the biosonar apertures were much more elliptical, and similarly the eccentricitywas measured and then plotted to look for trends based on location on the beamwidth curve(s. Figure 3.16). The eccentricity did not appear to effect how close a specific value felltowards the curve and there were not any apparent trends of eccentricity that were notedfrom the curve.

In circular plane arrays and engineered transducers there is an approximately linear rela-tionship between the ratio of the minimum and maximum diameters of the array or aper-ture and the minimum and maximum beamwidth. This relationship was compared for thebiosonar samples. For each of the biosonar samples, the ratio of minimum to maximum

38

2 4 6 8 10

D/λ

0

50

100

150

Half

-Pow

er

Beam

wid

th (

°)A

2 4 6 8 10

D/λ

0

50

100

150

Half

-Pow

er

Beam

wid

th (

°)

B

Figure 3.14: Comparison of minimum and maximum beamwidths: A) Minimumbeamwidth values matched with the maximum aperture diameters. B) Maximumbeamwidth values matched with the minimum aperture diameters.

beamwidth was averaged over the range of operating frequencies to compare to the tech-nical reference (s. Figure 3.17). The averages were found to be scattered around the lineof expected behavior, indicating that the biosonars do not follow the expected curve foreccentricity of geometry compared to eccentricity of beamwidth. Additionally, for a givenaperture over the ten operating frequencies that beampatterns were generated for, the ec-centricity of the beamwidth had an average increase of .21 eccentricity between the mostelliptical and most circular of the beampatterns. These results indicate that the complexgeometries of the biosonar apertures do not allow approximation of one beamwidth whengiven the other, unlike in elliptical transducers.

3.6.3 Distance To Limit

In the biosonar samples, the difference between the beamwidth values of the samples andthe respective elliptical-transducer limit values was found to depend on the ratio betweendiameter and wavelength. In absolute terms, this difference decreased from about 15◦ toabout 5◦, as the ratio diameter over wavelength increased, i.e., the larger the noseleavesor pinnae were compared to the wavelengths they operate on, the closer their beamwidthscame to the limit (s. Figure 3.18).

39

Figure 3.15: The reference beamwidth values is plotted as the black line with respect toaperture diameter (D) to wavelength (λ). The scattered points are on a grey scale, wherethe darker a point is, the flatter the aperture is.

40

Figure 3.16: The reference beamwidth value is plotted as the black line with respect toaperture diameter (D) to wavelength (λ). Eccentricity is measured by the greyscale of thepoints on the graph, where the darker a point is, the lower it’s eccentricity, i.e. the lesscircular the aperture is.

41

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

dmin

/dmax

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

bw

min

/ b

wm

ax

Figure 3.17: The eccentricity of the geometry is compared to the eccentricity of the beam-pattern. The black line in the middle represents the expected behaviour for elliptical-transducers. The grey o’s represent noseleaves while the black x’s are pinnae. Each of thepoints on the graphs is the average eccentricity of the beamwidths for the aperture over its10 measured frequencies.

42

1 2 3 4 5 6 7 8 9 10

D/λ

-20

-15

-10

-5

0

5

10

15

20

25

30

Aver

age

Dis

tance

to L

(°)

Figure 3.18: Distance between the beamwidths of the biosonar samples and the respec-tive elliptical-transducer limit as a function of the diameter to wavelength ratio (D

λ). The

beamwidth data has been arranged in bins of width 0.25 Dλ

. The averages for all data pointsin each bin are indicated by open circles; the error bars mark the standard deviations.

Chapter 4

Discussion

4.1 Importance of Beamwidth in Biosonar

The results obtained can be seen as indications that beamwidth may play very differentroles in bat biosonar and technical sonar. With few exceptions, the biological and tech-nical sonars included in the sample operated in very different diameter over wavelengthregimes with technical sonars operating at much larger size to wavelength ratios than thebat biosonars. Only 4 out of the 23 technical sonars included in this study overlappedwith the upper half of the range covered by the biosonar systems. Due to the basic in-verse relationship between beamwidth and the ratio of aperture diameter and wavelength,the different operating regimes of biological and technical sonars were manifest in dif-ferent beamwidths ranges: whereas the half-power bandwidths of technical sonars weretypically much less than 10◦, those of the biological sonars were typically much largerthan 10◦. This difference is to be expected based on the different sizes of biological andengineered sonar relative to the employed wavelength.

Indeed, the smallest beamwidths found in bats were predicted fairly well by the planarelliptical-transducer model. Small deviations towards smaller values, i.e., below the ref-erence curve of the elliptical could be due to measurement errors, e.g., in determiningthe equivalent transducer diameters or in handling local shape features of the beampatternsuch as sidelobes. They could also be due to inadequacies the elliptical-transducer modelmay have in describing three-dimensional structures. In either case, it is noteworthy thatthe scatter of the data points above the reference curve was found to be much larger thanthat below the curve. If the scatter below the curve can be taken as a estimate for the effect

43

44

of the various error sources associated with the current approach, it can be concluded thatthe much larger deviations in the biosonar data towards larger beamwidth were – to a largeextent – not due to measurement error.

For the technical sonar systems the scatter away from the limit curve was found to be verysmall. This can be taken as an indication that beamwidth is seen as a critical system char-acteristic by sonar engineers who will increase the size of their devices until the beamwidthrequirement of the respective application is met (or some other limit is reached). For thebiological sonars, the large upward scatter can be seen as evidence that factors other thanthe need to minimize beamwidth have been important to the evolutionary beampattern de-sign. Hence, bat species with a similar aperture-diameter-to-wavelength ratio can havevery different beamwidths. It could be the case that the different species benefit from dif-ferent beamwidths due to their specific sensory ecology or that the beamwidths are moreof a byproduct of other beampattern characteristics and do not have a substantial impacton the animals’ biosonar sensing capabilities by themselves.

The comparison between the bat biosonar structures and random aluminum baffles sup-ports this hypothesis as it shows that biological samples have scatter away from the limitcurve that is greater (or equal in places) than what would happen if the baffles were randomand not designed for a specific beamwidth at all. Hence, it could be argued the beampat-terns of the bats have been under the influence of evolutionary forces that were not aimedat beamwidth. An alternative explanation could be that the biological beamwidths are en-tirely the result of a random process (like the aluminum baffles), but that the randomness inthe biological baffles produced a greater scatter, e.g., because the design space was widerthan that of the crumpled aluminum cones.

A final argument against an evolutionary drive towards small beamwidth in bat biosonarcomes from the comparison of bat families believed to have some of the most sophisti-cated biosonar systems in nature (hipposiderids and rhinolophids) and a family with littlebiosonar use (Pteropodidae). Since no difference was obvious in the beamwidths betweenthose two groups, the results do not support the notion that narrow beamwidth is an adap-tation for use of biosonar.

4.2 Differences in Emission and Reception

An interesting finding that could be interpreted in the direction of functional specializa-tions in sonar beamwidth is beamwidth difference between emission (noseleaves) and re-ception (pinnae) beams, where noseleaves were found to be smaller relative to the em-

45

ployed wavelengths and hence produced larger beamwidths. This systematic differencecould be either the results of a functional specialization where biosonar systems benefitfrom operating with wider emission beams than what they use for reception. Alterna-tively, it could be a byproduct of other factors that push for noseleaves that are smallerthan their respective ears. Examples of such factors could be feeding behaviors where,for example, the bat may have to inserts its snout into a flower for feeding on nectar. Itcould also be that a large noseleaf could interfere with forward vision in species wherethe eyes contain important sensory information. While bat species with large noseleavesdo exist, e.g., the sword-nosed bats in the genus Lonchorhina, they seem to be few andfar between [39]. On the functional side, detection of targets would benefit from emis-sion and reception beams that act as ”matched filters”, i.e., have identical shapes so thatthe weighting imposed by the reception beam matches that of the emission. However, forother sensory tasks and signal-to-noise ratios that are not at a critical limit, this may not bethe best solution. It may be noteworthy in this context that many bat species, such as therhinolophids and hipposiderids that were prominently represented in the current sample,have very mobile pinnae that can be rotated over large angles, whereas the noseleaves candeform but are not subject to such large angular re-orientations [26]. In such a scenario,the wide emission beams could create an opportunity for conducting dynamic scans on thereception side where a larger volume is being swept over time.

Chapter 5

Conclusion

5.1 Summary

Biosonar has typically been studied by itself and in relation to the environment of theuser, typically bats. However, by creating a method for converting biosonar apertures intoplanar diameters, biosonar can be compared to engineered sonar in terms of commonlyused metrics, particularly beamwidth. Beamwidth is commonly used by engineered sonaras a measure of the sonar’s resolution and performance and can be calculated for thebiosonar apertures using numerically generated beampatterns calculated from aperturesderived from µCT scans of the bats.

Given the biosonar beamwidths and geometries a comparison between biosonar and tech-nical sonar could be performed which identified three key differences between them:biosonar tended to have beamwidths at least an order of magnitude larger, biosonar beam-widths tended to be further away from the reference limit of an equivalent planar array,and biosonar tended to be located at much lower values of Aperture Diameter (D), orarray-length, to wavelength (λ) ratios. The first two of these points were further high-lighted upon conducting an experiment measuring the beamwidth of randomly generatedaluminum baffles that were located in the same regime of aperture diameter to wavelengthas the biosonar where, on average, it was shown that the randomly generated baffles werecloser to the reference beamwidth than the biosonar.

The biosonar additionally showed differences between the emission and reception ele-ments. The emission elements (noseleaves) tend to have smaller ratios of D to λ whichin turn causes noseleaves to have larger beamwidths on average. This finding can be cou-

46

47

pled with the finding that as the biosonar apertures increase in values of D to λ they tendto converge to the reference beamwidth limit resulting in smaller beamwidths comparedto the limit. However, only reception elements are located at the higher values of D toλ where this convergence becomes more prevalent, indicating that narrow beamwidthsmay not have been evolutionarily important for biosonar emission elements or that largebeamwidths may be beneficial in biosonar emission.

An additional finding that supports beamwidth potentially not being an evolutionary con-cern of bats can be seen by comparing the performance of pinnae used by families of batswith sophisticated active sonar to a family of bats that do not use active sonar. Both fam-ilies were found to operate at equivalent D to λ ratios and have comparable beamwidthsand distance from the reference limit at those D to λ regimes. This lends further credenceto the concept that beamwidth may not be an important evolutionary factor for bats, unlikethe importance that sonar engineers have placed on developing sonar arrays with smallerbeamwidths.

5.2 Conclusion

The data present here supports the notion that technical and biological sonars may haveradically different operational principles. Whereas high-resolution angular imaging of theworld is key to technical sonars, bat biosonar tends to operate with beamwidth that are atleast one order of magnitude larger than those of typical engineered systems. Part of theperformance gap in terms of beamwidth and resolution observed in this research can beexplained by the larger sizes of the engineered sonar compared to the biosonar, but evenwith engineered sonar that operate at the same values of array-length, or aperture diameter,to wavelength there was a noticeable increase in average biosonar beamwidth.

Nevertheless, the evolutionary success of bats and the ability of many bat species to thrivein complex environments, such as dense vegetation, indicates that the animals must havefound a way to obtain the relevant sensory information in ways that does not rely on anarrow beamwidth and the high angular resolution it conveys. These strategies shouldbe of great interest to engineers, because reproducing the abilities of bats could supportbringing reliable navigation in complex environments to small platforms.

48

5.3 Importance of Results

Prior to this research it had been quantitatively shown that biosonar beamwidths werelarger than engineered sonar beamwidths. However, there were very few calculated beam-widths for the biosonar to use for comparisons, and the beamwidths calculated were fora single species of bat. This research created a large database of biosonar apertures andtheir beam information, across many different families and species of bat. This databasecontains all of the information used in comparison within this research, as well as ad-ditional information on the biosonar beampatterns such as locations and values of localminima and local maxima in the beampatterns and width of the main lobe of the biosonar.By using this database of information alongside the methods created for determining anengineering analogue for the biosonar apertures, it was able to be shown that the biosonarapertures have significant scatter from the reference limit.

This scatter is important for future research into understanding how biosonar operates.While it previously could be said that biosonar beamwidths were larger than engineeredsonar beamwidths, it can now be shown in a large sample size that having a narrowbeamwidth does not appear to be important to biosonar. The importance of this findingis that it means that bats may not be using alternative methods to supplement their widebeamwidths, but instead that narrow beamwidths are irrelevant or even potentially harmfulto the operation of the biosonar. These results show that the future of biosonar researchmay not be in finding out how to use biosonar operating differences, such as dynamicsof the baffle, to generate narrower beamwidths but instead attempting to understand theseeffects on their own and in relation to an entirely different sensing paradigm than what isused in engineered sonars.

These results are compounded by the additional tests and comparisons performed. Thenoseleaf simulate test further corroborated the idea that narrow beamwidths may actuallybe harmful to the operation of the biosonar apertures, as simulates of the same size andwith random internal geometries and imperfections were found to have less scatter thantheir biosonar equivalents.

The importance of having a large sample set of data could be seen by the analysis ofthe emission and reception elements. Prior to this research there was not any known,quantifiable differences between the beampatterns of the emission and reception elements.Finding that the emission elements had statistically larger beamwidths than their receptioncounterparts places another piece in the understanding of how the biosonar systems operateand helps further focus future research into how engineering analogue systems can becreated to mimic their performance.

49

5.4 Achievements

In this research, I have devised a methodology for equating biosonar apertures to two-dimensional transducers and calculating the beamwidth of numerically generated biosonarbeampatterns. With these methods, I was able to show that biosonar apertures follow thegeneral trend for beamwidth, though many samples did not follow the limit closely. Ad-ditionally, I was able to compare the biosonar to technical sonar to show that the biosonarhad a performance gap not present in the technical sonar. An experiment I performedalso showed that the biosonar apertures did not on average perform as well as randomlygenerated aluminum baffles, further highlighting a potential performance gap.

I am first author on one journal paper manuscript that has been submitted to Bioinspiration& Biomimetics and I have presented posters on this research at two Naval EngineeringEducation Consortium (NEEC) conferences.

Bibliography

[1] B. Barshan and R. Kuc. A bat-like sonar system for obstacle localization. IEEE T.Syst. Man Cyb., 22(4):636–646, Jul 1992.

[2] W. S. Burdic. Underwater Acoustic Systems Analysis. Prentice Hill, EnglewoodCliffs, NJ, 2nd edition, 1991.

[3] P. Caspers, A. Leonessa, and R. Muller. Eigenbeam analysis of the diversity in batbiosonar beampatterns. J. Acoust. Soc. Am., 135, 2014.

[4] P. B. Caspers. Analysis of Bat Biosonar Beampatterns: Biodiversity and Dynamics.PhD thesis, Virginia Polytechnic and State University, 2017.

[5] EdgeTech. 4200 Side Scan Sonar System.

[6] Robot Electronics. Air Ultrasonic Ceramic Transducers.

[7] L. A. Estroff and A. D. Hamilton. At the interface of organic and inorganic chem-istry: Bioinspired synthesis of composite materials. Chem. Mater., 13(10):3227–3235, 2001.

[8] T. Fortmann, Y. Bar-Shalom, and M. Scheffe. Sonar tracking of multiple targetsusing joint probabilistic data association. IEEE J.Oceanic Eng., 8(3):173–184, Jul1983.

[9] Y. Fu, P. Caspers, and R. Muller. A dynamic ultrasonic emitter inspired by horseshoebat noseleaves. Bioinspir. Boimim., 11(3):036007, 2016.

[10] D. R. Griffin, F. A. Webster, and C. R. Michael. The echolocation of flying insectsby bats. Anim. Behav., 8:141–154, 1960.

[11] R. Harrington. Sidelobe reduction by nonuniform element spacing. IRE Transactionson Antennas and Propagation, 9(2):187–192, March 1961.

50

51

[12] K.-Z. Ivanic, Z. Tadic, and M. A. Omazic. Biomimicry - an overview. The HolisticApproach to Environment, 5:19–36, 2015.

[13] G. Jones and M.W. Holderied. Bat echolocation calls: adaptation and convergentevolution. P. Roy. Soc. B-Biol. Sci., 274, 2007.

[14] J. Jonsson, E. Edqvist, H. Kratz, M. Almqvist, and G. Thornell. Simulation, manu-facturing, and evaluation of a sonar for a miniaturized submersible explorer - corre-spondence. IEEE Xplore, 57, 2010.

[15] E. K.V. Kalko and H.-U. Schnitzler. The echolocation and hunting behavior ofdaubenton’s bat, myotis daubentoni. Behav. Ecol. Sociobiol., 24:225–238, 1989.

[16] S. Kim, C. Laschi, and B. Trimmer. Soft robotics: a bioinspired evolution in robotics.Trends Biotechnol., 31(5):287 – 294, 2013.

[17] Kongsberg. Dual Frequency Side Scan Sonar.

[18] Kongsberg. High Resolution and Domed Sonar Heads.

[19] R. Kuc and B. Barshan. Bat-like sonar for guiding mobile robots. IEEE Contr.Sys.,12(4):4–12, Aug 1992.

[20] L. E. Llewellyn and S. J. Bainbridge. Getting up close and personal: The need toimmerse autonomous vehicles in coral reefs. In OCEANS 2015 - MTS/IEEE Wash-ington, pages 1–9, Oct 2015.

[21] MaxBotix. High Performance Sonar Range Finder.

[22] M. E. McConney, K. D. Anderson, L. L. Brott, R. R. Naik, and V. V Tsukruk. Bioin-spired material approaches to sensing. Adv. Funct. Mater., 19(16):2527–2544, 2009.

[23] Sound Metrics. Specifications UL300.

[24] R. Muller. Numerical analysis of biosonar beamforming mechanisms and strategiesin bats. J. Acoust. Soc. Am., 128(3):1414–1425, September 2010.

[25] R. Muller. Dynamics of biosonar systems in horseshoe bats. Eur. Phys. J. - Spec.Top., 224(17-18):3393–3406, December 2015.

[26] R. Muller, A.K. Gupta, H. Zhu, M. Pannala, U.S. Gillani, Y. Fu, P. Caspers, and J.R.Buck. Dynamic substrate for the encoding sensory information in bat biosonar. Phys.Rev. Lett., 118(15):158102, April 2017.

52

[27] M. F. A. B. M. Murad, M. I. B. Samah, Z. H. Ismail, and K. Sammut. Surveillance ofcoral reef development using an autonomous underwater vehicle. In 2016 IEEE/OESAutonomous Underwater Vehicles (AUV), pages 14–19, Nov 2016.

[28] R. Muller and R. Kuc. Biosonar-inspired technology: goals, challenges and insights.Bioinspir. Biomim., 2(4):S146, 2007.

[29] G. Neuweiler. The Biology of Bats. Oxford University Press, New York, NY, 2000.

[30] H. Nguyen, J. Jonsson, E. Edqvist, and J. Sundqvist. Heavily miniaturized submeris-ible - a terrestrial kickoff. 2008.

[31] V. H. Pascual, T. F. Otero, and J. Schumacher. Biomimetic reactions in conductingpolymers for artificial muscles: sensing working conditions. volume 10162, pages10162 – 10162 – 8, 2017.

[32] D. J. Peters. A bayesian method for localization by multistatic active sonar. IEEE JOceanic Eng, 42:135–142, 2016.

[33] R2Sonic. Sonic 2024/2022 Broadband Multibeam Echsounders.

[34] Reson. SeaBat 7125 Operator’s Manual.

[35] Reson. SeaBat 7130 Operator’s Manual.

[36] A. S. Rudolph, S. G. Wax, and L. Christodoulou. Bio-inspired dynamic robots, 2003.

[37] S. Schmidt, S. Hanke, and J. Pillat. The role of echolocation in the hunting of terres-trial prey – new evidence for an underestimated strategy in the gleaning bat, mega-derma lyra. J. Comp. Physiol., 186:975–988, 2000.

[38] H U Schnitzler, E Kalko, L Miller, and A Surlykke. The echolocation and huntingbehavior of the bat,pipistrellus kuhli. J. Comp. Physiol., 161:267–274, 1987.

[39] N. B. Simmons. Mammal Species of the World: A Taxonomic and Geographic Ref-erence. Johns Hopkins University Press, Baltimore, 3rd edition, 2005.

[40] Sonardyne Solstice. Search and Classify Side Scan Sonar.

[41] Far Sounder. FarSounder-1000 Navigation Sonar.

[42] D. D. Sternlicht, J. E. Fernandez, J. L. Prater, J. N. Weaver, J. C. Isaacs, T. C. Mont-gomery, C. M. Loeffler, and M. Purcell. Advanced sonar technologies for high clear-ance rate mine countermeasures. 2016.

53

[43] B. Su, Y. Tian, and L. Jiang. Bioinspired interfaces with superwettability: From ma-terials to chemistry. J. Am. Chem. Soc., 138(6):1727–1748, 2016. PMID: 26652501.

[44] J. Sutlive, B. Todd, E. Sachdeva, B. Nguyen, A. Yu, A. Farley, and R. Muller.Biomimetic sonar for encoding target class at small scales. NEEC Annual Meet-ing 2017, April 2017.

[45] Teledyne. M900 Series.

[46] Teledyne. P450 Series.

[47] Teledyne. P900 Series Deepwater 2D Imaging Sonar.

[48] J. E. Thorner. Approaches to sonar beamforming. In IEEE Technical Conference onSouthern Tier, pages 69–78, Apr 1990.

[49] R. J. Urick. Principles of Underwater Sound. McGraw-Hill Book Company, NewYork, NY, 3rd edition, 1983.

[50] Julian F.V Vincent, Olga A Bogatyreva, Nikolaj R Bogatyrev, Adrian Bowyer, andAnja-Karina Pahl. Biomimetics: its practice and theory. Journal of The Royal SocietyInterface, 3(9):471–482, 2006.

[51] Wassp. WMB-3230 / WMB-5230 / WMB-3250 Specifications.

[52] K.-K. Yan and Y. Lu. Sidelobe reduction in array-pattern synthesis using geneticalgorithm. IEEE Transactions on Antennas and Propagation, 45(7):1117–1122, Jul1997.

[53] A. Zhao, L. Ma, X. Ma, and J. Hui. An improved azimuth angle estimation methodwith a single acoustic vector sensor based on an active sonar detection system. Sen-sors, 17, 2017.

[54] Q. Zhuang and R. Muller. Noseleaf furrows in a horseshoe bat act as resonancecavities shaping the biosonar beam. Phys. Rev. Lett., 97(21):218701–4, November2006.

