Tomographic reconstruction of air pollutants: evaluation of measurement geometries

Tomographic reconstruction of airpollutants: evaluation of measurement geometries

Lori A. Todd and Runa Bhattacharyya

We use numerical studies to evaluate 13 novel optical remote-sensing geometries for tomographicallyreconstructing chemical pollutants in air. We simulate the imaging process from data acquisition toreconstruction using a battery of test images. We evaluate the reconstructions generated by eachgeometry for locating chemical leaks, identifying plumes, and evaluating human chemical exposures.This approach uses three numerical image-quality measures for both static and time-varying concen-tration maps. Visual evaluation is the most useful method of evaluating the geometries. The numer-ical measures are not always consistent with one another or with the visual evaluation. This researchdemonstrates the feasibility of using geometries with only a few detectors for tomographic imaging of airpollutants. © 1997 Optical Society of America

1. Introduction

At the present time air pollutants are monitored bydevices that collect contaminants at isolated points inspace and measure concentrations that are averagedover several hours. Although multiple measure-ments are obtained over an area, the number of lo-cations monitored concurrently is limited, and acomplete profile of air contaminant concentrationsand flows cannot be constructed. In addition, sam-pling is usually performed infrequently, and informa-tion about daily, weekly, or monthly variability islost. This type of sampling leads to poor spatial andtemporal resolution of contaminant species and con-centrations. Thus insufficient data are currentlyused to evaluate the impact of industrial source emis-sions, indoor air contaminants, and air pollution onthe health of the community.

Application of computed tomography ~CT! tech-niques to air pollution and industrial-source emissionmonitoring could enable reconstruction of spatiallyand temporally resolved pollutant distribution maps.These techniques provide a powerful tool for visual-izing air contaminant species, concentrations, andflows indoors in industry or outdoors in the commu-

The authors are with the Department of Environmental Sci-ences and Engineering, University of North Carolina at ChapelHill, Chapel Hill, North Carolina 27599.

Received 24 January 1996; revised manuscript received 6 May1997.

0003-6935y97y307678-11$10.00y0© 1997 Optical Society of America

7678 APPLIED OPTICS y Vol. 36, No. 30 y 20 October 1997

nity. Use of CT for measuring air pollution over acity, with a laser and a circle of mirrors, was proposedin the late 1970’s.1,2 In 1990 we were the first topropose using CT to measure human exposures toindoor industrial emissions.3

For CT imaging of air contaminants we employ adata-acquisition system that uses a scanning, active,open-path Fourier-transform IR spectrometer to senda beam of IR light across an open space to a corner-cube retroreflector, which then returns the beam di-rectly to its point of origin. As the beam traversesair, IR light is absorbed by contaminants at specificwavelengths. The reduction in light intensity re-corded by the detector is converted into a concentra-tion that represents an average over the optical path.The spectrometer then rotates to a new position,sends out another beam of IR light, and obtains an-other measurement. To obtain larger spatial cover-age, one can use mirrors to reflect IR rays across aspace to a retroreflector. The retroreflector then re-turns the ray to the mirror and then to the open-pathFourier-transform IR spectrometer. The numberand placement of the spectrometers, mirrors, and re-troreflectors, including a description of each IRbeam’s path, is called the geometry of the system.

In theory, any remote-sensing device could beused, such as a tunable diode laser. However, theopen-path Fourier-transform IR spectrometer hastwo advantages: ~1! simultaneous scanning ofwavelengths in the mid-IR region that enables a widerange of multiple chemicals to be detected at lowlimits of detection ~parts per billion! and ~2! a loweye-safety hazard.4 The main disadvantages are

water vapor and carbon dioxide interference in partof the spectrum and the difficulty in obtaining anappropriate background measurement that is free oftarget chemicals. The recent development in thelate 1980’s of this type of optical remote-sensing~ORS! instrumentation for commercial use makes to-mographic imaging of ambient air contaminants areal possibility.5–7

The path concentrations from the remote-sensingdetector can be combined using CT to reconstruct aconcentration distribution map over the area coveredby optical beams. Concentration maps are a set ofconcentration values at points on a two-dimensionalgrid. These maps can be thought of as images, inwhich the value at each pixel is the concentration atthat point in space. CT reconstruction of environ-mental contaminants has several challenges: ~1!the size of the area under reconstruction is large; ~2!air contaminant concentrations are not stationary;and ~3! buildings, equipment, and people all restrictthe number and symmetry of available line-of-sightmeasurements ~projections!. When these con-straints are placed on the ORS measurement geom-etry this can translate into insufficient andyor noisymeasurements, a limited number of views and rangeof angles, and, ultimately, artifacts in the recon-structed image.