Appendices

Appendix A: Code

Appendix A.1: Geometric Processing Code

%Main p r o c e s s i n g program used f o r t u r n i n g edge f i l t e r e d p o i n t c l o u d s i n t o%2D geomet ry and c a l l s s u b f u n c t i o n f o r p r o c e s s i n g b e a m p a t t e r n s t o f i n d%beamwidths% A c e l l o f s t r s ( R e f e r r e d t o as s t r . mat ) i s l o a d e d wi th each s t r% r e p r e s e n t i n g t h e f i l e name a s s o c i a t e d wi th a p o i n t c l o u d and b e a m p a t t e r n .% I n f o r m a t i o n f o r t h a t a p e r t u r e i s l o a d e d from t h e r e s p e c t i v e f i l e% l o c a t i o n f o r p r o c e s s i n g .% At t h e end of t h e program a l l o f t h e i n f o r m a t i o n i s l o a d e d i n t o and% u p d a t e d i n t o a s t r u c t u r e , c o n t a i n i n g t h e i n f o r m a t i o n g e n e r a t e d on t h e% a p e r t u r e geomet ry and t h e beamwidths and b e a m p a t t e r n s a t t h e 10% f r e q u e n c i e s .c l e a rc l cc l o s e a l l%Load a c e l l o f s t r i n g s , s t r , c o r r e s p o n d i n g t o t h e a p e r t u r e f i l e names

l o a d ( ’ s t r . mat ’ , ’ s t r ’ )%R e a s s i g n t h e v a r i a b l e s t r t o l s t r , a s s t r was used i n o t h e r p l a c e s i n t h e%programl s t r = s t r ;

%Load t h e c u r r e n t s t r u c t u r e so t h a t a d d i t i o n a l p o i n t s can be added i n t o%t h e s t r u c t u r e r a t h e r t h a n made s e p e r a t el o a d v s t r u c t . matf o r i =1 : l e n g t h ( l s t r )

54

55

c l o s e a l l %c l o s e a l l f i g u r e d i s p l a y windows f o r t h e p r e v i o u s runs t r = l s t r { i } %Update s t r t o r e p r e s e n t t h e c u r r e n t f i l e b e i n g p r o c e s s and

%d i s p l a y o n s c r e e n s t r i n g f o r l o a d i n g edge− f i l t e r e d and edge−s e l e c t e d p o i n t%cloud , c h a n g e d i r e c t o r y t o match l o c a t i o ns t r i n g = s t r c a t ( ’H:\ P o i n t Clouds \ ’ , s t r , ’ PLY2 . ply ’ ) ;p tC loud = p c r e a d ( s t r i n g ) ;%S t r i n g f o r l o a d i n g b e a m p a t t e r n , change d i r e c t o r y t o match l o c a t i o ns t r i n g 2 = s t r c a t ( ’H:\ a l l b e a m s \ ’ , s t r , ’ . mat ’ ) ;l o a d ( s t r i n g 2 ) ;

%R e l o a c t s t r u c t u r e c o n t a i n i n g a l l d a t a − Unsure why t h i s was n e c e s s a r y b u t%somet imes s t r u c t u r e would n o t p r o p e r l y u p d a t e wi th t h i s i n loopl o a d v s t r u c t . mat

% E x t r a c t l o c a t i o n s from t h e p o i n t c l o u d and p u t i n t o c a r t e s i a n compoenentsLoc= p tC loud . L o c a t i o n ;x=Loc ( : , 1 ) ;y=Loc ( : , 2 ) ;z=Loc ( : , 3 ) ;%Find m i d p o i n t s be tween t h e maximum and minimum x , y , and z c o o r d i n a t e smidV = [ ( ( max ( x )+ min ( x ) ) / 2 ) , ( ( max ( y )+ min ( y ) ) / 2 ) , ( ( max ( z )+ min ( z ) ) / 2 ) ] ;%Per fo rm an a f f i n e f i t ( r o o t mean s q u a r e ) t o f i n d t h e p l a n e o f b e s t f i t[ n , V, p ] = a f f i n e f i t ( Loc ) ;meanV=p ;%% 3D s u r f o f p o i n t c l o u d% ### Uncomment t o show a 3D s u r f o f t h e p o i n t c l o u d%%d = −p∗n ;% [ xx , yy ]= n d g r i d ( min ( x ) : ( ( max ( x)−min ( x ) ) / 1 0 ) : ( max ( x ) ) , min ( y ) : ( . . .%(max ( y)−min ( y ) ) / 1 0 ) : max ( y ) ) ;% [ xx , yy ]= n d g r i d ( ( min ( x)−mean ( x ) ) : ( mean ( x ) / 1 0 ) : ( max ( x )+ mean ( x ) ) , . . .%(min ( y)−mean ( y ) ) : ( mean ( y ) / 1 0 ) : ( max ( y )+ mean ( y ) ) ) ;% zp = (−n ( 1 )∗ xx − n ( 2 )∗ yy − d ) / n ( 3 ) ;% f i g u r e% s u r f ( xx , yy , zp )% ho ld on% s c a t t e r 3 ( x , y , z )% a x i s e q u a l%% New P l a n e G e n e r a t i o n%G e n e r a t e a p l a n e o f b e s t f i t from t h e v a l u e s foud u s i n g t h e a f f i n e f i t

56

syms xva r yva r z v a r %Sym v a r i a b l e s used t o d e f i n e p l a n eP=[ xvar , yvar , z v a r ] ; %C r e a t e a r r a y o f sym v a r i a b l e s f o r p l a n e%per fo rm d o t p r o d u c t o f no rma l s from RMS p l a n e o f b e s t f i t and a%p o i n t on t h e p l a n ep l a n e f u n c t i o n = d o t ( n , P−p ) ;z p l a n e = s o l v e ( p l a n e f u n c t i o n , z v a r ) ; %C r e a t e t h e p l a n e o f b e s t f i t

%Mesh p l a n e and p l o t t o s e efmesh ( zp l ane , [ min ( Loc ( : , 1 ) ) max ( Loc ( : , 1 ) ) min ( Loc ( : , 2 ) ) max ( Loc ( : , 2 ) ) ] )a x i s e q u a lho ld on%P l o t o r i g i n a l c a t e r s i a n c o o r d i n a t e s on p l a e n f o r compar i sons c a t t e r 3 ( Loc ( : , 1 ) , Loc ( : , 2 ) , Loc ( : , 3 ) )

%% P r o j e c t on to p l a n e%Per fo rm p r o j e c t i o n o f 3D p o i n t s on to 2D p l a n e o f b e s t f i t .p r o j =Loc∗ n u l l ( n ’ ) ; %c r e a t e x , y a r r a y o f p r o j e c t e d p o i n t sf i g u r es c a t t e r ( p r o j ( : , 1 ) , p r o j ( : , 2 ) ) %p l o t p r o j e c t e d p o i n t s t o compare shape t o 3Da x i s e q u a lho ld on%Find mean of p r o j e c t e d x p o i n t s − D e p r e c i a t e d i n Use

meanpro jx =( mean ( p r o j ( : , 1 ) ) ) ;%Find mean of p r o j e c t e d y p o i n t s − D e p r e c i a t e d i n Use

meanpro jy =( mean ( p r o j ( : , 2 ) ) ) ;s c a t t e r ( meanprojx , meanprojy , ’ r ’ ) %S c a t t e r t h e mean p o i n t on to p l o t%Find t h e midd le o f p r o j x p o i n t s

m i d p ro j x =(max ( p r o j ( : , 1 ) ) + min ( p r o j ( : , 1 ) ) ) / 2 ;m i d p ro j y =(max ( p r o j ( : , 2 ) ) + min ( p r o j ( : , 2 ) ) ) / 2 ; %Find t h e midd le o f y p o i n t ss c a t t e r ( midpro jx , midpro jy , ’g ’ ) %S c a t t e r mid p o i n t on to p l o ta x i s v = a x i s ; %Save c u r r e n t a x i s f o r l a t e r use

%% C a l c u l a t e D i s t a n c e Moved% Thi s s e t o f code f i n d s how f a r t h e p o i n t s had t o move i n o r d e r t o be on% t h e p l a n e o f b e s t f i tn r = [ 1 ; 0 ; 0 ] ;r r o t v e c = v r r o t v e c ( n ’ , nr ’ ) ;mro tvec = v r r o t v e c 2 m a t ( r r o t v e c ) ;Locr=Loc∗mrotvec ’ ;

57

Locrm=mean ( Locr ) ;Locrmc= b sx fu n ( @minus , Locr , Locrm ) ;[ nra , Vra , p r a ] = a f f i n e f i t ( Locrmc ) ;p r o j r =Locrmc∗ n u l l ( nra ’ ) ;

d i s tmoved =Locrmc ( : , 1 ) ; %a r r a y o f how f a r each p o i n t moved

dmmean=mean ( d i s tmoved ) ; %mean d i s t a n c e moved by a l l p o i n t s

dmstd= s t d ( d i s tmoved ) ; %s t a n d a r d d e v i a t i o n o f d i s t a n c e d moved by a l l p o i n t s

%% Find P r i n c i p l e Components% Find P r i n c i p l e compoennts o f t h e 2D p r o j e c t i o n . Th i s has s i n c e% d e p r e c i a t e d from use f o r p r o c e s s i n g as i t was d e c i d e d t h a t r a t h e r t h a n% use t h e p r i n c i p l e components o f t h e shapes , t h e minimum and maximum% t h r o u g h t h e c e n t r o i d ( found l a t e r i n code ) would be used f o r compar i son% b u t has been k e p t i n code f o r compar i son p u r p o s e sc o e f f =pca ( p r o j ) ; %Find PCA c o e f f i c i e n t sx1= c o e f f ( : , 1 ) ;x2= c o e f f ( : , 2 ) ;%Get s l o p e o f t h e f i r s t component

s l o p e 1 =( x1 (2)−meanpro jy ) / ( x1 (1)−meanpro jx ) ;y i n t 1 =meanprojy−s l o p e 1 ∗meanpro jx ; %Get y i n t e r c e p t o f f i r s t components l o p e 2 =( x2 (2)−meanpro jy ) / ( x2 (1)−meanpro jx ) ; %Get s l o p e o f t h e compoenenty i n t 2 =meanprojy−s l o p e 2 ∗meanpro jx ; %Get y i n t e r c e p t o f second componenty1= e z p l o t ( s l o p e 1 ∗ xva r + y i n t 1 ) ; %P l o t t h e f i r s t p r i n c i p l e componenty2= e z p l o t ( s l o p e 2 ∗ xva r + y i n t 2 ) ; %P l o t t h e second p r i n c i p l e componenta x i s ( a x i s v ) %R e s e t a x i s t o e a r l i e r a x i s f o r e a s i e r v i ewing

%% Find Length o f i n t e r s e c t i o n%Find t h e minimum and maximum d i s t a n c e from t h e p r i n c i p l e components : Th i s%p a r t o f code i s d e p r e c i a t e d i n use as t h e minimum and maximum t h r o u g h t h e%c e n t r o i d , found l a t e r i n t h e code , a r e i n s t e a d used f o r compar i son b u t t h e%code has been l e f t a s a p o i n t o f compar i son t o t h e o t h e r v a l u e s%c r e a t e an x l i n e l e n g t h t h a t s p a n s t h e e n t i r e shapex i l e n g t h = l i n s p a c e ( min ( p r o j ( : , 1 ) ) , max ( p r o j ( : , 1 ) ) ∗ 1 . 5 ) ;y i 1 = s l o p e 1 ∗ x i l e n g t h + y i n t 1 ; %C r e a t e a l i n e a r r a y c o r r e s p o n d i n g t o PC1

58

y i 2 = s l o p e 2 ∗ x i l e n g t h + y i n t 2 ; %C r e a t e a l i n e a r r a y c o r r e s p o n d i n g t o PC2%Find PC1 l e n g t h i n s i d e o f shape polygon[ x i n t 1 , y i n t 1 ]= p o l y x p o l y ( x i l e n g t h , yi1 , p r o j ( : , 1 ) , p r o j ( : , 2 ) ) ;

%Find PC2 l e n g t h i n s i d e o f shape polygon[ x i n t 2 , y i n t 2 ]= p o l y x p o l y ( x i l e n g t h , yi2 , p r o j ( : , 1 ) , p r o j ( : , 2 ) ) ;

x in t1max =max ( x i n t 1 ) ; %Find t h e l a r g e s t X v a l u e o f PC1 i n s i d e t h e po lygonx i n t 1 m i n =min ( x i n t 1 ) ; %Find t h e s m a l l e s t X v a l u e o f PC1 i n s i d e t h e po lygonyin t1max =max ( y i n t 1 ) ; %Find t h e l a r g e s t Y v a l u e o f PC1 i n s i d e t h e po lygony i n t 1 m i n =min ( y i n t 1 ) ; %Find t h e s m a l l e s t Y v a l u e o f PC1 i n s i d e t h e po lygon%Find l e n g t h o f i n t e r i o r p o i n t s

d1= s q r t ( ( xint1max−x i n t 1 m i n ) ˆ 2 + ( yint1max−y i n t 1 m i n ) ˆ 2 ) ;x i n t 1 m a t =[ x in t1max ; x i n t 1 m i n ] ; %C r e a t e X v e c t o r t o P l o ty i n t 1 m a t =[ y in t1max ; y i n t 1 m i n ] ; %C r e a t e Y Ve c t o r t o p l o t

%P l o t i n t e r s e c t i o n o f 1 s t p r i n c i p l e componentp l o t ( x in t1ma t , y in t1ma t , ’−− ’ , ’ l i n e w i d t h ’ , 2 )

x in t2max =max ( x i n t 2 ) ; %Find t h e l a r g e s t X v a l u e o f PC2 i n s i d e t h e po lygonx i n t 2 m i n =min ( x i n t 2 ) ; %Find t h e s m a l l e s t X v a l u e o f PC2 i n s i d e t h e po lygonyin t2max =max ( y i n t 2 ) ; %Find t h e l a r g e s t Y v a l u e o f PC2 i n s i d e t h e po lygony i n t 2 m i n =min ( y i n t 2 ) ; %Find t h e s m a l l e s t Y v a l u e o f PC2 i n s i d e t h e po lygon%Find l e n g t h o f i n t e r i o r p o i n t s

d2= s q r t ( ( xint2max−x i n t 2 m i n ) ˆ 2 + ( yint2max−y i n t 2 m i n ) ˆ 2 )x i n t 2 m a t =[ x in t2max ; x i n t 2 m i n ] ; %C r e a t e X v e c t o r t o P loy i n t 2 m a t =[ y i n t 2 m i n ; y in t2max ] ; %C r e a t e Y Ve c t o r t o p l o t

%P l o t i n t e r s e c t i o n o f 2nd p r i n c i p l e componentp l o t ( x in t2ma t , y in t2ma t , ’−− ’ , ’ l i n e w i d t h ’ , 2 )

t i t l e ( ’ P r o j e c t e d Convex Hu l l on P l a n e o f Bes t F i t ’ )x l a b e l ( ’ D i s t a n c e i n x−d i r e c t i o n (m) ’ )y l a b e l ( ’ D i s t a n c e i n y−d i r e c t i o n (m) ’ )l e g e n d ( ’ P o i n t Cloud ’ , ’ Mean P o i n t ’ , ’ C e n t e r p o i n t ’ , ’ Pr ime Component 1 ’ , . . .

’ Pr ime Component 2 ’ , ’ Ove r l ap Ve c t o r 1 ’ , ’ Ove r l ap Ve c to r 2 ’ )

%% Convex Hu l l method% Use of convex h u l l method t o f i n d t h e c e n t r o i d o f t h e 2D b a f f l e shape%Conver t t h e p r o j e c t i o n x and y v a l u e s t o d oub l e f o r m a t

59

p r o j d = d ou b l e ( p r o j ) ;xd= p r o j d ( : , 1 ) ;yd= p r o j d ( : , 2 ) ;c h u l l = c o n v h u l l ( xd , yd ) ; %C r e a t e convex h u l l from p r o j e c t i o nx c h u l l =xd ( c h u l l );% C r e a t e x v e c t o r c o n t a i n i n g on ly p o i n t s i n t h e convex h u l ly c h u l l =yd ( c h u l l );% C r e a t e y v e c t o r c o n t a i n i n g on ly p o i n t s i n t h e convex h u l lc h u l l p =[ x c h u l l , y c h u l l ] ; %C r e a t e 2D convex h u l l a r r a yxchu l lmean =mean ( x c h u l l ) ; %Find mean of convex h u l l i n xychu l lmean =mean ( y c h u l l ) ; %Find mean of convex h u l l i n y

c o e f f =pca ( c h u l l p ) ; %C r e a t e PCA c o e f f i c i e n t s o f t h e convex h u l l

f i g u r e

%C r e a t e a p l o t o f t h e convex h u l l and t h e mean p o i n t ss c a t t e r ( xd ( c h u l l ) , yd ( c h u l l ) )a x i s e q u a la x i s v = a x i s ;ho ld ons c a t t e r ( xchul lmean , ychul lmean , ’ r ’ )

% The f o l l o w i n g s e c t i o n g e n e r a t e s s l o p s and p l o t s from t h e PCA components% f o r t h e convex h u l l . The method i s t h e same as e a r l i e r PCA l i n e% g e n e r a t i o n ( Code l i n e s t a r t i n g 109 f o r l i n e by l i n e comments )x1= c o e f f ( : , 1 ) ;x2= c o e f f ( : , 2 ) ;s l o p e 1 =( x1 (2)− ychu l lmean ) / ( x1 (1)− xchu l lmean ) ;y i n t 1 = ychul lmean−s l o p e 1 ∗ xchu l lmean ;s l o p e 2 =( x2 (2)− ychu l lmean ) / ( x2 (1)− xchu l lmean ) ;y i n t 2 = ychul lmean−s l o p e 2 ∗ xchu l lmean ;y1= e z p l o t ( s l o p e 1 ∗ xva r + y i n t 1 ) ;y2= e z p l o t ( s l o p e 2 ∗ xva r + y i n t 2 ) ;a x i s ( a x i s v )t i t l e ( ’ P r o j e c t e d Convex Hu l l on P l a n e o f Bes t F i t ’ )x l a b e l ( ’ D i s t a n c e i n x−d i r e c t i o n (m) ’ )y l a b e l ( ’ D i s t a n c e i n y−d i r e c t i o n (m) ’ )l e g e n d ( ’ P o i n t Cloud ’ , ’ Mean P o i n t ’ , ’ Pr ime Component 1 ’ , . . .

’ Pr ime Component 2 ’ )

60

%% P r i n c i p l e Component Method 3% Use p r i n c i p l e components t o d e t e r m i n e and minimum and maximum d i s t a n c e −% While t h i s method i s c a l c u l a t e d , t h e method i n t h e l a t e r s e c t i o n ,% Min and Max d i s t a n c e s , was used i n f i n a l r e s u l t s . However , i n t h e f i r s t% p a r t o f t h e s e c t i o n t h e c e n t r o i d o f t h e g e o m e t r i c shape i s found

% C r e a t e an a r r a y o f p o i n t s ove r t h e x and y l e n g t h o f t h e convex h u l l and% t h e n f i n d which p o i n t s f a l l w i t h i n t h e po lygon . Th i s p o i n t s can be used% as a r e p r e s e n t a t i o n o f t h e a r e a o f t h e po lygon t o f i n d t h e c e n t r o i dx p c h u l l = l i n s p a c e ( min ( x c h u l l ) , max ( x c h u l l ) ) ;y p c h u l l = l i n s p a c e ( min ( y c h u l l ) , max ( y c h u l l ) ) ;[ x d c h u l l , y d c h u l l ]= meshgr id ( x p c h u l l , y p c h u l l ) ;i n c h u l l = i n p o l y g o n ( x d c h u l l , y d c h u l l , x c h u l l , y c h u l l ) ; %Find g r i d p o i n t s i n s i d ex d i n c h u l l = x d c h u l l ( i n c h u l l ) ; %X g r i d p o i n t s t h a t a r e i ny d i n c h u l l = y d c h u l l ( i n c h u l l ) ; %Y g r i d p o i n t s t h a t a r e i nc h u l l p d i n =[ x d i n c h u l l , y d i n c h u l l ] ; %a r r a y o f p o i n t s t h a t a r e i n

x d i n c h u l l m e a n =mean ( x d i n c h u l l ) ; %Mean of i n t e r i o r X P o i n t s − X c e n t r o i dy d i n c h u l l m e a n =mean ( y d i n c h u l l ) ; %mean of i n t e r i o r y p o i n t s − y c e n t r o i d

c o e f f =pca ( c h u l l p d i n ) ; %C r e a t e PCs of t h e i n t e r i o r g r i d

f i g u r ep l o t ( x c h u l l , y c h u l l , ’ l i n e w i d t h ’ , 2 ) ;s c a t t e r ( x d i n c h u l l , y d i n c h u l l , ’ marker ’ , ’ . ’ ) ;a x i s e q u a lho ld ons c a t t e r ( xd inchu l lmean , yd inchu l lmean , ’ r ’ , ’ l i n e w i d t h ’ , 4 )

%Per fo rm PC a n a l y s i s t o f i n d minimum and maximum of t h e g r i d wi th r e s p e c t%t o t h e p r i n c i p l e components . Min / Max v a l u e s used were c a l c u l a t e d i n l a t e r%s e c t i o n . For Line−by−Line e x p l a n a t i o n , t h e same c a l c u l a t i o n s a r e done%wi th e x p l a n a t i o n a t code l i n e 1 2 6 . These a r e e q u i v i l e n t c a l c u l a t i o n s%u s i n g a d i f f e r e n t s e t o f v a r i a b l e s

61

x1= c o e f f ( : , 1 ) ;x2= c o e f f ( : , 2 ) ;s l o p e 1 =( x1 (2)− y d i n c h u l l m e a n ) / ( x1 (1)− x d i n c h u l l m e a n ) ;y i n t 1 = yd inchu l lmean−s l o p e 1 ∗ x d i n c h u l l m e a n ;y i n t 1 s a v e = y i n t 1 ;s l o p e 2 =( x2 (2)− y d i n c h u l l m e a n ) / ( x2 (1)− x d i n c h u l l m e a n ) ;y i n t 2 = yd inchu l lmean−s l o p e 2 ∗ x d i n c h u l l m e a n ;y1= e z p l o t ( s l o p e 1 ∗ xva r + y i n t 1 ) ;y2= e z p l o t ( s l o p e 2 ∗ xva r + y i n t 2 ) ;a x i s ( a x i s v )t i t l e ( ’ P r o j e c t e d Convex Hu l l on P l a n e o f Bes t F i t ’ )x l a b e l ( ’ D i s t a n c e i n x−d i r e c t i o n (m) ’ )y l a b e l ( ’ D i s t a n c e i n y−d i r e c t i o n (m) ’ )l e g e n d ( ’ Evenly D i s t r i b u t e d P o i n t Cloud ’ , ’ Mean P o i n t ’ , . . .