We used computer simulations to investigate thefeasibility of CT for measuring industrial-sourceemissions; we did this by developing appropriate testimages8 and geometries9 and by evaluating iterativereconstruction algorithms.10 The purpose of this re-search was to use computer simulations to evaluate avariety of novel ORS geometries applicable to airmonitoring. A previous study evaluated reconstruc-tions from geometries with two to four detectors anda very large number ~320! of fanlike rays; these ge-ometries were combined with the iterative algorithmalgebraic reconstruction technique 3 and applied tostatic test images.9 For a given geometry using 50%fewer rays did not significantly decrease reconstruc-tion accuracy. In another study 120 total rays werefound to be an optimum number when one uses afour-detector geometry to reconstruct concentrationprofiles that change over space and time.8

For this study we designed geometries that as-sumed clear lines of sight throughout the area sam-pled, had achievable instrument sample times, andminimized the number of optical rays. These con-straints resulted in sparse and unequal samplingover the area of interest. We designed geometriesthat incorporated parallel rays, fanlike beams, andrays reflected off mirrors. Geometries included asmany as four scanning ORS detectors that createdfanlike beams with a 90–360° sweep. To mimic thecurrent design of ORS detectors, each ray of the fanwas taken sequentially, not simultaneously. Geom-etries with less than three detectors used mirrors toreflect the beam through another part of the image toa retroreflector.

Our purpose here was to develop a method of usingcomputer simulations to design and evaluate ORS

geometries for imaging air pollutants and to test 13simple geometries. In particular, we designed ge-ometries incorporating rays that were reflectedthrough the image. The entire imaging process wassimulated, from data acquisition to image reconstruc-tion, using a battery of test images. We evaluatedthese geometries based on how successfully these re-constructions were used to perform specifiedtasks.11,12 This approach involved evaluating a di-versity of appropriate test images, variations in thenumber of optical rays, and several different mea-sures of image quality. We used computer-generated test images because appropriate field datadid not exist; test data included both static and time-varying images. We evaluated reconstructionsbased on how well they could be used to quantifychemical exposures ~chemical concentrations at thepeaks!, identify chemical source locations, and delin-eate plume shapes. We chose this approach becausethe adoption of CT for environmental monitoring de-pends on the ability of scientists to use the recon-structed images to answer specific questions: ~1!What are the quantities of chemicals leaking from anindustrial process or emitted from an industry? ~2!From where are chemicals leaking? ~3! How muchdo people potentially inhale? and ~4! What are thechemical dispersion patterns in air?

2. Method

A. Test Concentration Maps

To evaluate the ORS geometries, we generated twotypes of test concentration image on a 40 by 40 grid torepresent a wide variety of spatial concentration pro-files.9,10 The first type of test image included 120static concentration profiles; bivariate normal distri-butions were used to model concentration profiles,and each concentration map had from one to six ran-domly located concentration peaks with maximumpeak heights of 500 ppm and minimum peak diame-ters of four square grid cells.8 This can representconcentration emissions that range from a medium-sized leak to a large evaporative source. Static im-ages can provide only a best-case evaluation ofgeometries because actual concentrations of chemi-cals in air are in flux. Therefore we created testimages that simulated the generation and movementof contaminants in air over time and space.8 Wegenerated these time-series maps using a two-dimensional advection–diffusion equation with a bi-variate Gaussian source.13 Two sets of time serieswere used. For each set we generated 720 originalmaps to simulate a 3-h time period; each map repre-sented the change in concentration in any grid cellafter 15 s. One time series modeled the movementand decay of a large single-contaminant source; thesecond set modeled the generation and decay of threesmaller contaminant sources in relatively stagnantair. The concentration and diameter of the smallestpeak in the time-series maps were four square gridcells. We selected these two time series from a li-