’ Pr ime Component 1 ’ , ’ Pr ime Component 2 ’ )

x i l e n g t h = l i n s p a c e ( min ( p r o j ( : , 1 ) ) , max ( p r o j ( : , 1 ) ) ∗ 1 . 5 ) ;y i 1 = s l o p e 1 ∗ x i l e n g t h + y i n t 1 ;y i 2 = s l o p e 2 ∗ x i l e n g t h + y i n t 2 ;[ x i n t 1 , y i n t 1 ]= p o l y x p o l y ( x i l e n g t h , yi1 , p r o j ( : , 1 ) , p r o j ( : , 2 ) ) ;[ x i n t 2 , y i n t 2 ]= p o l y x p o l y ( x i l e n g t h , yi2 , p r o j ( : , 1 ) , p r o j ( : , 2 ) ) ;

x in t1max =max ( x i n t 1 ) ;x i n t 1 m i n =min ( x i n t 1 ) ;y in t1max =max ( y i n t 1 ) ;y i n t 1 m i n =min ( y i n t 1 ) ;d1= s q r t ( ( xint1max−x i n t 1 m i n ) ˆ 2 + ( yint1max−y i n t 1 m i n ) ˆ 2 )x i n t 1 m a t =[ x in t1max ; x i n t 1 m i n ] ;y i n t 1 m a t =[ y in t1max ; y i n t 1 m i n ] ;p l o t ( x in t1ma t , y in t1ma t , ’−− ’ , ’ l i n e w i d t h ’ , 2 )

x in t2max =max ( x i n t 2 ) ;x i n t 2 m i n =min ( x i n t 2 ) ;y in t2max =max ( y i n t 2 ) ;y i n t 2 m i n =min ( y i n t 2 ) ;d2= s q r t ( ( xint2max−x i n t 2 m i n ) ˆ 2 + ( yint2max−y i n t 2 m i n ) ˆ 2 )x i n t 2 m a t =[ x in t2max ; x i n t 2 m i n ] ;y i n t 2 m a t =[ y i n t 2 m i n ; y in t2max ] ;

62

p l o t ( x in t2ma t , y in t2ma t , ’−− ’ , ’ l i n e w i d t h ’ , 2 )

%% Find R o t a t i o n a l I n f o r m a t i o n − C u r r e n t l y D e p r e c i a t e d%Thi s s e c t i o n f i n d s t h e amount o f r o t a t i o n f o r p o n t i n g t h e 3D mesh a l o n g%t h e x−a x i s%{a = [ 1 ; 0 ; 0 ] ;n r o t a =n−a ;n r o t a = n r o t a / norm ( n r o t a ) ;degx= acosd ( n r o t a ( 1 ) / s q r t ( n r o t a ( 1 ) ˆ 2 + n r o t a ( 2 ) ˆ 2 + n r o t a ( 3 ) ˆ 2 ) ) −9 0 ;degy= acosd ( n r o t a ( 2 ) / s q r t ( n r o t a ( 1 ) ˆ 2 + n r o t a ( 2 ) ˆ 2 + n r o t a ( 3 ) ˆ 2 ) ) ;degz= acosd ( n r o t a ( 3 ) / s q r t ( n r o t a ( 1 ) ˆ 2 + n r o t a ( 2 ) ˆ 2 + n r o t a ( 3 ) ˆ 2 ) ) ;degd =[ degx , degy , degz ] ;degd= round ( degd ) ;%}

%% Max and Min D i s t a n c e s%Thi s s e c t i o n s f i n d s t h e minimum and maximum d i s t a n c e s t h r o u g h t h e c e n t r o i dxd ; % p r o j e c t e d x v a l u e s i n do ub l e f o r m a tyd ; % p r o j e c t e d y v a l u e s i n do ub l e f o r m a tx d i n c h u l l m e a n ; % x v a l u e o f mean by convex h u l l methody d i n c h u l l m e a n ; % y v a l u e o f mean by convec h u l l method

xdo=xd−x d i n c h u l l m e a n ; %t r a n s l a t i o n o f xd mean on to o r i g i nydo=yd−y d i n c h u l l m e a n ; %t r a n s l a t i o n o f yd mean on to o r i g i n

% P l o t f i g u r e t o make s u r e i t s t i l l l o o k s r i g h t , j u s t t r a n s l a t e df i g u r eho ld onp l o t ( xdo , ydo )a x i s e q u a la x i s p l = a x i s ;

%Find minimum and maximum v a l u e s o f t h e t r a n s l a t e d convex h u l l and s e t them%t o be s l i g h t l y f u r t h e r o u t t o g a u r a n t e e o v e r l a p on a l l s i d e s o f t h e%polygonxdomax=max ( xdo ) ;xdomin=min ( xdo ) ;

63

xdomax=xdomax ∗ 1 . 1 ;xdomin=xdomin ∗ 1 . 1 ;ydomax=max ( ydo ) ;ydomin=min ( ydo ) ;ydomax=ydomax ∗ 1 . 1 ;ydomin=ydomin ∗ 1 . 1 ;%C r e a t e a l i n s p a c e l e n g t h t h a t s p a n s t h e X and Y r a n g e sx d o l i n s p a c e = l i n s p a c e ( xdomin , xdomax ) ;y d o l i n s p a c e = l i n s p a c e ( ydomin , ydomax ) ;dmax = [ 0 , 0 ] ; %p r e a l l o c a t e d max d i s t a n c e , max d i s t a n c e t h e t admin = [ 1 0 0 0 0 , 0 ] ; %p r e a l l o c a t e min d i s t a n c e , min d i s t a n c e t h e t a% Go t h r o u g h r o t a t i o n i t e r a t i o n , c r e a t i n g l i n e s t h r o u g h t h e c e n t r o i d a t 1% d e g r e e i n c r e m e n t s t o f i n d t h e maximum and minimum l e n g t h s t h r o u g hf o r i =0:179

t h r a d = p i /180∗ i ; %c o n v e r t a n g l e from deg t o r a d i a n s%G e n e r a t e p r o j e c t x v e c t o r s based o f f y l i n s p a c e

x d o l i n s p a c e 2 = y d o l i n s p a c e / t a n ( t h r a d ) ;%G e r n e r a t e p r o j e c t y v e c t o r based o f f x l i n s p a c ey d o l i n s p a c e 2 = x d o l i n s p a c e ∗ t a n ( t h r a d ) ;

%combine p r o j e c t e d v e c t o r s t o an a r r a yp r o j l s =[ x d o l i n s p a c e , y d o l i n s p a c e ] ;

%Find x p o i n t s i n[ xdinx , yd inx ]= p o l y x p o l y ( x d o l i n s p a c e , y d o l i n s p a c e 2 , xdo , ydo ) ;%f i n d y p o i n t s i n

[ xdiny , yd iny ]= p o l y x p o l y ( x d o l i n s p a c e 2 , y d o l i n s p a c e , xdo , ydo ) ;%Determin which of t h e two methods had more p o i n t s i n s i d e%( h i g h e r r e s o l u t i o n )i f l e n g t h ( xd inx ) >= l e n g t h ( xd iny )

xd in = xd inx ;yd in = yd inx ;

e l s exd in = xd iny ;yd in = yd iny ;

end%Find max and min x and y d i s t a n c e s and from t h o s e%c a l c u l a t e t h e l e n g t h i n t h i s i t e r a t i o nxdinmax=max ( xd in ) ;xdinmin =min ( xd in ) ;

64

ydinmax=max ( yd in ) ;ydinmin =min ( yd in ) ;d i t e r a t i o n = s q r t ( ( xdinmax−xdinmin ) ˆ 2 + ( ydinmax−ydinmin ) ˆ 2 ) ;x i n t 1 m a t =[ xdinmax ; xdinmin ] ;y i n t 1 m a t =[ ydinmax ; ydinmin ] ;

i f d i t e r a t i o n > dmax ( 1 )%i f t h i s i s b i g g e r t h a n t h e max va lue ,

%make i t t h e new max and r e c o r d i t s a n g l edmax ( 1 ) = d i t e r a t i o n ;dmax ( 2 ) = i ;

endi f d i t e r a t i o n < dmin ( 1 )

%i f t h i s i s s m a l l e r t h a n t h e min va lue ,%make i t t h e new min and r e c o r d i t s a n g l edmin ( 1 ) = d i t e r a t i o n ;dmin ( 2 ) = i ;

end

end

dmax ; %D i s p l a y t h e f i n a l max v a l u e founddmin ; %D i s p l a y t h e f i n a l min v a l u e found

%% P l o t min and max v e c t o r sdmaxth=dmax ( 2 ) ;y d o l i n s p a c e = x d o l i n s p a c e ∗ t a n ( dmaxth∗ p i / 1 8 0 ) ;ho ld onp l o t ( x d o l i n s p a c e , y d o l i n s p a c e , ’−− ’ , ’ l i n e w i d t h ’ , 2 )dminth =dmin ( 2 ) ;y d o l i n s p a c e = x d o l i n s p a c e ∗ t a n ( dminth ∗ p i / 1 8 0 ) ;ho ld onp l o t ( x d o l i n s p a c e , y d o l i n s p a c e , ’−− ’ , ’ l i n e w i d t h ’ , 2 )a x i s ( a x i s p l ) ;

%% I n p u t Geomet r i c i n f o r m a t i o n i n v a l u e s t r u c t u r ef i e l d s t r u c t n a m e = s t r ; %S e t t h e f i e l d name f o r s a v i n g as t h e f i l e name

65

%Save t h e g e o m e t r i c i n f o r m a t i o n i n t h e s t u c t u r ev a l s t r u c t . ( f i e l d s t r u c t n a m e ) . geom= s t r u c t ( ’ dmax ’ , dmax , ’ dmin ’ , dmin , . . .

’ d i s tmoved ’ , d i s tmoved , ’dmmean ’ , dmmean , ’ dmstd ’ , dmstd ) ;

%% G e n e r a t e Beamwidth i n f o r m a t i o n from b e a m p a t t e r n a t f r e q u e n c i e sf o r i i =1:10

[ bwmax , bwmin , bwsmax , bwsmin , rdbmax , rdbmin , Fm, v a lm a t ] . . .= p r o c e s s p a t t e r n ( s t r i n g 2 , i i ) ;

%% C r e a t e S t r u c t u r e I n f o r m a t i o n

f r e q f i e l d = s p r i n t f ( ’ f r e q%d ’ , i i )v a l s t r u c t . ( f i e l d s t r u c t n a m e ) . ( f r e q f i e l d )= s t r u c t ( ’ rdbmin ’ , rdbmin , ’ rdbmax ’ , . . .

rdbmax , ’bwsmax ’ , bwsmax , ’ bwsmin ’ , bwsmin , ’ i n t e r p v a l u e s ’ , va l ma t ) ;moviename= s t r c a t ( s t r , ’ freqnum ’ , num2s t r ( i i ) ) ;mvsavename= s t r c a t ( ’ F i g u r e s / ’ , moviename ) ;s ave ( mvsavename , ’Fm ’ ) ;%Save movie f i l e s e p e r a t e l y − Movie f i l e i s a 180 frame movie o f t h e% p r o g r e s s i o n o f t h e 2D beamwidths t h a t can ’ t be saved i n t h e s t r u c t u r e

end%Save t h e s t r u c t u r e f o r r e l o a d i n g n e x t p a s ssave ( ’ v s t r u c t . mat ’ , ’ v a l s t r u c t ’ )

end

Appendix A.2: Beampattern processing Code

f u n c t i o n [ bwmax , bwmin , bwsmax , bwsmin , rdbmax , rdbmin , Fm, va lma t ] = . . .p r o c e s s p a t t e r n ( m a t f i l e n a m e , freqnum )

% Thi s i s a f u n c t i o n f o r t a k i n g a b e a m p a t t e r n f i l e compr i s ed o f g a i n as a% f u n c t i o n o f az imu th and e l e v a t i o n , and t h e n f i n d i n g t h e −3dB and −6dB% beamwidths , bo th i n c l u d i n g and e x c l u d i n g s i d e l o b e s

%V e r i f y t h e f i l e we a r e l o o k i n g f o r e x i s t si f ( ˜ e x i s t ( ’ m a t f i l e n a m e ’ , ’ var ’ ) )

f p r i n t f ( ’ Must e n t e r mat f i l e name c o n t a i n i n g beam p a t t e r n d a t a \n ’ ) ;

66

r e t u r n ;end

%Load t h e b e a m p a t t e r n f i l e , i n c l u d i n g t h e v a r i a b l e s o f :%G: Gain , K: Frequency , naz : Number o f Azimuth a n g l e s , n e l : Number o f%e l e v a t i o n a n g l e sl o a d ( m a t f i l e n a m e , ’G’ , ’K’ , ’ naz ’ , ’ ne l ’ ) ;

%P u l l o u t t h e g a i n m a t r i x f o r t h e f r e q u e n c y we a r e working wi thG1 = G ( : , : , f reqnum ) ;x1 = [ −1 8 0 : 1 : 1 8 0 ] ; %C r e a t e a s e t o f X c o o r d i n a t e s i n d e g r e e sy1 = [ −9 0 : 1 : 9 0 ] ; %C r e a t e a s e t o f y c o o r d i n a t e s i n d e g r e e s

%For each a n g l e o f az imu th and e l e v a t i o n c r e a t e a c o r r e s p o n d i n g X and Y%v a l u ef o r i i = 1 : naz

Y ( : , i i ) = y1 ;end

f o r i i = 1 : n e lX( i i , : ) = x1 ;

end%% P l o t f o r Mesh%Uncomment t h i s s e c t i o n t o p l o t mesh t o look f o r i n c o n s i s t e n c i e s%{f i g u r e ;mesh (X, Y, G1 ) ;%}%% Reshape t h e b e a m p a t t e r n%Thi s s e c t i o n r e s h a p e s t h e b e a m p a t t e r n i n o r d e r t o c o n v e r t i t from%s p h e r i c a l c o o r d i n a t e t o c a r t e s i a n c o o r d i n a t e s f o r e a s i e r work l a t e rX reshaped = r e s h a p e (X, 1 , naz ∗ n e l ) ;Y re shaped = r e s h a p e (Y, 1 , naz ∗ n e l ) ;G re shaped = r e s h a p e ( G1 , 1 , naz ∗ n e l ) ;

Az = X reshaped ∗ p i / 1 8 0 ;De = Y reshaped ∗ p i / 1 8 0 ;

[CX, CY, CZ] = s p h 2 c a r t ( Az , De , G reshaped ) ;

67

%% P l o t f o r Reshaped Beam P a t t e r n%Uncomment t o view t h e r e s h a p e d beam p a t t e r n%{f i g u r e ;ho ld on ;p l o t 3 (CX, CY, CZ ) ;a x i s ([−1 1 −1 1 −1 1 ] , ’ equa l ’ ) ;%}%%%Find t h e Beam magni tude : Th i s s h o u l d be 1 , b u t may n o t be i f t h e r e were%prob lems wi th t h e s i m u l a t i o nbeam mag = beam max (CX, CY, CZ ) ;%Find t h e l o c a t i o n o f t h e MRA[ beam max val , beam max poin t ] = max ( beam mag ) ;

%Uncomment t o s e e i n i t i a l l o c a t i o n i n x , y , z o f MRACX( beam max poin t ) ;CY( beam max poin t ) ;CZ( beam max poin t ) ;

% −− Do f i r s t r o t a t i o n a round Z a x i s t o g e t MRA on X−Y p l a n e −−

%t h e t a = a t a n (CY( beam max poin t ) / CX( beam max poin t ) ) ;%t h e t a = −a t a n 2 (CY( beam max poin t ) ,CX( beam max poin t ) ) ;t h e t a = −a t a n 2 (CZ( beam max poin t ) ,CX( beam max poin t ) ) ;

%RZ = c a l c u l a t e R Z ( t h e t a ) ;RY = c a l c u l a t e R Y ( t h e t a ) ;

[ dum nrows ] = s i z e (CX ) ;

r o t m a t = z e r o s ( nrows , 3 ) ; %C r e a t e a p l a c e h o l d e r f o r t h e r o t a t e d m a t r i xr o t m a t ( : , 1 ) = CX;r o t m a t ( : , 2 ) = CY;r o t m a t ( : , 3 ) = CZ ;

%r o t a t e d = r o t m a t ∗ RZ ;r o t a t e d = r o t m a t ∗ RY;

68

% −−now f i n d max a g a i n and r o t a t e i t a ro u nc Y t o t h e Z a x i s −−

beam mag = beam max ( r o t a t e d ( : , 1 ) , r o t a t e d ( : , 2 ) , r o t a t e d ( : , 3 ) ) ; %Find m a g n i t u d e s a g a i n%Find l o c a t i o n and v a l u e o f m a g n i t u d e s[ beam max val beam max poin t ] = max ( beam mag ) ;

r o t a t e d ( beam max poin t , 1 ) , r o t a t e d ( beam max point , 2 ) , . . .r o t a t e d ( beam max point , 3 ) %d i s p l a y e r l o c a t i o n o f max magni tude

%p h i = a t a n ( r o t a t e d ( beam max poin t , 3 ) / r o t a t e d ( beam max poin t , 1 ) ) ;%p h i = −a t a n 2 ( r o t a t e d ( beam max point , 3 ) , r o t a t e d ( beam max poin t , 1 ) ) ;%g e t r o t a t i o np h i = a t a n 2 ( r o t a t e d ( beam max poin t , 2 ) , r o t a t e d ( beam max point , 1 ) ) ;

%RY = c a l c u l a t e R Y ( p h i ) ;

RZ = c a l c u l a t e R Z ( p h i ) ; %c a l c u l a t e r o t a t i o n%r o t a t e d f i n a l = r o t a t e d ∗ RY;r o t a t e d f i n a l = r o t a t e d ∗ RZ ; %per fo rm r o t a t i o n

%Do one f i n a l check of magn i tude and r o t a t i o n t o make s u r e we have t h e beam%p o i n t i n g where we want i t t o p o i n tbeam mag = beam max ( r o t a t e d f i n a l ( : , 1 ) , r o t a t e d f i n a l ( : , 2 ) , . . .

r o t a t e d f i n a l ( : , 3 ) ) ;

[ beam max val beam max poin t ] = max ( beam mag ) ;

r o t a t e d f i n a l ( beam max poin t , 1 ) , r o t a t e d f i n a l ( beam max point , 2 ) , . . .r o t a t e d f i n a l ( beam max point , 3 )

%Save t h e r o t a t e d m a t r i x i n c a s e o f l a t e r i s s u e s o r o t h e r needssave ( ’ r o t f i n a l . mat ’ , ’ r o t a t e d f i n a l ’ )

%% P l o t f o r F i n a l R o t a t e d Beam P a t t e r n%Uncomment t h i s s e c t i o n t o p l o t t h e f i n a l r o t a t e d beam p a t t e r n%{f i g u r e ;ho ld on ;p l o t 3 ( r o t a t e d f i n a l ( : , 1 ) , r o t a t e d f i n a l ( : , 2 ) , r o t a t e d f i n a l ( : , 3 ) , ’ .’ ) ;

69

a x i s ([−1 1 −1 1 −1 1 ] , ’ equa l ’ ) ;%}%% Find Beamwidth%Look a t beam e v e r y X d e g r e e s , c r e a t e a s l i c e o f t h e b e a m p a t t e r n , and t h e n%examine t h e s l i c e o f t h e b e a m p a t t e r n t o f i n d t h e beamwidth

%s e t a n g l e t o r o t a t e X d e g r e e sa n g l e d = 0 . 5 ;

a n g l e = deg2rad ( a n g l e d ) ;

r o t m a t = c a l c u l a t e R X ( a n g l e ) ;

c u r r e n t p a t t e r n = r o t a t e d f i n a l ; %S e t f i r s t p a t t e r n t o view

d e l t a = 0 . 0 2 ;l d a =180/ a n g l e d ;va lm a t = z e r o s ( 3 6 1 , l d a ) ;pg= f i g u r e ;

f o r i i = 1 : 1 8 0 / a n g l e d

% grab a s l i c e c l o s e t o t h e XY p l a n ec l e a r s l i c e ;[ s l i c e kk ] = g e t X Y s l i c e ( c u r r e n t p a t t e r n , d e l t a ) ;i f i i ==1

save ( ’ s l i c e . mat ’ , ’ s l i c e ’ )end%c o n v e r t t h e s l i c e t o p o l a r c o o r d i n a t e s

[ t h e t a , mag ] = p o l a r c o n v e r t ( s l i c e ( : , 1 ) , s l i c e ( : , 2 ) , s l i c e ( : , 3 ) ) ;

mag db = 20∗ l og10 ( mag ) ;

% f i g u r e ;% p o l a r p l o t ( t h e t a , mag db , ’ . ’ ) ;% r l i m ([−30 0 ] ) ;

70

%now s o r t t h e s l i c e i n p o l a r c o o r d i n a t e s

[ t h e t a s o r t e d , j d e x ] = s o r t ( t h e t a ) ;m a g d b s o r t e d = mag db ( j d e x ( : ) ) ;

[m, dex ] = max ( m a g d b s o r t e d ) ;

f o r l l = dex : kki f m a g d b s o r t e d ( l l ) <= −3.0

s i z e 1 = l l ;s ize1m1 = l l −1;b r e a k ;

endend

f o r l l = dex :−1:0i f m a g d b s o r t e d ( l l ) <= −3.0

s i z e 2 = l l ;s ize2m1 = l l +1 ;b r e a k ;

endend

%l i n e a r l y i n t e r p o l a t e t h e l o c a t i o n o f t h e two −3dB p o i n t s u s i n g%c i r c u l a r c o o r d i n a t e s − d e p r e c i a t e d

r i g h t m u l t = (−3 − m a g d b s o r t e d ( s ize1m1 ) ) / . . .( m a g d b s o r t e d ( s i z e 1 )−m a g d b s o r t e d ( s ize1m1 ) ) ;

r i g h t p o i n t = ( t h e t a s o r t e d ( s i z e 1 ) − t h e t a s o r t e d ( s ize1m1 ) ) . . .∗ r i g h t m u l t + t h e t a s o r t e d ( s ize1m1 ) ;

l e f t m u l t = (−3 − m a g d b s o r t e d ( s ize2m1 ) ) / . . .( m a g d b s o r t e d ( s i z e 2 )−m a g d b s o r t e d ( s ize2m1 ) ) ;

l e f t p o i n t = ( t h e t a s o r t e d ( s i z e 2 ) − t h e t a s o r t e d ( s ize2m1 ) ) . . .∗ l e f t m u l t + t h e t a s o r t e d ( s ize2m1 ) ;

beamwidth = abs ( r i g h t p o i n t − l e f t p o i n t ) / p i ∗180 ;

71

%% Do S c a t t e r e d I n t e r p o l a t e ( comment o u t when n o t p e r f o r m i n g s c a t t e r e d%i n t e r p o l a t i o n f o r e n t i r e s e t )

%{sy= s l i c e ( : , 2 ) ;