20 October 1997 y Vol. 36, No. 30 y APPLIED OPTICS 7679

brary of 15 maps that were evaluated in a previousstudy.8

B. Optical Remote-Sensing Geometries

We designed 13 geometries, which had from one tofour ORS detectors, on a 20 by 20 grid. This gridcould represent, for example, a 40 ft by 40 ft ~3 m by13 m! room with a 4-ft2 ~0.37-m2! pixel size. Fivegeometries used a single ORS detector in the center ofthe grid, which rotated 360° @see Figs. 1~a!–1~e!#. Toobtain intersecting rays, we ensured that all geome-tries used mirrors to reflect rays. Geometry 1sRef~one source, reflected rays!, Fig. 1~a!, had beams thatwere directed from the center of the grid to flat mir-rors on four sides of the grid. These mirrors re-flected the beams to retroreflectors, which thenreturned the beams directly to the ORS detector.The rays were reflected off the mirrors at angles thatcreated a virtual parallel-projection geometry withthree views ~0°, 45°, and 90°!. The first legs of thereflected rays were not parallel. To reduce the effectof these nonparallel segments on reconstruction qual-ity, we set up geometry 1sRefE, Fig. 1~b!, to use anextra set of beams that were directed to retroreflec-tors placed adjacent to each mirror; these beams weredirected back to the ORS detector. These extra rays,which detected concentrations similar to the first legsof the reflected rays, were used to cancel the contri-bution of the nonparallel ray segments to the recon-structions. Geometry 1sRefE was identical togeometry 1sRef, with the addition of the extra raysegments from the ORS detector to retroreflectorsplaced next to mirrors. Therefore 1sRefE had twiceas many beams as 1sRef. Geometry 1sRef4Cor ~onesource, reflected rays, four retroreflectors in the cor-ners of the grid!, Fig. 1~c!, had beams that were di-rected from the center of the grid to flat mirrors onfour sides of the grid, which then reflected the beams toone of the four corners to a retroreflector. Thus asingle ORS detector was used to create four virtualscanners with fanlike beams. Geometry 1sRef4CorE~one source, reflected rays, four retroreflectors in thecorners of the grid, extra rays!, Fig. 1~d!, was similarto 1sRef4Cor, except that an additional retroreflectorwas placed adjacent to each mirror, as in geometry1sRefE. This doubled the number of total rays used.Geometry 1sRef4Sid ~one source, reflected rays, fourretroreflectors on the sides of the grid!, Fig. 1~e!, wassimilar to 1sRef4Cor; however, the beams were re-flected to retroreflectors placed in the middle of eachside of the grid. We first evaluated the geometries inFigs. 1~a!, 1~c!, and 1~e! using a total of 120 rays, andwe evaluated the geometries in Fig. 1 with the extrarays @Figs. 1~b! and 1~d!# using 240 rays ~120 reflectedrays and 120 straight rays!. We then further eval-uated the best geometries to examine the effect ofincreased ray density on reconstruction quality using20% additional rays ~a total of 144 or 288 rays!.

Four geometries used two ORS detectors @see Figs.1~f !–1~i!#. Geometries 2sCor and 2sSid, Figs. 1~f !and 1~h!, had ORS detectors in adjacent corners or onthe sides of the grid that directed fanlike beams to-


ward retroreflectors. To create parallel projections,we developed geometries 2sCorRef and 2sSidRef,Figs. 1~g! and 1~i!. They were similar to geometries2sCor and 2sSid, except that the retroreflectors used

Fig. 1. Each geometry is illustrated by a pair of diagrams. Thefirst diagram of each pair shows a few rays, and the second dia-gram shows the overall pattern of the rays. A solid box indicatesa mirror, and a stippled box indicates a retroreflector. Single-detector geometries: ~a! 1sRef, ~b! 1sRefE, ~c! 1sRef4Cor ~d!1sRef4CorE, and ~e! 1sRef4Sid. Two-detector geometries: ~f !2sCor, ~g! 2sCorRef, ~h! 2sSid, and ~i! 2sSidRef. Three-detectorgeometries: ~j! 3sCor and ~k! 3sSid. Four-detector geometries:~l! 4sCor and ~m! 4sSid.

previously for one of the detectors were replaced withflat mirrors, which then reflected the beams acrossthe grid to retroreflectors to create two parallel pro-jections at 0° and 90°. We initially evaluated thesefour geometries using 120 rays ~60 per detector!. Wethen further evaluated the best geometry to examinethe effect of increased ray density on reconstructionquality using 20% additional rays ~72 per detector!.