[ sys , I s ]= s o r t ( abs ( sy ) ) ;s x s = s l i c e ( : , 1 ) ;s x s = s x s ( I s ) ;s z s = s l i c e ( : , 3 ) ;s z s = s z s ( I s ) ;

s y s = s y s ( 1 : 1 0 0 0 ) ;s x s = s x s ( 1 : 1 0 0 0 ) ;s z s = s z s ( 1 : 1 0 0 0 ) ;

[ t h e t a i n t e r p , p h i i n t e r p , r h o i n t e r p ] = c a r t 2 s p h ( sxs , sys , s z s ) ;%}

%% do l i n e a r I n t e r p o l a t e%(Comment o u t when do ing s c a t t e r e d I n t e r p o l a t i o n )

[ t h e t a i n t e r p , p h i i n t e r p , r h o i n t e r p ] = c a r t 2 s p h ( s l i c e ( : , 1 ) , . . .s l i c e ( : , 2 ) , s l i c e ( : , 3 ) ) ;

%% Conver t i n t e r p o l a t e d p o i n t s[ t h e t a 0 , phi0 , r h o i n t e r p ]= i n t e r p s p h ( t h e t a i n t e r p , p h i i n t e r p , r h o i n t e r p ) ;[ xpl , ypl , z p l ]= s p h 2 c a r t ( t h e t a 0 , phi0 , r h o i n t e r p ) ;rdb =20∗ l og10 ( r h o i n t e r p ) ; %Conve r t g a i n s t o dB power

va lm a t ( : , i i )= r h o i n t e r p ; %c r e a t e a 2D v e c t o r o f t h e power v a l u e s

%pg= f i g u r e ;%C l e a r f i g u r e , p l o t c u r r e n t 2D b e a m p a t t e r n , s ave f rame f o r moviec l fho ld onp l o t ( rdb ) ;a x i s ( [ 0 361 −40 0 ] )Fm( i i , 1 ) = g e t f r a m e ;%c l o s e ( pg )

72

%pg2= f i g u r e ;%C l e a r f i g u r e , p l o t c u r r e n t 3D s l i c e , s ave f o r moviec l fp l o t 3 ( s l i c e ( : , 1 ) , s l i c e ( : , 2 ) , s l i c e ( : , 3 ) , ’ . ’ ) ;ho ld onp l o t 3 ( xpl , ypl , zp l , ’ . r ’ ) ;a x i s e q u a lview ( 0 , 0 )Fm( i i , 2 ) = g e t f r a m e ;%c l o s e ( pg2 )

%Look f o r t h e beam : S p l i t beam p a t t e r n i n h a l f t o look a t t h e ” low ” v a l u e s%( i . e . d e g r e e v a l u e s l e s s t h a n 0) and h igh v a l u e s ( i . e . d e g r e e v a l u e s%g r e a t e r t h a n 0) wi th 0 ( p o i n t number 181 i n t h e v e c t o r ) b e i n g t h e MRA.%The d i s t a n c e from t h e MRA on bo th s i d e s o f t h e beamwidth a r e c a l c u l a t e d t o%where t h e y c r o s s t h e −3dB t h r e s h o l d and t h e n t h e beamdwidth i s c a l u c a l t e d%by ad d i ng bo th s i d e s t o g e t h e r .rdblow = rdb ( 1 : 1 8 1 ) ;rdb3low =rdblow>=−3;r d b 3 l o w d i f f = abs ( d i f f ( rdb3low ) ) ;r d b 3 l o w d i f f l = r d b 3 l o w d i f f ==1;rdb3 lowd i f fnum = l e n g t h ( rdblow ( r d b 3 l o w d i f f l ) ) ;i f rdb3 lowd i f fnum == 1 %no S ide l o b e srdb lows = rdblow ( rdb3low ) ;sz low = s i z e ( rdb lows ) ;lowdegadded =((−3− rdb (181− sz low ( 1 ) + 1 ) ) / ( rdb (181− sz low ( 1 ) ) − . . .

rdb (181− sz low ( 1 ) + 1 ) ) ) ;

e l s e %Side l o b e s p r e s e n t , f i n d j u s t ma in lobesz low =0;i k = 0 ;w h i l e i k == 0

sz low = sz low +1;i k = r d b 3 l o w d i f f l (181− sz low ) ;

endlowdegadded =((−3− rdb (181− sz low ( 1 ) + 1 ) ) / ( rdb (181− sz low ( 1 ) ) − . . .

73

rdb (181− sz low ( 1 ) + 1 ) ) ) ;

end

r d b h i g h = rdb ( 1 8 1 : 3 6 1 ) ;r d b 3 h i g h = rdbh igh >=−3;r d b 3 h i g h d i f f = abs ( d i f f ( r d b 3 h i g h ) ) ;r d b 3 h i g h d i f f l = r d b 3 h i g h d i f f ==1;r d b 3 h i g h d i f f n u m = l e n g t h ( r d b h i g h ( r d b 3 h i g h d i f f l ) ) ;i f r d b 3 h i g h d i f f n u m == 1 %no S ide l o b e sr d b h i g h s = r d b h i g h ( r d b 3 h i g h ) ;s z h i g h = s i z e ( r d b h i g h s ) ;h ighdegadded =((−3− r d b h i g h ( s z h i g h ( 1 ) ) ) / ( r d b h i g h ( s z h i g h ( 1 ) + 1 ) − . . .

r d b h i g h ( s z h i g h ( 1 ) ) ) ) ;

e l s e %Side l o b e s p r e s e n t , f i n d j u s t ma in lobes z h i g h =0;i k = 0 ;w h i l e i k == 0

s z h i g h = s z h i g h +1;i k = r d b 3 h i g h d i f f l ( s z h i g h ) ;

endh ighdegadded =((−3− r d b h i g h ( s z h i g h ( 1 ) ) ) / ( r d b h i g h ( s z h i g h ( 1 ) + 1 ) − . . .

r d b h i g h ( s z h i g h ( 1 ) ) ) ) ;

end

b w s c a t i n t e r p = sz low ( 1 ) + s z h i g h ( 1 ) + lowdegadded+ highdegadded −2;

i f i i == 1bwsmax ( 1 , 1 ) = b w s c a t i n t e r p ;bwsmin ( 1 , 1 ) = b w s c a t i n t e r p ;rdbmax= rdb ;bwsmax ( 1 , 2 ) = i i ;bwsmin ( 1 , 2 ) = i i ;rdbmin= rdb ;

e l s e

74

i f b w s c a t i n t e r p>bwsmax ( 1 , 1 )bwsmax ( 1 , 1 ) = b w s c a t i n t e r p ;bwsmax ( 1 , 2 ) = i i ;rdbmax= rdb ;

endi f b w s c a t i n t e r p<bwsmin ( 1 , 1 )

bwsmin ( 1 , 1 ) = b w s c a t i n t e r p ;bwsmin ( 1 , 2 ) = i i ;rdbmin= rdb ;

endend

%%

i f i i ==1bwmax ( 1 , 1 ) = beamwidth ;bwmin ( 1 , 1 ) = beamwidth ;bwmax ( 1 , 2 ) = i i ;bwmin ( 1 , 2 ) = i i ;

e l s ei f beamwidth>bwmax ( 1 , 1 )

bwmax ( 1 , 1 ) = beamwidth ;bwmax ( 1 , 2 ) = i i ∗180 / a n g l e d ;

endi f beamwidth<bwmin ( 1 , 1 )

bwmin ( 1 , 1 ) = beamwidth ;bwmin ( 1 , 2 ) = i i ∗180 / a n g l e d ;

endend

% CompMatrix ( i i , 1 ) = beamwidth ;% CompMatrix ( i i , 2 ) = b w s c a t i n t e r p ;% CompMatrix ( i i , 3 ) = beamwidth / b w s c a t i n t e r p ;

temp = c u r r e n t p a t t e r n ;c u r r e n t p a t t e r n = temp ∗ r o t m a t ;

% s p r i n t f ( ’ Run %d of %d f i n i s h e d ’ , i i , 180 / a n g l e d )

75

endc l o s e ( pg )

%% Go back and f i n d t h e min and max s l i c e from p o l a r coords , i n t e r p o l a t e ,%and o u t p u t beam p a t t e r n s − D e p r e c i a t e d%Thi s s e c t i o n i s d e p r e c i a t e d and n o t i n use , uncomment i f t h e r e i s a%d e s i r e t o use t h e p o l a r c o o r d i n a t e s%i n s t e a d t o c a l c u l a t e beamwidth%{

angledmax=bwmax ( 1 , 2 ) ; %Get Max BW Angleang ledmin =bwmin ( 1 , 2 ) ; %Get Min BW Angleanglemax = deg2rad ( angledmax ) ;ang lemin = deg2rad ( ang ledmin ) ;r o t m a t m a x = c a l c u l a t e R X ( anglemax ) ; %Get t h e r o t a t i o n m a t r i x f o r maxr o t m a t m i n = c a l c u l a t e R X ( ang lemin ) ; %Get t h e r o t a t i o n m a t r i x f o r min

m a x p a t t e r n = r o t a t e d f i n a l ∗ r o t m a t m a x ;m i n p a t t e r n = r o t a t e d f i n a l ∗ r o t m a t m i n ;

% grab a s l i c e c l o s e t o t h e XY p l a n ec l e a r s l i c e ;[ s l i c e m a x kk ] = g e t X Y s l i c e ( m a x p a t t e r n , d e l t a ) ;[ s l i c e m i n kk ] = g e t X Y s l i c e ( m i n p a t t e r n , d e l t a ) ;

%% Look a t s l i c e s and i n t e r p o l a t ef o r i i = 1 : 2

i f i i == 1s l i c e = s l i c e m a x ;

e l s e i f i i == 2s l i c e = s l i c e m i n ;

endsy= s l i c e ( : , 2 ) ;[ sys , I s ]= s o r t ( abs ( sy ) ) ;s x s = s l i c e ( : , 1 ) ;s x s = s x s ( I s ) ;s z s = s l i c e ( : , 3 ) ;s z s = s z s ( I s ) ;

76

s y s = s y s ( 1 : 1 0 0 0 ) ;s x s = s x s ( 1 : 1 0 0 0 ) ;s z s = s z s ( 1 : 1 0 0 0 ) ;

[ t h e t a i n t e r p , p h i i n t e r p , r h o i n t e r p ] = c a r t 2 s p h ( sxs , sys , s z s ) ;

[ t h e t a 0 , phi0 , r h o i n t e r p ]= i n t e r p s p h ( t h e t a i n t e r p , p h i i n t e r p , r h o i n t e r p ) ;rdb =20∗ l og10 ( r h o i n t e r p ) ;

%% Thi s p a r t commented o u t f o r g e n e r a t i n g movie f rames , uncomment s e c t i o ni f you want t o c r e a t e a move from t h e s l i c e s t o view t h e p r o g r e s i o nt h r o u g h t h e beam a n g l e s%{

pg= f i g u r e ;ho ld onp l o t ( rdb ) ;a x i s ( [ 0 361 −40 0 ] )Fm( i i )= g e t f r a m e ;c l o s e ( pg )

%}%}

%% Movie : C r e a t e and show Movie%Uncomment t h i s s e c t i o n to , a f t e r r u n n i n g t h e program , run t h e movie%c r e a t e d from t h e s l i c e s o f t h e b e a m p a t t e r n% movie%movie (Fm)

%c l a ;

%movie (M)

77

f u n c t i o n [ mag ] = beam max (CX, CY, CZ)%Find t h e maximum of t h e beam from i t ’ s c a r t e i s i a n c o o r d i n a t e s[ r c ] = s i z e (CX ) ;

f o r j j = 1 : r

f o r i i = 1 : c

mag ( j j , i i ) = s q r t (CX( j j , i i ) . ˆ 2 +CY( j j , i i ) . ˆ 2 + CZ( j j , i i ) . ˆ 2 ) ;

end

end

f u n c t i o n [ t h e t a , mag ] = p o l a r c o n v e r t (X, Y, Z )%Conver t t h e beam t o po ly c o o r d i n a t e s from c a r t e s i a n c o o r d i n a t e s[ r , c ] = s i z e (X ) ;

f o r j j = 1 : r

mag ( j j ) = s q r t (X( j j ) . ˆ 2 +Y( j j ) . ˆ 2 + Z ( j j ) . ˆ 2 ) ;t h e t a ( j j ) = a t a n 2 ( Z ( j j ) ,X( j j ) ) ;

end

f u n c t i o n [R] = c a l c u l a t e R X ( t h e t a )%C a l c u l a t e a r o t a t i o n m a t r i x a round t h e X−a x i s

R = [1 0 00 cos ( t h e t a ) −s i n ( t h e t a )0 s i n ( t h e t a ) cos ( t h e t a ) ] ;

f u n c t i o n [R] = c a l c u l a t e R Y ( t h e t a )%C a l c u l a t e a r o t a t i o n m a t r i x a round t h e Y−a x i s

R = [ cos ( t h e t a ) 0 s i n ( t h e t a )0 1 0−s i n ( t h e t a ) 0 cos ( t h e t a ) ] ;

f u n c t i o n [R] = c a l c u l a t e R Z ( t h e t a )

78

%C a l c u l a t e a r o t a t i o n m a t r i x a round t h e Z−a x i sR = [ cos ( t h e t a ) −s i n ( t h e t a ) 0

s i n ( t h e t a ) cos ( t h e t a ) 00 0 1 ] ;

f u n c t i o n [ s l i c e c o u n t ] = g e t X Y s l i c e ( beam , d e l t a )%C r e a t e a b e a m p a t t e r n s l i c e a t a g i v e n l o c a t i o n from a l l p o i n t s%of t h e b e a m p a t t e r n w i t h i n a r a n g e of d e l t a o f t h e s l i c e

c o u n t = 0 ;[ nrows dum ] = s i z e ( beam ) ;f o r j j = 1 : nrowsi f abs ( beam ( j j , 2 ) ) < d e l t a

c o u n t = c o u n t + 1 ;s l i c e ( count , : ) = beam ( j j , : ) ;

endend

Appendix A.3: Beampattern Post Processing Code

%This progarm t a k e s t h e v a l u e s p r e v i o u s l y c a l c u l a t e d − Geometry and%b e a m p a t t e r n s l i c e s − and t h e n f i n d s a d d i t o n a l i n f o r m a t i o n i n t e r m s of −3dB%beamwidth i n c l u d i n g s i d e l o b e s and −6dB beamwidth bo th i n c l u d i n g and%e x c l u d i n g s i d e l o b e s

%% Load i n v a r i a b l e sl o a d v s t r u c t . mat %Load i n t h e s t r u c t u r e o f i n f o r m a t i o nl o a d s t r d o n e . mat %Load i n t h e l i s t o f f i l e s which need t h i s work done

%% P r o c e s s t h e code

l s t r d = l e n g t h ( s t r d ) ; %Find t h e number o f i t e m s t h a t need t o be done

f o r i i =1 : l s t r dn a m e s t r = s t r d { i i } ; %Grab t h e i t em b e i n g done t h i s i t e r a t i o nf o r j j =1:10 %Per fo rm t h e f o l l o w i n g ove r a l l 10 r e c o r d e d f r e q u e n c i e s

sn= num2s t r ( j j ) ;%C r e a t e a f i e l d name f o r t h e c u r r e n t f r e q u e n c yf r e q s t r = s t r c a t ( ’ f r e q ’ , sn ) ;

79

%Get t h e i n t e r p o l a t e d v a l u e s f o r t h i s d a t a s e ti n t v = v a l s t r u c t . ( n a m e s t r ) . ( f r e q s t r ) . i n t e r p v a l u e s ;bw3maxi =0; %P r e a l l o c a t e Max BW between r u n sbw3mini =1000; %P r e a l l o c a t e Min BW Between Runsbw6maxi =0; %P r e a l l o c a t e Max BW between r u n sbw6mini =1000; %P r e a l l o c a t e Min BW Between Runsbw6maxo =0; %P r e a l l o c a t e Max BW between r u n sbw6mino =1000; %P r e a l l o c a t e Min BW Between Runsmlwidthmin =1000; %P r e a l l o c a t e ma in lobe wid th Between Runsmlwidthmax =0; %P r e a l l o c a t e Main Lobe Width between r u n sn u l l 1 v a l h i g h m l m a x =0;% P r e a l l o c a t e Nu l l Value between r u n snu l l1va l lowmlmax =0; %P r e a l l o c a t e Nu l l Value between r u n sn u l l 1 v a l h i g h m l m i n =0;% P r e a l l o c a t e Nu l l Value between r u n sn u l l 1 v a l l o w m l m i n =0;% P r e a l l o c a t e Nu l l Value between r u n s

s l1maxh igh =0;s l1maxlow =0;

f o r kk =1:180%Do t h i s ove r 180 d e g r e e s ( Assuming 1 d e g r e e s l i c e s ,%change as needed )i n t v t e m p = i n t v ( : , kk ) ; %Get d a t a s e t f o r t h i s runrdb =20∗ l og10 ( i n t v t e m p ) ;% F i r s t f i n d t h e −3db and −6dB downpo in t s i n c l u d i n g s i d e l o b e s%% Find lower p o i n t v a l u e srdblow = rdb ( 1 : 1 8 1 ) ; %Get lower h a l f o f d a t a s e ti n t v t e m p l o w = i n t v t e m p ( 1 : 1 8 1 ) ; % Get lower h a l f o f d a t a s e trdb3low =rdblow>=−3; %T h r e s h o l d t o −3dBrdb6low =rdblow>=−6; %T h r e s h o l d t o −6dBr d b 3 l o w d i f f = d i f f ( rdb3low ) ; %C r e a t e L o g i c a l t o t h r e s h o l dr d b 6 l o w d i f f = d i f f ( rdb6low ) ; %C r e a t e l o g i c a l t o t h r e s h o l din3 low =0; %R e a l l o c a t e f o r each runin6 low =0;% R e a l l o c a t e f o r each runou t6 low =0;% R e a l l o c a t e f o r each runrun =0;% R e a l l o c a t e f o r each runv a l =0;% R e a l l o c a t e f o r each run%Find f i r s t s p o t where −3dBBW goes ove r t h r e s h o l d from%p e r i p h e r y ( c o u n t i n g s i d e l o b e s )

80

w h i l e v a l ˜=1run = run +1;i f run == 180

v a l =1;run =0;

e l s ev a l = r d b 3 l o w d i f f ( run ) ;end

endin3 low = run ; %Save Lower Valuerun =0; %R e a l l o c a t e f o r Next Runv a l =0 ; %R e a l l o c a t e f o r Next Run

%Find f i r s t s p o t where −6dBBW goes ove r t h r e s h o l d from%p e r i p h e r y ( c o u n t i n g s i d e l o b e s )w h i l e v a l ˜=1

run = run +1;i f run == 180

v a l =1;run =0;

e l s ev a l = r d b 6 l o w d i f f ( run ) ;end

endin6 low = run ; %Save Lower Valuerun =181; %R e a l l o c a t e f o r Next Runv a l =0 ; %R e a l l o c a t e f o r Next Run

%Find f i r s t s p o t where −6dB BW goes ove r t h r e s h o l d%from MRA ( No BW)w h i l e v a l ˜=1

run =run −1;i f run ==1

v a l =1;run =0;

e l s ev a l = r d b 6 l o w d i f f ( run ) ;end

endout6 low = run ; %Save Lower Value

81

%Look f o r max s i d e l o b e v a l u e s[ MaximaLow , MaximaLocLow ]= f i n d p e a k s ( i n t v t e m p l o w ) ;

%There i s no bot tom peak ( Values c o n t s t a n t l y d e c r e a s i n g )%s e t t o edgei f i s e m p t y ( MaximaLow )

s l1maxlowva l t emp = i n t v t e m p l o w ( 1 ) ;s l1maxlowloc temp =1;

e l s e%S e t max v a l u e o f s i d e l o b e

s l1maxlowva l t emp =MaximaLow ( l e n g t h ( MaximaLow ) ) ;%S e t p o s i t i o n o f s i d e l o b es l1maxlowloc temp =MaximaLocLow ( l e n g t h ( MaximaLocLow ) ) ;end%I n v e r t t o f i n d min s i d e l o b e si n v i n t v t e m p l o w =1.01∗max ( i n t v t e m p l o w )− i n t v t e m p l o w ;%Find min s i d e l o b e s

[ MinimaLow , MinimaLocLow ]= f i n d p e a k s ( i n v i n t v t e m p l o w ) ;i f i s e m p t y ( MinimaLow ) %There were no n u l l s , s e t t o edge

n u l l 1 v a l l o w t e m p = i n t v t e m p l o w ( 1 ) ;mlwidthlowtemp =1;

e l s e%S e t t h e f i r s t n u l l v a l u e

n u l l 1 v a l l o w t e m p =MinimaLow ( l e n g t h ( MinimaLow ) ) ;mlwidthlowtemp=MinimaLocLow ( l e n g t h ( MinimaLocLow ) ) ;end

%% Find Higher P o i n t Va lues%Thi s s e c t i o n f u n c t i o n s i d e n t i c a l l y t o t h e above s e c t i o n ,%e x c e p t a l l o f t h e v a l u e s and c a l c u l a t i o n s a r e done f o r t h e%upper p o i n t v a l u e s .

i n t v t e m p h i g h = i n t v t e m p ( 1 8 1 : 3 6 1 ) ; %Take High v a l u e sr d b h i g h = rdb ( 1 8 1 : 3 6 1 ) ; %Get h igh dB v a l u e sr d b 3 h i g h = rdbh igh >=−3; %T h r e s h o l d v a l u e sr d b 6 h i g h = rdbh igh >=−6;%T h r e s h o l d v a l u e sr d b 3 h i g h d i f f = d i f f ( r d b 3 h i g h ) ; %C r e a t e d i f f e r e n c e l o g i c a l m a t r i xr d b 6 h i g h d i f f = d i f f ( r d b 6 h i g h ) ; %C r e a t e d i f f e r e n c e l o g i c a l m a t r i xi n 3 h i g h =0; %P r e a l l o c a t e Value f o r each runi n 6 h i g h =0; %P r e a l l o c a t e Value f o r each run

82

o u t 6 h i g h =0; %P r e a l l o c a t e Value f o r each runrun =181; %P r e a l l o c a t e Value f o r each runv a l =0 ; %P r e a l l o c a t e Value f o r each run

%Find t h e f i r s t p o i n t coming from p e r i h p e r y where t h e v a l u e%c r o s s e d −3dB ( s i d e l o b e s i n c l u d e d )w h i l e v a l ˜=−1

run =run −1;i f run ==1

v a l =−1;run =181;

e l s ev a l = r d b 3 h i g h d i f f ( run ) ;end

endi n 3 h i g h = run ; %Save v a l u erun =181;v a l =0 ;

%Find t h e f i r s t p o i n t coming from p e r i h p e r y where t h e v a l u e%c r o s s e d −6dB ( s i d e l o b e s i n c l u d e d )w h i l e v a l ˜=−1

run =run −1;i f run ==1

v a l =−1;run =181;

e l s ev a l = r d b 6 h i g h d i f f ( run ) ;end

endi n 6 h i g h = run ; %Save Valuerun =0;v a l =0 ;

%Find t h e f i r s t p o i n t coming from MRA where t h e v a l u e%c r o s s e d −6dB ( s i d e l o b e s d i s c l u d e d )w h i l e v a l ˜=−1

run = run +1;i f run ==180

v a l =−1;run =181;

83

e l s ev a l = r d b 6 h i g h d i f f ( run ) ;end

endo u t 6 h i g h = run ; %Save Value

%Find N u l l s and s i d e l o b e peaks i n t h e upper s e c t i o n%Find max peaks o f s i d e l o b e s[ Maximahigh , MaximaLochigh ]= f i n d p e a k s ( i n t v t e m p h i g h ) ;i f i s e m p t y ( Maximahigh )

%I f none , t h e n we have no peaks , s e t t o edges l 1 m a x h i g h v a l t e m p = i n t v t e m p h i g h ( 1 8 1 ) ;s l 1 m a x h i g h l o c t e m p =181;

e l s e%S e t s i d e l o b e peak

s l 1 m a x h i g h v a l t e m p =Maximahigh ( 1 ) ;%s e t s i d e l o b e peak l o c a t i o n

s l 1 m a x h i g h l o c t e m p =MaximaLochigh ( 1 ) ;end%I n v e r t v a l u e s t o f i n d n u l l si n v i n t v t e m p h i g h =1.01∗max ( i n t v t e m p h i g h )− i n t v t e m p h i g h ;

%Find N u l l s[ Minimahigh , MinimaLochigh ]= f i n d p e a k s ( i n v i n t v t e m p h i g h ) ;i f i s e m p t y ( Minimahigh ) %I f no n u l l s , s e t n u l l t o t h e edge

n u l l 1 v a l h i g h t e m p = i n t v t e m p h i g h ( 1 8 1 ) ;mlwid thh igh temp =181;

e l s e%S e t Nu l l v a l u e t o f i r s t n u l l found

n u l l 1 v a l h i g h t e m p = i n t v t e m p h i g h ( MinimaLochigh ( 1 ) ) ;mlwid thh igh temp =MinimaLochigh ( 1 ) ; %S e t Nu l l l o c a t i o nend

%% Do i n t e r p o l a t i o n and add v a l u e s t o f i n d beamwidths%Take t h e p r e v i o u s l y found change l o c a t i o n s , i n t e r p o l a t e t o%f i n d beamwidth f r a c t i o n a l d e g r e e s , and t h e n add h i g h e r and%lower beamwidths t o f i n d t o t a l beamwidth% Find f o r −3db coming i ni f i n 3 h i g h ==181

84

h ighdegadded =0;e l s eh ighdegadded =((−3− r d b h i g h ( i n 3 h i g h ) ) / ( r d b h i g h ( i n 3 h i g h + 1 ) . . .