Two geometries used three ORS detectors @seeFigs. 1~j! and 1~k!#. Geometries 3sCor and 3sSidhad ORS detectors in the corners and sides of thegrid, respectively, and created fanlike beams directedtoward retroreflectors. We initially evaluated geom-etries 3sCor and 3sSid using 120 rays ~40 rays perdetector!. We then further evaluated the best geom-etry to examine the effect of increased ray density onreconstruction quality using 20% additional rays ~48rays per detector!. Two geometries used four ORSdetectors @see Figs. 1~l! and 1~m!#. Geometries4sCor and 4sSid had ORS detectors in the corners orsides of the grid, respectively, and created fanlikebeams directed toward retroreflectors. We initiallyevaluated geometries 4sCor and 4sSid using 120 rays~30 rays per detector!. We then further evaluatedthe best geometry to examine the effect of increasedray density on reconstruction quality using 20% ad-ditional rays ~38 rays per detector!.

We evaluated all 13 geometries using the same setof 120 static-test maps. We further evaluated a sub-set of geometries from each group using the two setsof time-series maps. When using the time-seriestest maps with a geometry that had more than onedetector, we assumed that all detectors operated si-multaneously but that the individual rays in eachdetector were taken sequentially. For the time-series maps it was also assumed that each ray re-quired a minimum of 15 s per measurement; this ratewas achievable in practice. Thus, for a total of 120rays, it would require 7.5, 10, 15, and 30 min to scanan entire area once using four-, three-, two-, and one-detector geometries, respectively. We also per-formed simulations to evaluate the differentgeometries with equal times allowed to scan an entirearea.

C. Reconstruction Algorithm

We chose an iterative reconstruction method for thisstudy because iterative techniques allow flexibility inthe measurement geometry, perform somewhat bet-ter than other types of algorithms when there is mea-surement noise and limited data, and allowincorporation of a priori information.8,10,14,15 Theseattributes are important for reconstructing chemicalconcentrations in which the quality and quantity ofusable data are limited, such as in the application ofCT to environmental monitoring. We selected themaximum likelihood with expectation maximization~MLEM! algorithm16,17 for this study because recon-structions performed by MLEM were found to be sta-tistically superior to other iterative techniques weevaluated for the air pollution application. Our lab-oratory has been evaluating a variety of iterative

algorithms, including MLEM, ART, simultaneous it-erative reconstruction technique ~SIRT!, and simulta-neous algebraic reconstruction technique ~SART!.8,10

MLEM is a simultaneous technique; at each itera-tion all pixels are corrected simultaneously afterreading an entire set of ray sum data. We used 50iterations for all reconstructions. Using the MLEMalgorithm, we estimated the concentration distribu-tion by maximizing the log-likelihood function, whichis given by Eq. ~1!. The likelihood strictly increasesat each step unless it is at a maximum; therefore allthe cells have positive values of concentration:

ln L~C! 5 S@2Stijcj 1 pi ln~Stijcj! 2 ln~pi!#, (1)

where L~C! is the likelihood of generating the imageC, tij is the transfer matrix from image pixel j to theset of parallel projections i, cj is the concentration atpixel j after the nth iteration, pi is the ray sum for theith set of projections, i is the number of rays ~1 to M!,and j is the number of pixels ~1 to N2!.

D. Evaluating Reconstruction Quality

We evaluated geometries by numerically and visuallycomparing reconstructed images with original im-ages. We developed a measure of peak exposure er-ror to reflect the error in estimating the averageconcentration of a chemical inhaled by a person.Most regulations of hazardous air pollutants ~for thegeneral public and industrial workers! are based onaverages of concentrations over time. We comparedconcentrations for a footprint of 5 by 5 pixels over thepeaks in the original image with concentrations forthe same locations in the reconstructed image.3This could represent the area within which a personmay travel when stationed adjacent to a chemicalsource. For the time-series maps we calculated anaverage peak exposure error for the entire simulated3-h period @see Eq. ~2!#:

peak exposure error 5

(time

(space

cj* 2 (time

(space

cj

(time

(space

cj*3 100,

(2)

where time varies from the first time-series map tothe 720th map, space represents the 5 by 5 cell win-dow around a peak, cj* is the concentration of the jthcell in the test image, and cj is the concentration inthe jth cell in the reconstructed image.