−r d b h i g h ( i n 3 h i g h ) ) ) ; %I n t e r p o l a t e t h e d e g r e e addedendi f in3 low == 0

lowdegadded =0;e l s elowdegadded =((−3− rdblow ( in3 low + 1 ) ) / ( rdblow ( in3 low ) . . .

−rdblow ( in3 low + 1 ) ) ) ; % I n t e r p o l a t e t h e d e g r e e addedend%Get −3dB beamwidth i n c l u d i n g s i d e l o b e sbw3dbin=181− i n3 low + i n 3 h i g h + lowdegadded+ highdegadded −1;

% Find f o r −6db coming i ni f i n 6 h i g h == 181

h ighdegadded =0;e l s eh ighdegadded =((−6− r d b h i g h ( i n 6 h i g h ) ) / ( r d b h i g h ( i n 6 h i g h + 1 ) . . .

−r d b h i g h ( i n 6 h i g h ) ) ) ; %I n t e r p o l a t e t h e d e g r e e addedendi f in6 low == 0

lowdegadded =0;e l s elowdegadded =((−6− rdblow ( in6 low + 1 ) ) / ( rdblow ( in6 low ) . . .

−rdblow ( in6 low + 1 ) ) ) ; % I n t e r p o l a t e t h e d e g r e e addedend%Get −6dB beamwidth i n c l u d i n g s i d e l o b e s

bw6dbin=181− i n6 low + i n 6 h i g h + lowdegadded+ highdegadded −1;

% Find f o r −6db go ing o u ti f o u t 6 h i g h == 181

h ighdegadded =0;e l s eh ighdegadded =((−6− r d b h i g h ( o u t 6 h i g h ) ) / ( r d b h i g h ( o u t 6 h i g h + 1 ) . . .

−r d b h i g h ( o u t 6 h i g h ) ) ) ; % I n t e r p o l a t e t h e d e g r e e addedendi f ou t6 low == 0

85

lowdegadded =0;e l s elowdegadded =((−6− rdblow ( out6 low + 1 ) ) / ( rdblow ( out6 low ) . . .

−rdblow ( out6 low + 1 ) ) ) ; % I n t e r p o l a t e t h e d e g r e e addedend%Get −6dB beamwidth d i s c l u d i n g s i d e l o b e sbw6dbout=181−out6 low + o u t 6 h i g h + lowdegadded+ highdegadded −1;

% C o n d i t i o n a l s t o s e e i f we have new min / max v a l u e si f bw3dbin > bw3maxi %Check t o s e e i f t h i s i s t h e new max

bw3maxi=bw3dbin ;endi f bw3dbin <bw3mini %Check t o s e e i f t h i s i s t h e new min

bw3mini=bw3dbin ;endi f bw6dbin > bw6maxi %Check t o s e e i f t h i s i s t h e new max

bw6maxi=bw6dbin ;endi f bw6dbin < bw6mini %Check t o s e e i f t h i s i s t h e new min

bw6mini=bw6dbin ;endi f bw6dbout > bw6maxo %Check t o s e e i f t h i s i s t h e new max

bw6maxo=bw6dbout ;endi f bw6dbout < bw6mino %Check t o s e e i f t h i s i s t h e new min

bw6mino=bw6dbout ;end

% compute main l o b e wid th and d e t e r m i n e i f max or min main l o b emlbwtemp= mlwidthhightemp−1+181−mlwidthlowtemp ;

i f mlbwtemp > mlwidthmaxmlwidthmax=mlbwtemp ;n u l l 1 v a l h i g h m l m a x = n u l l 1 v a l h i g h t e m p ;nu l l1va l lowmlmax = n u l l 1 v a l l o w t e m p ;

endi f mlbwtemp < mlwidthmin

mlwidthmin=mlbwtemp ;

86

n u l l 1 v a l h i g h m l m i n = n u l l 1 v a l h i g h t e m p ;n u l l 1 v a l l o w m l m i n = n u l l 1 v a l l o w t e m p ;

end

% Dete rmine whe the r o r n o t t h i s i s t h e l a r g e s t s i d e l o b e

i f s l 1 m a x h i g h v a l t e m p >s l1maxh ighs l1maxh igh = s l 1 m a x h i g h v a l t e m p ;

end

i f s l1maxlowva l t emp > s l1maxlowsl1maxlow= s l1maxlowva l t emp ;

end

% Move on t o t h e n e x t s l i c eend

% Find o u t i f t h e r e were s i d e l o b e s and save t h e 3db and 6db% min / max beamwidths%Get −3dB max beamwidth wi th no s i d e l o b e sbwsmax= v a l s t r u c t . ( n a m e s t r ) . ( f r e q s t r ) . bwsmax ;bw3maxo=bwsmax ( 1 ) ;%Get −3dB min beamwidth wi th no s i d e l o b e sbwsmin= v a l s t r u c t . ( n a m e s t r ) . ( f r e q s t r ) . bwsmin ;bw3mino=bwsmin ( 1 ) ;rdbmin= v a l s t r u c t . ( n a m e s t r ) . ( f r e q s t r ) . rdbmin ;rdbmax= v a l s t r u c t . ( n a m e s t r ) . ( f r e q s t r ) . rdbmax ;%Get i n t e r p v a l u e s

va lm a t = v a l s t r u c t . ( n a m e s t r ) . ( f r e q s t r ) . i n t e r p v a l u e s ;%See i f t h e y a r e t h e same or d i f f e r e n t i n c l u d i n g and%e x l c u d i n g s i d e l o b e si f bw3maxo==bw3maxi && bw3mino==bw3mini

s l 3 =0; %No 3dB s i d e l o b e se l s e

s l 3 =1; %3dB s i d e l o b e send%See i f t h e y a r e t h e same or d i f f e r e n t i n c l u d i n g and%e x l c u d i n g s i d e l o b e s

87

i f bw6maxo==bw6maxi && bw6mino==bw6minis l 6 =0; %no 6dB s i d e l o b e s

e l s es l 6 =1; %6dB s i d e l o b e s

end%Save a l l o f t h e c a l c u l a t e d i n f o r m a t i o n back i n t o t h e s t r u c t u r ev a l s t r u c t . ( n a m e s t r ) . ( f r e q s t r )= s t r u c t ( ’ rdbmin ’ , rdbmin , ’ rdbmax ’ , . . .

rdbmax , ’bwsmax ’ , bwsmax , ’ bwsmin ’ , bwsmin , . . .’ i n t e r p v a l u e s ’ , va lmat , ’ bw3maxi ’ , bw3maxi , ’ bw3mini ’ , . . .bw3mini , ’ bw6maxi ’ , bw6maxi , ’ bw6mini ’ , bw6mini , . . .’bw6maxo ’ , bw6maxo , ’ bw6mino ’ , bw6mino , ’ s l 3 ’ , s l 3 , ’ s l 6 ’ , s l 6 , . . .’ mlwidthmax ’ , mlwidthmax , ’ mlwidthmin ’ , mlwidthmin , . . .’ nu l l 1va lh ighmlmax ’ , nu l l 1va lh ighmlmax , ’ nu l l1va l lowmlmax ’ , . . .nu l l1va l lowmlmax , ’ n u l l 1 v a l h i g h m l m i n ’ , n u l l 1 v a l h i g h m l m i n , . . .’ nu l l1va l lowmlmin ’ , nu l l1va l lowmlmin , ’ s l1maxhigh ’ , . . .s l1maxhigh , ’ sl1maxlow ’ , s l1maxlow ) ;

% Move on t o t h e n e x t f r e q u e n c y

end

endsave ( ’ v s t r u c t . mat ’ , ’ v a l s t r u c t ’ ) %save t h e s t r u c t u r e

88

Appendix B: Raw Data Table

89

Table 5.1: Table Containing Geometry and Beamwidth Data for Samples sorted by Sci-entific Name. Species denoted as sp. represent an unknown species within a genera.Beamwidths given as the half-power beamwidths for that aperture at a given frequencyexcluding sidelobes. The 10 frequencies are equally spaced between the minimum andmaximum frequency.

Scientific Name Aperture Minimum Aperture Maximum Aperture Min Freq Max Freq Min BW 1 Max BW 1 Min BW 2 Max BW 2 Min BW 3 Max BW 3 Min BW 4 Max BW 4 Min BW 5 Max BW 5 Min BW 6 Max BW 6 Min BW 7 Max BW 7 Min BW 8 Max BW 8 Min BW 9 Max BW 9 Min BW 10 Max BW 10Type Diameter (mm) Diameter (mm) (kHz) (kHz) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees)

Artibeus jamaicensis Noseleaf 7.11 13.9 36.6 107. 46.9 57.6 43.1 107. 47.9 66.6 49.4 69.0 46.5 60.6 36.1 63.5 30.5 60.6 25.3 67.6 24.1 60.8 38.3 52.0Artibeus jamaicensis Noseleaf 12.2 14.1 36.6 107. 69.4 150. 54.7 104. 49.9 134. 51.3 119. 31.2 47.9 33.6 63.5 34.5 66.8 32.9 82.8 24.2 82.2 28.3 37.8

Asellia tridens Noseleaf 6.49 9.45 101. 120 18.6 21.4 36.5 55.8 17.8 24.3 35.2 59.2 37.6 58.8 30.3 53.1 27.8 51.0 27.5 33.6 27.0 31.9 26.4 32.8Asellia tridens Noseleaf 6.98 12.2 101. 122. 30.4 33.2 29.9 33.3 28.9 32.3 28.8 32.7 28.2 31.7 27.6 31.0 27.8 30.0 27.0 31.4 26.9 29.3 26.8 28.8

Aselliscus stoliczkanus Noseleaf 4.86 6.54 91.5 127. 36.4 44.5 36.3 43.7 33.2 44.7 32.8 44.7 33.4 51.5 28.8 56.0 23.8 54.6 24.3 44.5 23.3 39.4 20.3 33.5Aselliscus stoliczkanus Pinna 6.04 8.81 91.5 127. 35.3 42.6 40.5 46.3 35.2 41.8 35.0 39.4 31.7 63.0 27.9 65.8 19.1 66.1 18.2 50.5 19.8 41.1 19.0 51.0Barbastella leucomelas Pinna 12.5 16.0 23.3 44.7 63.1 81.9 61.7 75.9 61.9 71.9 59.2 67.1 62.3 66.3 56.2 62.1 52.9 60.1 40.5 56.4 33.5 52.2 34.0 53.3Barbastella leucomelas Pinna 11.4 18.6 23.3 44.7 46.9 93.8 44.9 87.4 47.6 85.2 44.0 123. 40.5 112. 39.6 100. 35.9 81.0 23.6 83.1 31.0 41.4 34.5 60.4

Brachyphylla cavernarum Noseleaf 7.98 10.4 17.2 71.1 89.8 133. 89.0 167. 80.5 157. 54.4 108. 46.9 86.8 44.0 72.2 41.5 88.7 37.7 74.6 29.5 59.8 27.7 61.4Chrotopterus auritus Noseleaf 7.76 19.5 71.1 81.3 26.7 33.7 27.1 32.2 25.4 31.3 23.5 32.9 25.6 64.4 41.5 79.9 36.3 77.8 34.3 77.1 36.7 75.4 27.6 73.7

Coelops frithii Pinna 11.1 14.7 112. 189. 11.5 21.9 10.8 20.6 10.1 16.7 10.8 15.5 11.2 17.0 10.2 14.8 9.35 16.8 8.23 21.8 7.82 18.8 7.72 17.1Cynopterus brachyotis Pinna 9.52 18.1 20.3 127. 63.8 104. 46.2 71.2 39.7 55.9 35.2 59.5 19.5 52.3 15.9 61.7 22.0 35.9 14.3 28.6 11.9 29.0 10.7 45.5

Cynopterus sphinx Pinna 9.77 20.3 20.3 127. 59.0 89.1 42.3 60.9 41.1 62.9 33.6 43.1 21.5 48.1 27.3 39.5 18.9 42.7 15.5 48.2 16.5 24.1 12.8 31.8Eonycteris spelaea Pinna 8.31 19.4 20.3 127. 58.5 88.9 45.6 61.6 41.4 49.1 27.0 39.0 18.2 43.4 17.8 37.5 15.3 34.9 13.8 23.4 13.2 30.9 11.1 19.3

Erophylla sezekorni Noseleaf 3.05 4.77 25.3 60 180. 204. 178. 209. 152. 204. 86.7 140. 64.5 128. 66.3 147. 68.7 171. 63.3 199. 66.6 156. 53.9 89.9Erophylla sezekorni Noseleaf 2.91 4.94 25.3 60 135. 171. 146. 235. 105. 188. 111. 203. 98.8 190. 84.3 168. 71.7 175. 74.4 182. 64.1 156. 60.2 121.Hipposideros caffer Noseleaf 4.00 6.16 50.8 140. 82.9 99.4 68.5 73.6 40.2 67.6 45.6 93.3 41.7 87.9 43.7 68.5 58.4 85.8 52.3 79.5 42.5 92.6 42.1 77.2Hipposideros caffer Noseleaf 5.09 6.75 50.8 140. 97.7 116. 85.4 117. 69.2 101. 40.9 63.8 45.1 67.4 52.3 79.8 40.8 59.8 49.1 68.0 52.3 65.2 39.0 55.6

Hipposideros cervinus Noseleaf 5.92 7.55 50.8 140. 76.5 101. 62.8 127. 56.0 80.8 48.2 77.7 55.1 83.9 44.5 57.5 36.6 93.3 33.1 104. 36.6 55.4 22.1 44.1Hipposideros cineraceus Pinna 12.1 16.8 50.8 140. 31.9 39.8 27.3 35.9 22.2 32.8 18.6 30.2 16.1 28.0 21.8 23.7 16.5 21.6 15.1 20.2 15.6 23.3 13.5 22.1Hipposideros cineraceus Pinna 12.7 15.9 50.8 140. 30.6 39.5 25.8 34.9 21.1 32.3 19.3 36.8 13.9 27.0 16.0 25.2 15.6 36.1 15.0 24.6 10.3 19.8 10.3 20.6Hipposideros cineraceus Noseleaf 4.39 5.93 50.8 140. 71.9 157. 59.9 127. 52.7 96.5 58.8 107. 63.0 80.1 46.7 64.8 44.8 76.5 48.1 62.0 30.1 58.2 36.2 53.2Hipposideros galeritus Noseleaf 6.01 8.54 50.8 140. 43.1 74.7 43.1 76.6 43.0 85.0 47.7 64.3 42.2 51.7 38.8 47.9 40.3 50.7 37.6 55.4 29.5 38.8 27.4 43.7Hipposideros galeritus Pinna 10.0 13.4 50.8 140. 31.9 44.6 27.3 38.7 23.7 34.9 21.1 30.6 18.3 29.0 18.4 26.6 15.6 27.9 17.0 26.2 16.6 26.6 13.5 29.6Hipposideros galeritus Pinna 10.5 13.5 50.8 140. 31.1 50.6 26.9 43.6 23.2 36.7 23.5 36.0 19.9 31.0 18.1 28.1 16.7 28.2 15.7 25.7 19.5 27.2 14.1 26.3Hipposideros galeritus Pinna 11.1 14.0 50.8 140. 29.8 48.5 23.1 36.4 19.7 25.7 17.8 33.9 20.2 23.2 19.3 22.2 17.7 24.6 16.4 24.7 12.2 20.3 9.70 23.7Hipposideros larvatus Pinna 12.9 23.5 50.8 111. 28.3 34.8 27.4 33.4 25.3 42.6 19.2 24.3 18.5 27.5 17.7 26.9 16.6 33.6 10.9 24.2 13.4 16.0 13.5 21.3Hipposideros larvatus Noseleaf 6.51 9.12 50.8 111. 56.1 67.3 41.5 72.0 38.5 64.9 55.9 66.4 54.3 87.2 43.8 62.9 32.0 70.4 30.8 46.7 33.5 83.9 33.5 85.8Hipposideros larvatus Pinna 12.5 17.4 50.8 111. 27.0 37.0 28.5 48.3 23.3 44.2 24.9 41.6 20.4 47.2 20.1 28.0 16.5 20.7 14.8 24.0 12.4 25.4 12.1 21.6

Hipposideros lylei Pinna 15.8 21.4 50.8 140. 29.7 51.9 18.7 37.2 14.9 28.3 16.4 36.2 13.8 27.5 15.8 43.4 12.8 21.5 11.0 15.7 19.5 28.1 14.6 18.3Hipposideros lylei Pinna 13.3 25.5 50.8 140. 21.4 43.8 18.5 39.3 18.4 38.8 20.0 29.2 17.9 36.1 13.1 64.6 11.1 56.5 12.3 17.7 13.1 27.7 9.65 24.3

Hipposideros pomona Pinna 16.6 21.8 99.6 140. 16.1 22.4 18.4 23.8 17.7 23.7 18.7 26.3 15.9 21.7 14.0 19.4 13.3 18.2 13.4 17.1 12.3 16.7 12.0 16.2Hipposideros pomona Pinna 15.9 22.7 99.6 140. 21.3 33.4 21.1 32.8 16.6 30.4 19.8 35.1 12.6 32.2 12.6 29.4 17.0 30.8 14.7 30.6 12.8 36.8 16.2 41.6

Ia io Pinna 9.35 23.0 15.2 45.7 57.9 73.2 52.1 63.4 45.3 57.2 43.1 62.8 44.5 57.9 44.0 59.3 28.8 53.9 25.3 50.6 21.2 49.4 21.4 52.6Ia io Pinna 16.4 22.1 15.2 45.7 68.3 83.5 57.3 71.7 56.4 74.1 40.8 59.3 45.7 52.6 37.0 47.5 38.7 46.8 34.5 45.9 31.8 45.6 31.3 56.6Ia io Pinna 16.4 23.1 15.2 45.7 65.8 80.3 57.0 69.5 51.3 60.4 45.3 53.3 38.6 51.5 37.2 47.2 35.2 44.9 27.7 42.2 28.8 48.2 21.9 40.8Ia io Pinna 15.6 22.1 15.2 45.7 55.6 77.7 49.5 66.8 43.6 59.2 38.2 48.6 34.1 44.1 34.4 40.0 35.3 39.0 22.1 46.5 19.7 46.0 19.7 46.0Ia io Pinna 12.8 20.8 15.2 45.7 73.6 94.9 61.3 79.6 51.1 68.8 47.2 60.6 47.9 58.2 41.5 58.8 39.3 52.5 36.7 61.9 30.0 42.3 31.6 63.4Ia io Pinna 9.07 22.0 15.2 45.7 65.7 97.6 57.0 83.1 54.9 73.3 51.1 65.7 56.1 62.7 47.1 55.4 50.4 60.4 44.5 60.7 40.1 52.8 40.7 49.7Ia io Pinna 10.8 21.4 15.2 45.7 79.9 111. 57.3 86.4 58.2 98.3 45.9 68.4 39.6 58.9 45.4 119. 42.2 59.7 35.5 49.5 39.0 48.7 41.4 48.1Ia io Pinna 11.1 20.4 15.2 45.7 68.1 104. 66.2 84.7 59.7 82.5 58.2 85.4 46.8 82.6 58.9 73.6 39.7 56.6 32.7 54.9 32.3 48.2 27.7 45.1Ia io Pinna 8.92 21.6 15.2 45.7 72.2 106. 61.9 89.7 53.1 76.3 59.9 75.6 35.6 61.5 36.3 56.5 37.0 52.7 37.7 47.9 35.9 47.2 41.2 46.9

Kerivoula sp. Pinna 7.44 12.0 30.5 192. 68.7 116. 42.6 60.2 34.1 47.4 34.4 41.8 24.1 33.0 23.2 29.0 20.4 37.2 13.7 23.6 15.0 28.8 8.38 19.5Kerivoula sp. Pinna 6.30 14.3 30.5 192. 51.3 110. 39.7 69.2 33.5 51.7 26.6 41.8 25.2 36.6 19.8 35.7 21.1 30.1 19.5 26.4 19.1 31.0 9.84 27.0Kerivoula sp. Pinna 5.79 14.1 30.5 192. 48.4 109. 40.6 75.0 31.8 55.4 29.7 50.8 14.4 41.0 18.6 32.0 15.3 29.7 17.5 28.1 12.9 23.8 10.9 20.7Kerivoula sp. Pinna 6.05 14.0 30.5 192. 54.2 138. 41.5 84.9 28.6 55.5 32.9 52.2 18.6 45.3 16.0 33.1 13.9 34.9 17.4 37.6 18.7 29.2 9.04 42.0

Lonchophylla thomasi Noseleaf 6.47 24.8 12.1 46.7 140. 216. 111. 116. 101. 148. 71.2 89.1 72.5 160. 54.8 83.4 48.2 58.5 43.3 114. 50.2 69.5 49.3 71.3Lonchorhina orinocensis Noseleaf 3.76 5.55 20.3 127. 106. 135. 71.7 77.6 54.7 159. 56.1 97.7 41.5 99.1 47.9 59.0 37.0 60.7 38.1 52.6 42.9 79.9 38.3 52.0Macroglossus sobrinus Pinna 10.1 14.6 20.3 127. 64.7 94.6 48.3 63.5 38.9 48.4 33.4 42.3 20.8 39.0 29.8 43.8 18.6 31.6 16.8 29.5 18.8 27.8 16.2 28.5

Megaderma lyra Pinna 15.7 33.3 20.3 122. 45.6 61.7 32.5 47.8 23.2 49.0 16.5 24.9 15.0 28.7 17.3 27.0 13.3 23.3 12.8 20.8 6.17 16.1 9.33 22.6Miniopterus schreibersi Pinna 0.33 10.7 50.8 100. 47.9 62.7 39.2 63.8 40.3 55.6 33.4 59.1 25.8 53.7 26.6 50.1 33.8 62.9 22.3 61.6 21.7 46.1 17.9 44.3Miniopterus schreibersi Pinna 8.00 13.2 50.8 100. 39.0 58.9 38.6 52.1 30.8 51.5 36.8 75.3 27.9 45.5 32.0 55.8 26.6 42.4 23.1 34.0 22.4 36.1 29.1 41.5

Murina cyclotis Pinna 8.35 15.3 38.6 183. 46.2 62.4 44.6 51.6 32.1 41.6 13.6 30.3 22.5 31.1 14.0 35.0 13.8 30.3 12.7 46.6 23.5 37.6 13.9 21.5Murina cyclotis Pinna 7.91 15.1 38.6 183. 41.6 74.3 39.3 52.7 30.2 40.9 24.3 36.8 17.8 35.5 13.8 31.2 16.7 27.5 21.9 29.9 14.8 24.3 9.52 22.9Murina cyclotis Pinna 8.20 15.1 38.6 183. 45.5 65.8 38.8 48.2 33.8 41.6 21.7 53.5 19.5 33.4 17.8 27.9 17.0 24.2 13.4 29.9 13.4 19.9 11.7 15.3Myotis altarium Pinna 8.96 20.0 40.6 73.2 33.0 43.7 34.8 40.0 30.4 38.1 30.1 37.0 28.5 41.7 29.5 34.1 21.3 30.3 19.9 32.1 17.6 29.7 15.7 28.0Myotis blythii Pinna 10.1 19.4 26.4 108. 49.2 71.9 37.3 55.6 26.3 46.8 38.0 50.2 15.1 40.0 23.3 34.1 20.8 28.2 19.5 30.4 22.4 41.3 19.1 27.1Myotis ricketti Pinna 8.11 18.0 27.0 73.7 52.3 80.8 47.8 70.7 45.0 64.9 35.2 53.3 33.8 48.8 33.3 45.7 26.1 48.9 18.9 46.2 23.2 43.2 26.1 38.5Myotis ricketti Pinna 8.34 18.1 27.0 73.7 54.8 85.0 48.8 70.8 43.4 66.1 45.5 60.2 39.2 51.6 34.9 49.9 30.5 43.8 20.6 45.9 28.4 45.3 19.1 43.0

Myotis sp. Pinna 5520 1374 15.2 160. 80.4 122. 55.1 86.1 45.8 65.2 29.2 49.6 22.0 70.8 18.7 33.9 20.2 37.9 26.3 50.3 23.0 27.4 11.8 28.1Myotis sp. Pinna 8.81 18.9 15.2 160. 84.0 125. 46.0 68.9 36.2 47.4 36.9 40.4 15.7 36.7 20.3 27.9 19.9 28.1 18.4 28.2 13.5 20.5 16.1 24.1

Nyctalus noctula Pinna 5.50 7.88 61 101. 50.4 77.0 38.9 83.0 39.5 68.0 27.2 70.4 30.4 49.8 33.2 70.5 21.0 49.8 23.1 41.8 19.7 40.8 20.3 35.3Nyctalus noctula Pinna 5.83 10.7 61 101. 15.0 33.0 31.8 50.8 29.1 42.5 27.9 44.5 12.9 45.3 13.1 31.6 13.3 30.4 13.0 35.0 12.4 35.0 14.1 40.1Nyctalus noctula Pinna 6.16 10.0 61 101. 18.7 67.5 20.0 58.2 14.7 52.1 16.7 62.1 16.5 42.0 14.8 47.5 15.7 40.9 14.4 48.5 13.9 50.9 15.0 51.7Nycteris aurita Noseleaf 4.18 7.35 61 101. 51.2 111. 57.0 107. 63.8 94.3 55.3 84.9 35.0 97.7 42.8 101. 43.1 97.1 46.7 60.7 40.2 55.2 25.8 60.7

Nycteris grandis Noseleaf 5.70 8.22 61 101. 33.1 99.9 49.2 98.0 24.6 71.8 22.1 84.5 21.2 92.2 22.3 53.7 21.5 74.4 25.4 48.6 19.7 120. 16.9 85.1Nycteris grandis Noseleaf 4.30 11.8 61 101. 38.2 79.9 38.2 82.5 19.5 71.0 25.8 88.2 40.3 100. 14.4 44.6 11.3 40.0 10.9 47.1 11.8 46.2 10.6 46.7Nycteris hispida Noseleaf 6.51 9.98 61 101. 35.1 58.7 42.4 66.6 31.9 56.1 26.1 42.3 24.4 39.5 24.9 43.8 25.0 45.0 21.1 43.1 23.7 44.7 21.1 35.6Nycteris hispida Noseleaf 4.96 10.2 61 101. 62.0 85.6 49.9 68.3 28.5 75.7 51.1 77.4 44.1 57.5 23.9 36.8 18.1 31.8 18.3 45.7 16.6 46.2 17.9 34.8

Nycteris intermedia Noseleaf 4.64 8.88 61 101. 46.0 79.0 53.9 78.7 46.9 82.5 40.5 84.7 33.1 84.8 36.8 76.4 22.2 51.7 25.5 33.7 24.5 42.9 19.5 35.9Nycteris intermedia Noseleaf 6.80 9.78 61 101. 26.0 39.9 25.8 36.4 29.0 32.8 26.5 38.2 25.9 47.2 22.9 36.9 25.2 74.0 20.9 24.8 18.5 29.8 18.8 21.7Nycteris javanica Noseleaf 3.32 8.88 61 101. 25.3 78.1 41.0 94.4 19.9 93.9 15.7 81.3 13.9 39.0 14.0 39.0 17.4 43.9 21.3 47.4 15.3 44.8 14.4 55.1Nycteris javanica Noseleaf 9.99 15.4 17.5 53.0 88.5 100. 75.3 81.8 66.6 71.5 58.0 64.2 52.0 61.2 47.0 59.3 49.3 70.8 38.2 51.7 34.2 54.1 29.0 51.8Nycteris macrotis Noseleaf 11.1 14.4 17.5 53.0 71.6 96.9 65.0 68.7 44.6 113. 52.3 75.1 45.1 59.9 39.5 60.4 34.4 51.3 33.9 54.4 33.4 51.6 18.0 46.4Nycteris macrotis Noseleaf 9.45 16.2 17.5 53.0 87.0 104. 63.6 80.9 68.3 76.9 50.8 66.2 41.9 57.5 41.8 63.4 36.4 51.4 35.5 50.8 37.9 51.7 38.8 64.1Nycteris tragata Noseleaf 7.00 13.8 71.1 101. 16.1 37.5 15.7 54.9 14.6 64.0 16.1 41.0 15.3 42.4 13.6 39.6 12.8 49.7 12.1 50.4 12.3 36.7 13.3 30.4

Phyllostomus hastatus Noseleaf 9.63 15.8 25.3 50.8 67.4 80.0 62.8 74.6 59.6 72.1 57.3 67.4 53.1 58.5 48.5 52.2 45.9 50.1 42.9 45.2 38.9 41.4 36.4 39.9Phyllostomus hastatus Noseleaf 8.80 15.2 25.3 50.8 69.9 87.8 59.8 75.2 58.3 74.4 52.8 79.1 49.6 69.6 42.9 59.9 40.2 64.2 42.0 48.8 38.2 58.4 32.8 43.9Phyllostomus hastatus Noseleaf 10.2 14.1 25.3 50.8 60.5 81.5 57.5 81.6 59.1 80.4 55.4 68.7 49.1 57.6 46.3 62.9 45.8 60.9 44.1 49.9 36.7 48.7 35.2 45.6Pipistrellus nathusii Pinna 0.06 0.12 35.5 76.2 71.4 98.8 71.4 91.4 59.5 76.9 53.9 70.9 51.3 68.8 50.0 65.7 50.1 63.3 41.5 63.7 26.2 65.5 37.8 60.2Pipistrellus nathusii Pinna 0.05 0.11 35.5 76.2 66.1 98.5 57.4 86.7 51.1 80.4 48.6 76.9 45.5 70.5 42.0 66.3 39.6 61.6 36.4 60.4 34.7 60.0 34.0 54.8

Pipistrellus pipistrellus Pinna 0.04 0.07 45.7 79.3 59.5 78.3 59.0 73.6 56.6 67.1 51.6 61.8 46.8 60.0 41.5 61.1 37.4 64.6 34.2 70.7 27.4 67.6 26.3 61.7Pipistrellus sp. Pinna 6.04 9.78 33.5 101. 65.2 93.5 56.3 80.1 49.3 71.2 47.8 65.9 42.6 56.7 39.2 51.5 34.5 47.9 32.0 47.3 32.2 44.8 43.6 54.8Pipistrellus sp. Pinna 6.32 8.71 33.5 101. 63.7 93.7 51.9 78.9 55.5 70.9 47.9 61.9 47.4 58.1 39.0 54.9 37.1 53.8 30.5 52.6 31.1 53.7 30.7 46.6Pipistrellus sp. Pinna 6.19 10.0 33.5 101. 53.5 94.9 45.4 83.1 44.7 76.9 43.9 70.4 37.1 57.5 35.4 52.2 33.6 51.5 34.5 47.2 36.1 65.3 29.9 45.2

Platyrrhinus helleri Noseleaf 4.27 9.99 77.2 133. 45.9 118. 39.4 94.6 37.2 107. 32.3 77.8 27.9 61.5 26.4 79.2 26.0 84.0 24.8 76.1 24.2 45.4 27.9 46.6Platyrrhinus helleri Noseleaf 5.37 11.4 77.2 133. 35.4 68.1 29.5 55.2 37.0 59.7 32.2 52.3 30.0 57.6 22.5 51.6 24.5 63.2 21.5 46.2 19.7 23.4 22.5 71.7

Plecotus auritus Pinna 0.29 0.60 21.3 62 40.6 65.1 38.3 56.6 35.2 49.4 31.7 43.4 33.8 42.9 32.8 65.7 31.0 41.4 26.9 37.6 22.2 32.2 20.6 53.4Pteropus lylei Pinna 15.6 31.8 20.3 127. 41.0 64.3 32.1 42.9 27.3 34.2 23.8 33.3 19.1 25.5 12.9 21.3 10.9 35.9 9.87 19.3 7.65 24.7 9.39 12.2

Rhinolophus acuminatus Noseleaf 6.66 12.8 61 96.6 39.1 76.6 50.4 78.5 42.5 76.9 47.4 87.6 40.7 63.5 37.6 67.3 35.7 52.6 35.8 39.7 33.6 66.9 29.0 58.7Rhinolophus acuminatus Pinna 11.1 17.2 61 91.5 30.7 49.4 29.2 46.8 27.1 45.3 25.9 45.1 24.1 44.0 23.9 42.7 23.8 41.5 22.6 39.3 23.8 39.1 22.5 37.1Rhinolophus acuminatus Noseleaf 7.40 13.3 61 101. 39.5 76.5 30.0 49.4 28.7 39.0 26.9 44.5 27.3 58.8 32.3 50.7 22.5 60.8 21.1 56.9 21.7 60.7 24.5 38.4Rhinolophus acuminatus Pinna 11.5 17.8 61 91.5 28.9 36.5 30.3 35.9 27.4 35.4 26.8 34.7 26.8 32.5 24.0 31.1 25.1 31.1 22.3 32.2 24.7 30.7 22.8 30.4

Rhinolophus affinis Pinna 12.8 20.8 71.1 90 25.7 32.8 25.8 31.1 26.2 30.3 26.1 34.4 27.1 28.9 25.4 29.9 25.8 31.1 24.8 27.1 24.2 28.5 23.5 28.2Rhinolophus celebensis Noseleaf 4.91 11.8 111. 128. 30.2 54.0 31.6 74.3 32.9 81.3 32.4 82.0 31.7 83.5 21.2 76.4 21.8 85.3 27.1 84.8 25.9 68.8 25.2 42.9

Rhinolophus denti Noseleaf 8.97 15.4 58.6 88.7 33.0 45.9 32.8 42.8 31.2 42.3 29.5 39.7 28.7 39.3 25.8 38.6 25.8 39.4 24.2 35.9 23.8 34.5 23.7 34.0Rhinolophus ferrumequinum Noseleaf 10.4 16.4 58.6 88.7 36.2 39.0 34.1 38.1 33.4 35.1 31.4 35.0 31.2 33.0 27.7 32.6 26.9 30.8 25.3 31.0 23.9 29.6 23.6 30.0Rhinolophus ferrumequinum Pinna 10.2 15.6 58.6 88.7 33.7 39.4 32.4 35.7 30.9 35.1 29.8 32.7 27.7 30.6 26.3 30.3 25.3 29.3 23.5 27.9 22.6 28.1 21.1 27.3Rhinolophus ferrumequinum Pinna 6.89 11.8 58.6 88.7 52.0 100. 42.4 79.6 59.8 108. 51.3 80.8 50.5 66.2 43.3 54.7 32.5 49.0 29.1 44.0 30.0 44.6 35.2 48.8

Rhinolophus landeri Noseleaf 11.3 16.6 58.6 88.7 33.6 43.2 34.9 41.3 30.0 40.1 30.2 37.9 29.4 36.5 25.4 35.3 29.0 31.7 25.7 29.7 26.5 33.1 24.7 27.2Rhinolophus luctus Pinna 6.03 10.0 83.3 113. 48.2 73.7 51.2 68.8 46.1 73.6 39.4 71.3 39.2 66.5 42.1 59.5 46.5 58.6 33.1 57.1 27.7 46.2 31.5 50.3Rhinolophus luctus Noseleaf 5.71 10.0 73.2 84.4 26.6 32.4 26.3 31.8 27.4 44.5 29.3 45.2 39.4 64.1 39.9 69.9 39.9 72.9 28.2 71.8 24.9 41.4 28.8 39.9

Rhinolophus macrotis Pinna 11.5 20.0 73.2 84.4 22.5 34.0 21.8 34.5 20.5 38.1 22.2 44.0 18.9 25.9 21.1 28.4 22.1 35.4 23.4 33.8 20.7 32.6 19.4 32.5Rhinolophus macrotis Noseleaf 9.71 18.4 73.2 84.4 19.2 30.2 19.1 30.0 18.5 31.4 18.3 31.9 17.4 30.4 15.3 27.9 14.8 28.2 15.3 28.2 15.4 28.3 16.2 29.6Rhinolophus macrotis Noseleaf 5.21 8.97 106. 111. 31.9 39.1 39.6 43.8 26.8 38.4 37.0 42.0 28.4 36.9 30.2 37.4 27.0 40.3 29.3 35.7 28.4 35.1 32.0 36.7

Rhinolophus malayanus Pinna 19.7 31.7 33.1 43.3 27.5 38.3 28.0 37.3 25.9 36.6 25.5 35.7 25.7 33.4 24.5 33.1 23.6 31.5 23.1 32.2 23.7 32.0 22.5 30.0Rhinolophus malayanus Pinna 2536 7000 33.1 43.3 45.1 49.7 42.8 50.1 38.6 46.5 37.6 47.2 37.9 50.9 38.3 82.2 33.2 56.0 29.9 57.0 26.8 63.2 27.6 46.9Rhinolophus marshalli Noseleaf 10.0 16.2 48 54.8 35.8 51.4 34.7 55.9 33.8 61.2 32.8 65.9 32.2 66.0 32.5 73.8 30.7 74.6 31.2 72.4 29.6 75.3 29.3 70.5Rhinolophus mehelyi Noseleaf 5.99 12.7 48 54.8 56.6 77.8 53.0 76.6 50.1 75.8 47.9 74.0 46.2 73.0 44.8 71.1 43.9 69.6 42.1 64.2 42.0 68.6 41.7 67.2Rhinolophus mehelyi Noseleaf 6.82 13.3 48 54.8 45.0 67.7 44.1 68.2 43.2 68.0 42.6 67.8 42.0 67.5 41.4 67.2 40.9 66.3 40.3 65.5 39.7 64.7 39.1 63.9Rhinolophus mehelyi Noseleaf 9.21 13.2 74.2 91.5 29.9 45.3 29.0 44.8 29.1 45.8 28.8 46.3 28.1 46.0 27.2 46.3 26.8 47.5 27.0 51.1 27.5 56.7 29.7 58.5Rhinolophus pearsoni Pinna 17.9 24.2 39.8 43 30.3 36.4 30.1 36.3 29.8 35.8 29.6 35.1 29.3 34.1 29.0 33.5 28.4 32.9 27.9 32.5 27.6 32.4 27.2 32.5Rhinolophus pearsoni Noseleaf 8.01 12.9 39.8 43 45.6 73.1 45.7 73.1 46.0 72.6 46.5 72.3 47.1 71.2 47.8 69.3 48.1 66.3 48.5 63.5 48.7 61.6 48.6 60.5Rhinolophus pearsoni Pinna 6.25 12.4 101. 110. 21.4 33.6 20.9 39.0 20.6 54.5 19.9 60.0 20.5 64.5 30.6 67.7 28.6 62.9 26.9 55.7 25.1 50.2 24.4 47.5Rhinolophus pearsoni Noseleaf 6.15 11.8 101. 110. 22.8 37.5 22.6 35.6 22.3 33.6 22.1 32.2 21.9 31.1 21.8 30.3 21.7 29.9 21.6 29.8 21.6 30.1 21.5 30.2Rhinolophus pusillus Pinna 5.67 8.30 101. 110. 34.2 37.6 34.2 38.4 34.5 39.8 33.8 40.4 32.7 40.1 31.8 39.7 30.7 39.5 30.1 39.0 29.4 38.9 29.0 38.0Rhinolophus pusillus Noseleaf 13.7 22.5 58.6 71.2 24.0 31.8 23.2 31.6 23.0 32.6 23.7 34.6 23.6 32.3 23.0 30.9 23.4 31.2 23.4 30.9 22.9 30.0 23.4 30.7Rhinolophus pusillus Pinna 6.18 15.6 58.6 71.2 28.4 78.4 29.5 73.3 30.9 58.5 33.0 49.4 33.0 62.4 30.2 44.5 30.2 40.8 30.4 42.8 32.6 40.6 24.2 54.2Rhinolophus pusillus Noseleaf 15.9 26.9 58.6 71.2 21.0 34.4 23.4 25.8 22.1 26.7 22.5 25.8 22.5 25.6 20.9 24.4 21.1 25.5 20.9 24.2 20.8 23.3 20.4 25.0

Rhinolophus roux Pinna 11.0 18.1 58.6 71.2 29.3 62.0 37.6 61.7 36.6 54.2 34.2 54.3 32.5 54.9 30.5 50.6 29.3 36.4 28.7 34.0 28.5 33.7 27.9 56.7Rhinolophus roux Pinna 9038 1484 102 113. 27.7 37.3 26.5 38.9 25.8 37.7 24.5 36.4 23.8 34.8 23.3 33.5 23.5 33.7 23.7 34.3 22.9 33.9 22.7 33.0

Rhinolophus sedulus Noseleaf 5.05 11.0 102 113. 29.0 35.1 28.5 34.6 28.3 34.0 28.2 33.8 28.5 33.3 29.2 33.0 29.9 33.7 31.1 35.7 32.7 37.5 33.5 38.6Rhinolophus sedulus Noseleaf 10.3 16.7 102 113. 22.2 31.2 22.9 30.6 22.9 30.1 22.4 29.8 22.0 29.9 21.3 29.9 20.5 29.7 20.4 29.3 20.8 28.5 21.1 28.2Rhinolophus sinicus Pinna 5.94 11.0 102 113. 32.9 46.4 32.6 47.5 33.1 47.8 34.8 48.3 37.0 50.1 39.7 51.7 38.9 48.9 37.5 45.3 35.3 42.1 34.1 39.5Rhinolophus sinicus Pinna 1.28 17.0 35.6 66.1 42.8 52.6 41.1 77.7 42.3 50.9 40.3 44.9 36.9 39.4 35.1 39.9 31.2 36.2 31.0 36.0 30.7 34.8 27.9 33.3

Rhinolophus sp. Pinna 10.6 15.3 35.6 66.1 79.3 106. 73.5 103. 68.9 97.9 65.4 88.4 62.5 80.1 59.7 74.6 56.8 71.4 53.5 67.9 50.7 64.3 48.2 60.9Rhinolophus sp. Pinna 4.67 14.3 63.0 77.3 35.1 45.2 34.3 41.8 32.1 38.2 31.5 39.3 32.8 38.2 31.8 36.8 31.3 36.6 32.3 38.2 31.6 40.5 31.6 39.8Rhinolophus sp. Pinna 7.40 10.9 63.0 77.3 32.8 43.0 33.8 45.1 36.0 50.4 32.2 42.2 28.4 40.6 26.3 42.3 26.1 45.8 27.8 58.4 29.5 65.8 28.3 65.6Rhinolophus sp. Pinna 9.62 18.4 74.6 88.7 27.5 34.7 26.8 34.0 27.2 33.6 27.0 33.3 25.9 33.1 24.4 33.6 23.7 35.3 24.4 34.7 25.5 32.3 24.7 31.5Rhinolophus sp. Pinna 11.5 17.9 74.6 88.7 25.3 27.3 26.2 28.7 25.4 28.1 23.5 27.2 23.4 25.9 23.6 26.2 25.0 27.7 24.9 26.8 22.5 25.4 22.2 24.3

Rhinolophus thomasi Noseleaf 7.32 13.4 77.2 87.5 46.5 90.1 29.8 85.2 27.6 83.3 26.5 82.0 26.1 79.8 25.7 79.0 25.6 81.4 37.1 57.0 37.6 53.4 39.1 50.7Rhinolophus thomasi Pinna 8.49 12.1 77.2 87.5 34.9 44.7 34.5 44.5 34.2 45.6 33.8 46.1 33.2 45.9 33.1 44.6 32.5 43.2 31.6 41.6 31.3 41.0 30.8 41.3Rhinolophus thomasi Pinna 10.5 13.6 77.2 87.5 27.5 40.6 26.8 39.6 26.8 38.7 26.9 39.0 27.1 39.4 26.4 39.7 25.6 39.3 25.4 38.0 25.5 37.1 25.7 36.4Rhinonicteris aurantia Noseleaf 10.7 16.3 58.6 88.7 35.7 39.3 34.0 37.3 32.7 36.2 30.6 34.5 28.3 33.9 27.7 32.5 25.4 32.2 26.6 32.2 24.7 30.5 25.0 29.3Scotomanes ornatus Pinna 7.57 13.0 36.7 88.6 50.6 69.2 52.4 66.4 45.1 56.1 35.5 49.2 38.6 49.3 44.1 58.3 23.6 56.7 19.6 59.8 18.9 64.8 16.9 51.8Scotomanes ornatus Pinna 7.15 13.6 36.7 88.6 52.7 75.3 44.2 67.7 40.3 56.6 39.2 51.9 38.2 53.9 28.8 47.8 23.0 51.0 19.2 48.8 16.5 43.8 17.8 37.1Scotophilus kuhlii Pinna 7.13 12.3 36.7 88.6 49.2 79.5 46.4 71.1 42.4 61.4 38.1 57.1 36.7 53.5 38.8 54.8 33.3 49.6 27.5 52.5 21.6 60.8 22.9 32.6Scotophilus kuhlii Pinna 6.89 12.8 36.7 88.6 48.8 73.3 43.6 64.4 41.3 56.7 34.3 56.0 20.5 57.8 25.5 56.1 21.1 76.1 29.0 61.7 21.0 47.9 17.8 40.9

Scotophilus sp. Pinna 9.10 18.3 25.4 81.3 52.5 86.0 48.7 65.3 41.8 57.0 36.2 48.9 20.6 74.9 24.1 51.3 23.8 49.4 19.2 47.8 26.0 40.6 19.5 34.4Scotophilus sp. Pinna 9.23 17.3 25.4 81.3 58.9 85.5 58.1 76.2 46.7 61.7 35.5 53.8 22.7 57.5 32.1 69.7 22.8 58.5 19.4 41.7 16.1 43.0 15.7 41.3

Sphaeronycteris toxophyllum Noseleaf 11.3 16.1 38.4 109. 68.9 102. 53.6 96.8 34.7 63.6 51.5 82.2 37.5 48.7 31.0 48.5 32.3 72.6 31.5 57.4 26.2 41.4 30.2 45.5Tadarida teniotis Pinna 15.3 27.1 5.05 15.2 148. 160. 113. 122. 96.9 107. 85.5 97.2 76.3 90.6 67.7 84.6 64.4 82.6 63.4 76.1 54.7 70.4 50.2 74.9

Taphozous melanopogon Pinna 12.7 19.6 8.44 65.6 120. 129. 76.8 96.2 56.8 77.2 47.5 61.5 43.2 58.3 40.8 52.6 37.4 45.3 36.6 44.3 26.2 47.5 21.2 43.5Taphozous melanopogon Pinna 8.74 16.1 8.44 65.6 129. 136. 80.2 98.1 58.4 85.0 48.5 71.7 41.1 57.7 38.4 54.9 38.3 55.6 42.4 61.1 23.1 41.6 19.4 42.1Taphozous melanopogon Pinna 11.4 18.7 8.44 65.6 114. 135. 83.4 106. 58.6 77.5 47.7 65.9 44.2 58.2 43.3 56.0 35.4 48.5 35.7 64.2 24.1 52.0 20.2 43.8Taphozous melanopogon Pinna 11.7 19.2 8.44 65.6 119. 139. 72.3 97.3 54.3 75.8 46.8 64.2 46.9 59.2 40.2 56.0 33.8 55.5 23.0 50.1 24.9 55.0 18.8 49.5

Trachops cirrhosus Noseleaf 5.50 12.9 50.8 101. 35.7 135. 43.4 74.3 33.3 46.6 46.9 66.9 34.5 57.0 33.8 56.1 33.7 52.4 31.2 44.4 25.7 45.1 25.1 41.8Trachops cirrhosus Noseleaf 6.30 13.4 50.8 101. 47.1 119. 48.8 74.4 38.7 61.7 39.8 80.0 32.8 93.6 32.6 95.6 28.2 83.4 27.9 95.0 30.5 65.7 29.4 47.9Triaenops persicus Noseleaf 8.75 13.2 73.2 90 41.8 61.7 40.6 60.4 39.8 58.6 37.6 55.3 36.2 52.4 36.3 50.1 38.8 46.8 40.9 47.1 37.2 48.6 32.4 54.1Triaenops persicus Noseleaf 8.86 13.6 73.2 90 32.7 40.7 30.3 39.2 28.7 39.0 27.8 40.1 28.1 42.7 30.4 46.7 34.6 49.7 40.7 55.8 36.1 46.6 34.8 44.0

Vampyrum spectrum Noseleaf 8.63 15.0 71.2 91.5 15.0 36.5 18.2 43.5 26.5 56.4 27.8 49.5 20.0 49.0 20.4 49.5 23.4 45.1 23.7 43.5 20.6 48.4 22.9 52.1

90

Table 5.2: Table Containing Geometry and Beamwidth Data for Samples sorted by Sci-entific Name. Species denoted as sp. represent an unknown species within a genera.Beamwidths given as the quarter-power beamwidths for that aperture at a given frequencyexcluding sidelobes. The 10 frequencies are equally spaced between the minimum andmaximum frequency.

Scientific Aperture Minimum Aperture Maximum Aperture Min Freq Max Freq Min BW 1 Max BW 1 Min BW 2 Max BW 2 Min BW 3 Max BW 3 Min BW 4 Max BW 4 Min BW 5 Max BW 5 Min BW 6 Max BW 6 Min BW 7 Max BW 7 Min BW 8 Max BW 8 Min BW 9 Max BW 9 Min BW 10 Max BW 10Name Type Diameter (mm) Diameter (mm) (kHz) (kHz) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees) (Degrees)

Artibeus jamaicensis Noseleaf 7.11 13.9 36.6 107. 69.7 129. 94.0 142. 77.3 124. 74.0 97.4 65.0 94.0 52.4 97.2 43.6 82.7 36.8 91.2 35.1 89.2 55.1 92.0Artibeus jamaicensis Noseleaf 12.2 14.1 36.6 107. 103. 207. 115. 212. 90.6 198. 95.3 162. 69.9 124. 63.8 91.3 56.5 99.8 51.2 107. 39.4 105. 41.8 102.

Asellia tridens Noseleaf 4.86 6.54 91.5 127. 55.5 73.2 56.2 67.5 47.1 139. 47.5 75.6 46.0 72.4 41.5 80.0 34.3 87.2 35.5 75.6 34.7 72.7 29.9 56.5Asellia tridens Noseleaf 6.04 8.81 91.5 127. 59.9 81.8 57.8 85.3 52.9 79.9 51.5 83.5 45.7 83.2 40.1 87.7 28.8 87.1 26.9 75.1 29.5 80.4 46.7 102.

Aselliscus stoliczkanus Noseleaf 6.49 9.45 101. 120 27.7 33.2 68.3 79.3 26.4 58.6 53.9 79.7 51.8 85.1 49.7 86.1 44.5 64.6 41.7 63.6 40.3 61.2 39.3 62.4Aselliscus stoliczkanus Pinna 6.98 12.2 101. 122. 43.5 48.6 42.7 48.4 41.3 47.5 41.0 48.3 40.5 46.5 40.1 44.9 40.4 44.5 39.1 45.5 38.7 42.6 38.8 41.5Barbastella leucomelas Pinna 12.5 16.0 23.3 44.7 93.9 121. 91.9 111. 92.0 104. 88.4 96.8 90.7 96.2 87.7 92.7 82.1 88.1 64.6 80.5 53.8 74.8 56.5 77.0Barbastella leucomelas Pinna 11.4 18.6 23.3 44.7 130. 274. 118. 206. 98.1 225. 67.1 184. 60.9 167. 65.0 139. 62.7 114. 33.3 122. 57.4 86.7 50.1 79.4

Brachyphylla cavernarum Noseleaf 7.98 10.4 17.2 71.1 128. 179. 131. 215. 121. 210. 80.1 154. 69.1 128. 67.2 107. 59.2 144. 54.2 160. 42.4 119. 40.0 81.1Chrotopterus auritus Noseleaf 7.76 19.5 71.1 81.3 42.4 59.1 41.8 69.3 41.0 67.9 41.6 88.9 48.4 82.7 57.9 101. 57.4 97.2 59.1 94.9 59.7 92.9 53.1 90.8

Coelops frithii Pinna 11.1 14.7 112. 189. 16.8 31.1 15.6 30.1 15.1 24.5 16.1 34.8 17.3 35.1 15.1 32.8 15.6 44.2 12.3 27.9 11.9 25.0 11.6 23.9Cynopterus brachyotis Pinna 9.52 18.1 20.3 127. 99.4 148. 70.9 99.0 60.5 81.6 52.8 86.2 29.2 84.2 24.7 83.5 33.3 73.1 21.6 41.7 17.3 43.0 16.1 57.7

Cynopterus sphinx Pinna 9.77 20.3 20.3 127. 87.6 128. 62.2 85.2 61.9 103. 47.4 64.3 29.9 73.2 40.0 55.7 27.6 63.6 22.8 64.6 24.0 50.0 19.0 75.3Eonycteris spelaea Pinna 8.31 19.4 20.3 127. 88.3 130. 68.0 87.6 60.7 70.6 43.2 54.9 27.6 63.1 26.4 54.8 23.2 53.5 25.5 40.3 19.2 60.4 16.9 32.2

Erophylla sezekorni Noseleaf 3.05 4.77 25.3 60 236. 361 233. 336. 220. 250. 146. 190. 99.6 213. 93.7 199. 93.4 224. 120. 243. 102. 265. 81.1 201.Erophylla sezekorni Noseleaf 2.91 4.94 25.3 60 191. 221. 274. 361 155. 315. 166. 243. 146. 243. 131. 220. 106. 243. 104. 247. 95.8 263. 85.9 222.Hipposideros caffer Noseleaf 4.00 6.16 50.8 140. 128. 152. 108. 162. 64.2 110. 67.2 138. 65.6 143. 79.8 122. 80.3 118. 72.4 124. 65.2 122. 65.3 107.Hipposideros caffer Noseleaf 5.09 6.75 50.8 140. 161. 181. 128. 176. 114. 140. 65.3 129. 68.6 111. 89.3 104. 60.8 95.1 71.5 99.0 69.8 93.5 59.7 82.1

Hipposideros cervinus Noseleaf 5.92 7.55 50.8 140. 111. 184. 107. 201. 93.4 184. 79.6 116. 74.9 149. 64.6 122. 56.1 138. 50.1 145. 49.2 88.8 32.3 68.1Hipposideros cineraceus Pinna 12.1 16.8 50.8 140. 45.4 58.5 38.9 53.0 31.6 48.3 26.6 44.7 23.3 41.9 32.0 34.5 24.0 31.3 22.6 29.3 22.9 33.2 22.0 33.1Hipposideros cineraceus Pinna 12.7 15.9 50.8 140. 43.2 58.7 36.8 51.0 30.1 47.6 27.9 51.8 20.3 43.5 23.7 37.8 24.0 48.5 22.2 36.9 15.8 30.6 16.3 32.0Hipposideros cineraceus Noseleaf 4.39 5.93 50.8 140. 139. 209. 91.3 182. 82.7 194. 95.6 155. 96.1 129. 80.9 108. 65.1 113. 66.9 100. 55.6 94.3 54.5 83.3Hipposideros galeritus Noseleaf 6.01 8.54 50.8 140. 76.1 112. 92.8 160. 69.1 121. 75.0 86.8 67.0 75.2 58.2 75.4 57.5 78.9 52.3 76.3 45.5 58.3 47.1 65.4Hipposideros galeritus Pinna 10.0 13.4 50.8 140. 45.6 67.5 39.8 57.0 34.2 51.4 30.3 44.1 26.4 42.9 27.1 37.9 22.7 38.9 24.9 37.8 24.7 42.5 20.8 55.8Hipposideros galeritus Pinna 10.5 13.5 50.8 140. 44.7 74.2 39.2 63.7 34.4 54.7 34.3 50.8 28.6 44.8 27.0 40.5 25.5 39.8 23.2 37.7 29.6 40.3 22.6 39.6Hipposideros galeritus Pinna 1111 1406 50.8 140. 42.5 69.6 33.2 53.1 28.1 37.1 25.6 52.8 30.3 34.1 28.4 32.5 26.3 33.6 23.4 34.1 18.1 32.1 14.9 33.9Hipposideros larvatus Pinna 12.9 23.5 50.8 111. 42.2 50.6 40.2 57.6 37.4 60.9 28.0 35.4 27.0 42.5 26.0 41.3 26.8 48.5 17.1 48.7 19.4 23.0 19.7 31.5Hipposideros larvatus Noseleaf 6.51 9.12 50.8 111. 82.7 195. 67.6 138. 75.3 111. 85.9 123. 78.4 132. 62.9 93.9 60.9 92.1 48.3 108. 50.5 109. 49.7 106.Hipposideros larvatus Pinna 12.5 17.4 50.8 111. 39.0 87.9 41.3 71.6 34.2 61.8 36.1 57.4 29.6 74.0 30.2 39.5 24.2 32.5 22.7 36.4 18.4 40.2 18.0 65.0

Hipposideros lylei Pinna 15.8 21.4 50.8 140. 42.6 72.7 32.2 55.4 21.4 42.7 24.4 61.1 20.2 49.9 26.0 73.8 18.8 37.2 18.0 23.9 26.4 57.4 21.0 28.0Hipposideros lylei Pinna 13.3 25.5 50.8 140. 30.9 67.0 27.3 59.3 27.4 54.7 30.6 44.4 26.8 54.7 19.7 78.4 17.7 76.2 19.2 28.0 19.1 82.0 15.1 38.1

Hipposideros pomona Pinna 16.6 21.8 99.6 140. 25.3 35.6 29.3 39.2 32.1 39.7 30.0 35.6 24.8 30.9 21.0 28.1 19.9 26.5 20.0 24.8 19.2 24.5 18.5 24.3Hipposideros pomona Pinna 15.9 22.7 99.6 140. 31.7 45.3 32.6 44.0 27.0 42.5 27.7 46.1 23.6 52.6 25.7 46.3 26.6 49.7 24.5 49.5 21.6 47.3 25.0 50.8

Ia io Pinna 9.35 23.0 15.2 45.7 90.0 135. 79.0 117. 68.7 94.3 63.4 89.1 68.4 97.1 59.3 87.0 46.1 70.5 39.7 65.5 32.3 65.3 36.6 77.1Ia io Pinna 16.4 22.1 15.2 45.7 102. 125. 86.2 104. 83.3 100. 61.9 85.3 65.8 78.8 53.8 68.7 56.1 70.1 49.8 69.5 44.5 65.2 44.6 86.2Ia io Pinna 16.4 23.1 15.2 45.7 97.9 119. 84.8 101. 76.8 88.3 67.8 76.2 57.2 75.9 55.2 70.2 51.3 65.2 46.2 65.9 42.7 95.9 32.1 59.5Ia io Pinna 15.6 22.1 15.2 45.7 86.0 113. 77.2 97.4 66.5 88.9 58.1 68.9 50.9 61.2 50.9 59.2 50.6 58.6 32.4 76.0 28.9 73.1 28.9 73.1Ia io Pinna 12.8 20.8 15.2 45.7 109. 141. 91.2 120. 75.6 100. 70.5 87.5 70.1 87.8 60.2 120. 60.4 117. 54.0 100. 43.9 63.7 51.0 109.Ia io Pinna 9.07 22.0 15.2 45.7 96.9 144. 85.5 121. 82.5 105. 79.4 94.1 82.2 95.7 73.7 87.2 72.5 88.0 63.3 84.4 59.3 78.3 58.4 71.8Ia io Pinna 10.8 21.4 15.2 45.7 116. 163. 89.6 126. 86.7 155. 68.1 97.3 58.8 83.4 69.6 162. 65.9 86.5 51.1 82.0 55.6 69.9 59.2 71.9Ia io Pinna 11.1 20.4 15.2 45.7 135. 151. 108. 142. 89.7 124. 92.1 123. 67.7 103. 83.6 121. 60.1 113. 48.6 81.4 48.7 63.5 39.2 64.0Ia io Pinna 8.92 21.6 15.2 45.7 106. 155. 91.7 129. 79.5 109. 87.8 106. 53.4 91.9 54.0 79.9 55.0 73.6 58.4 70.3 53.0 75.5 60.4 70.8

Kerivoula sp. Pinna 7.44 12.0 30.5 192. 134. 220. 62.8 89.4 49.7 68.8 49.7 59.6 36.8 52.6 36.4 44.2 29.3 50.1 20.5 36.2 22.8 46.8 13.3 44.2Kerivoula sp. Pinna 6.30 14.3 30.5 192. 74.4 150. 58.2 97.4 49.3 73.4 40.1 60.2 36.9 54.7 30.0 49.4 31.6 43.6 30.6 43.8 29.2 42.6 14.7 43.0Kerivoula sp. Pinna 5.79 14.1 30.5 192. 71.0 152. 58.5 110. 47.7 78.6 46.0 78.1 21.2 75.3 28.1 44.6 33.5 43.8 29.2 43.6 19.2 32.6 17.3 30.6Kerivoula sp. Pinna 6.05 14.0 30.5 192. 105. 196. 62.4 108. 41.6 76.1 48.1 71.6 35.9 67.8 23.5 49.3 22.1 61.4 26.6 56.9 28.8 63.1 14.9 60.8

Lonchophylla thomasi Noseleaf 3.76 5.55 20.3 127. 161. 316. 103. 118. 78.2 227. 95.9 170. 61.8 131. 69.7 109. 55.8 84.0 58.0 83.3 58.1 93.7 55.1 92.0Lonchorhina orinocensis Noseleaf 6.47 24.8 12.1 46.7 361 361 161. 260. 155. 239. 115. 162. 111. 184. 88.3 118. 72.6 81.7 60.6 141. 84.4 124. 83.2 117.Macroglossus sobrinus Pinna 10.1 14.6 20.3 127. 97.9 135. 72.9 89.7 58.3 68.8 48.1 61.3 34.4 55.8 46.6 68.0 28.9 47.7 25.1 42.9 28.4 50.5 24.4 42.7

Megaderma lyra Pinna 15.7 33.3 20.3 122. 68.2 89.1 48.1 72.3 33.8 69.3 23.9 47.8 22.4 67.9 25.7 51.8 20.1 34.0 20.0 31.3 12.6 36.0 15.5 28.5Miniopterus schreibersi Pinna 0.33 10.7 50.8 100. 68.5 97.1 61.8 90.9 55.3 80.5 49.9 83.8 40.0 84.2 42.3 66.5 52.2 83.7 37.2 100. 36.9 69.2 25.9 60.8Miniopterus schreibersi Pinna 8.00 13.2 50.8 100. 58.5 87.8 55.8 77.1 45.6 76.4 55.9 96.4 39.4 105. 52.2 76.8 39.5 85.9 32.7 50.6 32.9 52.2 43.5 65.8

Murina cyclotis Pinna 8.35 15.3 38.6 183. 66.7 89.4 63.6 76.5 47.3 61.6 20.4 44.9 33.4 45.2 20.8 52.5 21.7 45.5 22.3 59.8 34.7 46.9 21.8 38.7Murina cyclotis Pinna 7.91 15.1 38.6 183. 60.0 105. 57.8 77.0 44.6 58.2 35.4 54.0 27.2 51.7 20.5 47.2 27.5 53.9 32.9 44.9 24.8 37.7 14.3 33.3Murina cyclotis Pinna 8.20 15.1 38.6 183. 66.4 93.6 57.8 69.2 50.0 61.5 33.6 72.5 27.5 52.5 26.7 40.4 27.7 45.6 20.1 48.3 19.4 30.3 18.5 23.1Myotis altarium Pinna 8966 2000 40.6 73.2 49.9 61.0 54.8 59.7 46.3 54.5 44.9 59.2 40.7 62.6 42.6 67.8 32.6 44.4 30.6 45.1 26.5 43.6 23.7 39.4Myotis blythii Pinna 10.1 19.4 26.4 108. 73.6 103. 56.6 78.2 39.3 67.0 53.7 78.6 22.5 60.8 36.1 59.2 31.6 40.2 29.0 44.1 31.1 60.7 32.8 41.4Myotis ricketti Pinna 8.11 18.0 27.0 73.7 79.1 120. 72.2 103. 67.5 92.5 52.7 71.7 51.8 67.1 50.8 66.9 38.9 68.8 27.9 65.5 34.6 62.1 37.2 56.8Myotis ricketti Pinna 8.34 18.1 27.0 73.7 80.2 122. 72.8 100. 63.9 94.4 67.8 90.3 59.0 74.0 52.5 71.1 46.5 62.5 39.4 73.6 39.6 63.4 29.3 60.9

Myotis sp. Pinna 5520 1374 15.2 160. 124. 257. 82.3 126. 67.4 90.9 43.5 66.8 35.0 93.3 28.2 49.3 31.9 53.2 36.6 71.2 34.6 60.6 17.3 40.9Myotis sp. Pinna 8.81 18.9 15.2 160. 126. 269. 68.1 98.4 54.0 66.6 53.9 61.3 23.0 54.2 30.4 40.5 28.9 61.8 27.8 44.4 21.9 32.0 24.3 39.1

Nyctalus noctula Pinna 9.99 15.4 17.5 53.0 130. 155. 113. 123. 99.1 106. 86.1 94.9 77.3 90.0 70.2 85.5 73.1 98.8 56.5 78.1 50.0 83.4 42.0 82.8Nyctalus noctula Pinna 11.1 14.4 17.5 53.0 108. 130. 85.3 93.3 68.7 138. 74.5 107. 66.3 85.7 57.3 102. 50.9 74.7 51.1 91.8 50.4 95.7 26.1 79.0Nyctalus noctula Pinna 9.45 16.2 17.5 53.0 129. 156. 93.6 122. 98.8 119. 75.3 95.9 61.1 82.5 61.7 88.2 54.0 75.5 52.8 75.5 57.0 71.4 63.0 95.9Nycteris aurita Noseleaf 5.50 7.88 61 101. 75.1 108. 67.6 105. 59.2 117. 52.0 104. 50.4 104. 52.5 105. 35.4 80.5 39.6 64.3 29.9 58.9 31.0 51.3

Nycteris grandis Noseleaf 5.83 10.7 61 101. 22.1 49.1 54.6 83.3 43.6 61.4 40.9 65.0 19.5 64.5 19.4 50.2 19.5 46.3 19.1 50.8 18.6 52.9 20.4 57.6Nycteris grandis Noseleaf 6.16 10.0 61 101. 26.7 97.8 30.2 82.3 21.1 77.9 24.3 79.7 24.6 72.1 21.4 65.4 23.3 57.2 21.0 64.1 20.4 67.9 21.9 70.4Nycteris hispida Noseleaf 4.18 7.35 61 101. 75.2 149. 89.3 171. 93.6 168. 75.8 117. 58.7 141. 66.6 137. 79.1 132. 67.3 94.5 65.9 91.0 50.1 95.3Nycteris hispida Noseleaf 5.70 8.22 61 101. 71.5 138. 79.4 131. 36.8 109. 32.4 122. 30.7 141. 33.8 127. 38.4 116. 46.3 147. 28.2 168. 24.4 114.

Nycteris intermedia Noseleaf 4.30 11.8 61 101. 86.6 119. 52.0 114. 29.2 99.7 42.8 114. 61.5 117. 21.1 84.8 16.4 66.5 15.7 70.7 17.2 66.8 15.6 67.3Nycteris intermedia Noseleaf 6.51 9.98 61 101. 59.2 160. 65.1 99.1 47.4 85.3 37.9 69.5 35.3 66.4 38.2 71.5 36.8 73.6 30.9 72.5 34.8 75.3 30.7 56.4Nycteris javanica Noseleaf 4.96 10.2 61 101. 94.3 136. 89.9 109. 57.4 145. 74.8 114. 66.8 83.7 50.6 68.1 27.6 62.0 27.6 75.8 24.1 61.6 27.3 58.2Nycteris javanica Noseleaf 4.64 8.88 61 101. 67.3 117. 73.1 112. 64.4 105. 56.9 105. 59.4 112. 53.9 92.1 34.2 77.6 38.4 85.7 36.9 71.7 35.3 55.9Nycteris macrotis Noseleaf 6.80 9.78 61 101. 37.9 55.8 39.3 51.5 44.3 53.2 38.7 56.6 37.0 59.0 34.6 61.2 39.8 97.8 32.6 93.3 28.2 132. 27.4 32.7Nycteris macrotis Noseleaf 3.32 8.88 61 101. 73.5 111. 62.8 126. 67.9 141. 24.8 99.2 20.0 58.6 20.2 73.1 35.6 72.9 39.0 73.7 28.6 72.3 21.4 70.9Nycteris tragata Noseleaf 7.00 13.8 71.1 101. 23.4 74.8 23.2 99.1 21.2 108. 23.2 78.8 22.3 71.9 19.8 66.2 18.8 67.5 17.8 60.4 17.8 55.2 19.5 50.3

Phyllostomus hastatus Noseleaf 9.63 15.8 25.3 50.8 107. 120. 99.0 111. 94.7 105. 90.6 98.2 81.6 85.9 72.8 77.7 67.6 75.6 62.3 70.9 56.2 65.0 52.4 62.3Phyllostomus hastatus Noseleaf 8.80 15.2 25.3 50.8 108. 132. 90.5 116. 88.4 109. 81.4 114. 77.8 100. 68.7 86.6 60.0 90.3 63.0 72.2 62.2 79.9 51.5 65.6Phyllostomus hastatus Noseleaf 10.2 14.1 25.3 50.8 98.3 126. 89.9 119. 91.1 116. 88.8 104. 73.3 99.9 67.4 97.8 66.1 89.8 64.4 74.4 54.7 69.1 52.5 63.6Pipistrellus nathusii Pinna 0.06 0.12 35.5 76.2 106. 149. 107. 136. 92.6 111. 82.1 101. 77.8 98.5 76.1 95.2 80.9 122. 63.0 90.2 38.5 99.9 70.0 97.0Pipistrellus nathusii Pinna 0.05 0.11 35.5 76.2 99.1 141. 86.3 124. 75.9 113. 72.3 107. 68.2 97.5 62.6 90.3 58.8 84.6 54.5 81.8 51.6 82.2 50.4 76.5

Pipistrellus pipistrellus Pinna 0.04 0.07 45.7 79.3 97.3 112. 97.4 105. 92.4 104. 81.0 98.9 70.4 95.7 60.8 94.9 54.0 103. 49.7 120. 39.9 116. 39.3 96.0Pipistrellus sp. Pinna 6.04 9.78 33.5 101. 100. 139. 84.4 118. 73.9 103. 71.6 92.5 62.9 82.1 58.5 74.0 51.6 69.6 49.1 68.2 52.6 88.5 65.0 78.0Pipistrellus sp. Pinna 6.32 8.71 33.5 101. 94.3 138. 76.9 115. 81.3 103. 70.3 90.3 67.7 86.8 57.7 78.4 54.6 76.1 47.1 77.4 47.3 78.8 45.4 69.4Pipistrellus sp. Pinna 6.19 10.0 33.5 101. 79.1 133. 67.3 114. 65.7 107. 63.4 100. 53.5 78.9 52.8 75.3 49.2 73.1 49.6 72.8 55.6 93.5 49.6 65.8

Platyrrhinus helleri Noseleaf 4.27 9.99 77.2 133. 68.7 156. 61.4 145. 53.2 142. 46.5 156. 40.5 129. 38.7 128. 36.9 107. 37.1 113. 38.2 121. 41.4 118.Platyrrhinus helleri Noseleaf 5.37 11.4 77.2 133. 70.9 128. 48.6 90.7 63.6 110. 48.9 84.5 40.9 86.5 32.8 79.5 35.9 92.2 32.0 85.6 30.8 96.7 32.3 121.

Plecotus auritus Pinna 0.29 0.60 21.3 62 60.6 91.1 57.5 78.8 53.1 68.6 47.7 61.5 50.5 65.8 47.8 82.5 43.9 79.9 40.4 75.1 35.9 64.0 31.5 67.4Pteropus lylei Pinna 15.6 31.8 20.3 127. 61.1 90.2 48.2 59.7 41.7 48.6 33.8 47.5 27.6 38.2 20.7 31.4 16.2 48.7 14.8 26.7 18.5 45.2 14.0 33.1

Rhinolophus acuminatus Noseleaf 6.66 12.8 61 96.6 68.8 120. 75.7 121. 70.9 107. 73.6 112. 65.1 105. 63.2 109. 53.7 93.9 51.5 63.0 49.8 112. 42.9 94.2Rhinolophus acuminatus Pinna 11.1 17.2 61 91.5 43.7 69.8 41.2 66.5 38.5 64.6 37.2 64.6 34.6 63.0 34.2 60.0 34.2 58.7 32.6 56.0 35.3 55.4 34.0 52.7Rhinolophus acuminatus Noseleaf 7.40 13.3 61 101. 76.4 134. 45.7 93.0 49.6 86.7 55.6 80.1 56.1 73.0 59.2 74.4 52.8 82.8 33.5 73.2 32.5 150. 37.1 59.3Rhinolophus acuminatus Pinna 11.5 17.8 61 91.5 41.4 53.5 43.8 53.1 39.2 52.2 38.6 51.0 39.0 47.4 34.6 45.9 36.9 45.8 32.3 47.6 36.0 45.8 33.7 45.2

Rhinolophus affinis Pinna 12.8 20.8 71.1 90 38.2 48.0 38.6 45.7 38.1 44.7 38.1 47.7 38.9 44.0 36.8 45.1 37.4 44.3 35.7 39.6 34.5 41.2 33.7 41.1Rhinolophus celebensis Noseleaf 4.91 11.8 111. 128. 48.0 98.9 46.8 103. 47.4 106. 47.1 105. 46.7 104. 38.6 97.5 41.6 105. 42.6 110. 42.0 108. 41.6 106.

Rhinolophus denti Noseleaf 8.97 15.4 58.6 88.7 48.3 66.0 48.1 60.7 45.7 59.9 43.7 56.7 41.9 55.8 37.3 55.5 38.0 55.9 35.5 51.7 35.0 49.5 34.7 49.0Rhinolophus ferrumequinum Noseleaf 10.4 16.4 58.6 88.7 53.9 56.2 50.3 55.1 48.9 51.6 46.1 50.2 44.6 48.6 39.8 46.9 38.9 45.0 36.3 44.8 34.3 42.8 34.0 43.3Rhinolophus ferrumequinum Pinna 10.2 15.6 58.6 88.7 47.6 60.5 46.3 52.8 44.7 52.2 43.2 48.0 40.6 44.0 38.6 42.4 37.2 41.9 34.6 38.9 33.4 40.1 31.2 38.8Rhinolophus ferrumequinum Pinna 6.89 11.8 58.6 88.7 78.3 136. 68.1 113. 79.9 130. 71.3 115. 68.5 95.2 61.0 75.6 52.0 67.4 46.3 64.1 49.0 64.9 50.5 68.3

Rhinolophus landeri Noseleaf 11.3 16.6 58.6 88.7 49.2 62.5 50.7 59.8 42.9 58.4 44.0 54.6 43.0 52.6 36.6 50.8 42.1 46.1 37.0 42.8 38.0 51.0 35.6 40.9Rhinolophus luctus Pinna 6.03 10.0 83.3 113. 79.9 113. 83.7 104. 75.6 99.3 65.7 95.8 65.3 91.2 67.3 83.0 71.2 83.3 65.4 76.5 51.2 68.8 51.4 67.7Rhinolophus luctus Noseleaf 5716 1000 73.2 84.4 41.6 68.2 42.2 62.6 42.5 57.5 43.9 59.0 67.1 96.2 62.6 96.5 63.6 95.3 44.2 98.0 42.7 131. 56.2 120.

Rhinolophus macrotis Pinna 11.5 20.0 73.2 84.4 32.5 51.1 31.3 53.6 29.3 54.9 31.2 56.7 28.6 50.6 30.9 46.7 31.5 55.9 32.9 49.4 29.4 47.7 27.8 49.7Rhinolophus macrotis Noseleaf 9.71 18.4 73.2 84.4 29.0 46.8 28.5 47.6 26.7 48.9 27.5 47.7 27.6 45.2 24.7 44.6 23.1 50.0 23.8 46.7 23.9 44.4 25.2 44.6Rhinolophus macrotis Noseleaf 5.21 8.97 106. 111. 48.4 55.9 55.5 62.6 40.2 53.5 53.8 60.5 42.8 53.7 45.3 53.5 42.3 57.6 44.5 52.0 42.6 51.3 49.1 53.7

Rhinolophus malayanus Pinna 19.7 31.7 33.1 43.3 39.9 54.9 41.2 53.5 37.7 53.1 37.7 51.9 37.7 48.7 35.8 48.0 34.8 45.7 34.2 46.6 35.1 47.0 33.2 43.2Rhinolophus malayanus Pinna 2536 7000 33.1 43.3 62.3 71.1 60.1 69.5 56.2 66.8 55.2 66.9 56.2 71.2 56.6 104. 48.3 90.4 42.3 96.0 37.4 97.4 38.3 135.Rhinolophus marshalli Noseleaf 10.0 16.2 48 54.8 51.5 88.4 50.2 90.2 48.2 87.4 47.0 90.9 46.6 94.6 46.4 99.9 43.6 101. 44.3 93.7 42.0 97.2 42.0 94.9Rhinolophus mehelyi Noseleaf 5.99 12.7 48 54.8 95.6 124. 91.8 119. 88.8 116. 85.5 114. 82.5 112. 80.1 110. 77.9 107. 71.8 95.4 70.3 104. 69.4 102.Rhinolophus mehelyi Noseleaf 6.82 13.3 48 54.8 77.2 111. 74.8 107. 72.4 102. 70.9 99.5 69.3 99.2 68.0 99.3 67.2 98.7 66.1 98.0 64.8 96.6 64.3 95.7Rhinolophus mehelyi Noseleaf 9.21 13.2 74.2 91.5 42.5 66.5 41.5 66.0 41.7 67.1 41.6 68.7 40.7 68.4 39.4 67.9 38.5 68.9 38.6 72.1 40.8 76.5 44.9 77.5Rhinolophus pearsoni Pinna 17.9 24.2 39.8 43 44.2 52.1 43.7 51.8 43.4 51.4 43.0 50.4 42.3 49.4 41.8 48.4 41.1 47.3 40.3 46.8 39.5 46.6 39.1 46.6Rhinolophus pearsoni Noseleaf 8.01 12.9 39.8 43 67.1 104. 67.4 105. 67.9 107. 68.6 108. 69.1 109. 69.8 110. 69.9 111. 70.3 110. 70.5 110. 70.4 109.Rhinolophus pearsoni Pinna 6.25 12.4 101. 110. 31.7 69.9 30.8 74.5 31.4 78.3 32.1 82.0 34.0 110. 42.5 129. 40.4 132. 39.3 126. 39.4 130. 40.9 132.Rhinolophus pearsoni Noseleaf 6.15 11.8 101. 110. 33.9 56.9 33.8 54.5 33.6 51.6 33.6 49.2 33.5 47.3 33.8 45.7 34.4 44.6 35.3 44.2 36.2 45.9 36.7 47.4Rhinolophus pusillus Pinna 5.67 8.30 101. 110. 49.2 56.3 48.9 56.7 49.3 57.9 48.4 58.8 46.9 59.0 45.5 59.7 44.1 65.3 42.7 70.1 42.1 70.3 41.3 69.0Rhinolophus pusillus Noseleaf 13.7 22.5 58.6 71.2 34.3 47.2 33.7 46.8 33.2 48.6 34.4 50.9 34.4 48.6 33.2 46.3 33.9 46.7 33.7 45.9 32.9 46.3 34.6 50.2Rhinolophus pusillus Pinna 6.18 15.6 58.6 71.2 40.7 102. 43.2 96.0 46.1 83.8 51.6 76.0 48.4 93.7 46.0 68.0 45.7 60.7 45.0 59.3 46.5 57.7 33.6 89.5Rhinolophus pusillus Noseleaf 15.9 26.9 58.6 71.2 30.3 48.5 33.7 38.1 32.2 39.2 32.4 37.8 32.4 37.3 30.2 35.2 30.9 37.3 30.3 37.8 30.1 37.5 29.6 38.5

Rhinolophus roux Pinna 11.0 18.1 58.6 71.2 45.8 82.9 57.1 85.5 54.6 76.5 51.7 72.6 48.3 71.8 45.0 70.5 43.2 68.9 41.8 70.4 40.5 74.9 39.2 80.9Rhinolophus roux Pinna 9038 1484 102 113. 39.3 52.3 38.8 54.0 37.6 53.9 35.8 51.4 34.7 49.6 33.8 48.1 34.1 47.6 34.2 48.2 34.0 47.9 33.7 46.8

Rhinolophus sedulus Noseleaf 5.05 11.0 102 113. 43.6 51.0 43.4 49.7 43.2 49.0 43.0 48.3 43.2 48.1 44.3 49.7 46.1 52.2 47.1 54.3 47.9 55.7 49.2 56.1Rhinolophus sedulus Noseleaf 10.3 16.7 102 113. 33.1 47.3 34.3 47.1 34.3 46.1 33.4 45.7 32.5 45.6 31.5 45.5 30.1 45.9 30.1 47.7 30.8 44.9 31.4 43.2Rhinolophus sinicus Pinna 5.94 11.0 102 113. 60.7 83.6 54.5 84.3 52.8 84.8 53.2 83.5 54.6 80.9 55.4 80.1 54.0 75.8 51.8 71.1 50.5 67.1 49.7 63.9Rhinolophus sinicus Pinna 1285 1702 35.6 66.1 60.9 80.1 59.9 111. 61.6 79.3 58.7 67.2 53.7 57.7 50.3 58.9 45.6 52.9 46.1 52.0 43.5 50.5 40.8 48.6

Rhinolophus sp. Pinna 1060 1533 35.6 66.1 118. 186. 109. 180. 101. 170. 95.6 145. 91.0 125. 86.3 114. 81.5 108. 77.1 103. 73.2 98.7 69.2 94.9Rhinolophus sp. Pinna 4.67 14.3 63.0 77.3 51.1 64.9 50.4 61.7 47.4 55.8 45.5 55.9 47.4 56.7 48.2 53.8 48.0 55.2 48.3 58.7 46.6 59.6 46.5 57.9Rhinolophus sp. Pinna 7.40 10.9 63.0 77.3 46.7 70.2 47.6 82.6 53.3 81.5 47.6 71.6 41.3 65.1 37.2 67.5 37.2 73.3 40.2 77.1 42.9 81.2 43.0 83.8Rhinolophus sp. Pinna 9.62 18.4 74.6 88.7 40.5 50.9 39.9 50.6 40.4 49.4 40.2 49.0 38.5 48.4 36.0 49.3 34.8 52.8 36.0 52.6 37.5 48.1 36.5 47.4Rhinolophus sp. Pinna 11.5 17.9 74.6 88.7 36.4 39.9 37.8 42.5 36.7 41.5 34.1 39.7 33.7 38.3 34.0 39.0 36.5 41.1 36.2 40.2 33.4 38.3 33.8 36.5

Rhinolophus thomasi Noseleaf 7.32 13.4 77.2 87.5 73.3 116. 54.5 116. 43.8 116. 40.3 111. 38.5 112. 37.4 113. 36.9 118. 54.0 121. 53.9 115. 56.6 107.Rhinolophus thomasi Pinna 8.49 12.1 77.2 87.5 51.7 64.0 50.8 63.6 50.3 64.5 49.3 65.1 48.4 64.6 48.4 63.4 48.5 62.0 47.6 59.9 47.0 57.7 46.5 58.4Rhinolophus thomasi Pinna 10.5 13.6 77.2 87.5 39.6 60.0 38.9 57.9 38.7 56.8 38.9 57.3 38.7 57.9 38.4 57.9 37.3 57.6 36.9 56.5 36.9 55.6 37.1 55.1Rhinonicteris aurantia Noseleaf 10.7 16.3 58.6 88.7 51.2 56.8 48.5 54.5 46.9 52.5 43.5 50.1 40.7 49.7 39.5 47.3 36.6 46.7 38.8 47.1 35.9 44.6 36.0 42.8Scotomanes ornatus Pinna 9.10 18.3 25.4 81.3 82.1 119. 74.3 90.2 63.1 77.9 53.8 69.2 29.3 99.7 35.1 74.7 33.7 68.5 27.8 67.8 39.9 92.1 28.8 55.8Scotomanes ornatus Pinna 9.23 17.3 25.4 81.3 89.0 119. 82.1 106. 69.9 91.9 53.3 81.4 34.1 88.2 43.8 100. 34.4 83.3 28.3 59.2 23.8 62.3 23.5 59.5Scotophilus kuhlii Pinna 7.13 12.3 36.7 88.6 74.1 112. 69.3 101. 62.9 87.0 56.4 81.2 54.8 75.2 56.3 76.5 49.1 69.2 39.5 70.8 32.2 76.0 33.2 47.3Scotophilus kuhlii Pinna 6.89 12.8 36.7 88.6 73.5 107. 64.5 90.8 60.7 80.8 50.4 78.2 30.5 97.0 38.0 91.5 32.3 114. 42.0 100. 31.6 69.3 25.5 57.7

Scotophilus sp. Pinna 7.57 13.0 36.7 88.6 76.0 101. 81.5 99.1 67.5 82.1 52.9 70.4 58.3 72.2 65.0 84.0 34.9 90.6 28.5 90.3 27.8 99.6 24.8 73.3Scotophilus sp. Pinna 7.15 13.6 36.7 88.6 79.2 109. 66.1 94.1 59.2 78.9 58.6 74.4 61.6 77.3 44.3 68.5 34.1 73.7 28.0 71.4 27.5 71.6 26.4 52.2

Sphaeronycteris toxophyllum Noseleaf 11.3 16.1 38.4 109. 131. 201. 77.0 208. 51.8 128. 80.9 145. 56.4 102. 53.8 80.4 48.2 98.9 47.1 80.1 39.8 75.5 54.2 73.7Tadarida teniotis Pinna 15.3 27.1 5.05 15.2 361 361 202. 284. 155. 165. 134. 146. 118. 135. 103. 130. 101. 129. 95.2 119. 81.5 103. 76.3 102.

Taphozous melanopogon Pinna 12.7 19.6 8.44 65.6 361 361 116. 139. 84.7 110. 70.7 89.3 64.7 79.8 61.3 71.4 55.8 66.3 58.2 79.2 38.5 70.7 30.0 63.4Taphozous melanopogon Pinna 8.74 16.1 8.44 65.6 361 361 122. 143. 87.3 123. 72.1 101. 61.5 83.7 57.3 75.6 58.6 97.1 64.3 77.9 34.1 61.4 29.0 58.6Taphozous melanopogon Pinna 11.4 18.7 8.44 65.6 273. 361 124. 156. 88.6 111. 71.5 92.3 66.4 81.7 64.7 78.9 52.4 70.5 55.0 87.1 35.8 74.1 29.5 63.9Taphozous melanopogon Pinna 11.7 19.2 8.44 65.6 280. 361 109. 141. 80.4 108. 72.1 91.1 68.4 82.4 65.6 76.6 50.6 114. 35.5 74.7 36.4 73.5 27.5 68.5

Trachops cirrhosus Noseleaf 5.50 12.9 50.8 101. 59.5 218. 69.8 105. 52.1 128. 70.1 106. 49.4 85.8 48.5 105. 49.0 100. 43.2 86.4 37.4 74.6 36.1 61.9Trachops cirrhosus Noseleaf 6.30 13.4 50.8 101. 68.9 171. 69.4 142. 56.2 112. 57.5 136. 47.1 123. 46.0 144. 40.3 135. 40.4 121. 46.0 127. 43.1 116.Triaenops persicus Noseleaf 8.75 13.2 73.2 90 61.1 88.7 60.6 85.6 61.2 91.7 56.7 81.4 55.0 76.6 55.7 72.1 59.1 70.6 58.6 77.0 56.0 79.8 52.0 77.8Triaenops persicus Noseleaf 8.86 13.6 73.2 90 51.5 65.9 48.5 59.8 46.7 60.2 45.6 63.1 45.6 69.5 48.5 69.8 51.6 72.5 56.9 74.5 56.2 74.9 50.6 85.2

Vampyrum spectrum Noseleaf 8.63 15.0 71.2 91.5 30.7 112. 34.1 120. 39.3 134. 37.6 101. 36.9 128. 36.2 125. 42.3 137. 38.3 133. 40.0 127. 34.8 134.