We developed a second-measure peak location er-ror to reflect how accurately a reconstructed mappinpoints the location of a chemical leak or emissionsource. It was the rms difference in the location ofthe peak in the original and reconstructed image @seeEq. ~3!#.12 For example, for a 20 m by 20 m area ona 20 by 20 grid a location error of 2 would be equiv-alent to a distance of 2 m. The significance of thiserror relates to the level of accuracy required to pin-point a chemical for a specific application. For ex-


ample, only a coarse approximation would berequired to detect leaks from industrial processes:

peak location error 5 @~x 2 x*!2 1 ~y 2 y*!2#,1y2 (3)

where x is the x coordinate of the peak location in thereconstructed image, x* is the x coordinate of thepeak location in the test map, y is the y coordinate ofthe peak location in the reconstructed image, and y*is the y coordinate of the peak location in the testmap. A third, conventional measure, nearness, de-scribes the discrepancy between the original concen-tration map and the reconstructed concentrationmap18,19:

nearness 5 3 (j51

N2

~cj* 2 cj!2

(j51

N2

~cj* 2 cavg*!241y2

, (4)

where cj* is the true value for the jth cell in the map,cj is the estimated value for the jth cell in the map,and cavg* is the mean true concentration in the map.

Finally, we visually compared surface plots of thereconstructed two-dimensional maps with the origi-nal maps with respect to peak shape, peak height,and manifestation of artifacts. Artifacts includedunpredictable irregularities that resembled noise,patterns such as streaking, and false concentrationpeaks. Geometries were evaluated for their abilityto eliminate certain artifacts. Visual assessment isimportant; in practice, concentration maps are linkedtogether and visually examined to determine peaklocation and peak concentration. We generated sur-face plots using Spyglass Transform, Format, andView ~Spyglass, Inc., Champaign, Ill.!. We linkedmaps together to animate the 3-h simulated sampleperiod for the time-series test maps.

3. Results and Discussion

A. Static Maps

Based on nearness, peak exposure error, and peaklocation error, reconstructions improved as the num-ber of ORS detectors increased from one to four, givenequal numbers of rays in each geometry number ~seeTable 1!. Given the same number of total rays, in-creasing the number of detectors resulted in betterimage quality; more detectors resulted in an in-creased number of angles and views. Given thesame number of rays per detector, geometries withrays that scanned 180° were usually superior to ge-ometries with rays that scanned 90°.

When 20% more rays were added to all the geom-etries, the ranking of the geometries did not change;however, nearness, peak exposure error, peak loca-tion errors, and the number of artifacts in the recon-structions decreased ~improved!. When reflectedrays were used to create a pseudoparallel projectionin geometries with one and two detectors, reconstruc-tion accuracy improved based on both quantitative


and qualitative measures. Qualitatively, the num-ber of artifacts diminished.

When the number of total rays was doubled in twoof the single-detector geometries, to compensate forthe effect of reflected rays, both nearness and peakerror decreased ~improved! dramatically to withinthe range seen in geometries using three and fourdetectors. Visually, reconstructions using the1sRefE and 4sCor geometries were close in appear-ance; however, the 1sRefE, which used double thenumber of rays, usually had fewer artifacts. Usingthe static maps, we ranked the geometries from bestto worst as the following: 1sRefE and 4sCor, 3sSid,and 1sRef and 2sSidRef. Specific results for differ-ent geometries using the same number of detectorsare provided below.

1. Geometries With a Single Optical RemoteSensing DetectorWithin the geometries using a single detector, basedon nearness, peak exposure error, and peak locationerror, the 1sRefE geometry ~parallel projections withextra rays! gave the best reconstructions ~see Table1!. Among the single-detector geometries that usedthe same number of rays, the 1sRef geometry gavethe best reconstructions. This geometry requiresthe use of the same number of mirrors as rays toreflect the rays around the space and mimic aparallel-projection geometry with three angles. Theranking of all the single-detector geometries was thesame whether using nearness or peak exposure error~see Table 1!. The average mean peak exposure er-rors ranged from 7 to 34%.

In terms of location error, for the best geometry~1sRefE! the points of highest concentrations of peakswere located within a mean error of 0.8 pixels fromthe points of highest concentrations of actual peaks.All geometries reconstructed peaks within a meanlocation error of 2.0 pixels of the actual locations.

Using visual evaluation of the reconstructed maps,

Table 1. Nearness and Peak Error Results for Static-Test Maps

Configuration NearnessPeak Exposure

Error

1 Detector1sRefE 0.28 7.321sRef4CorE 0.34 13.251sRef 0.37 13.961sRef4Cor 0.51 28.231sRef4Sid 0.68 33.27

2 Detectors2sSidRef 0.37 15.352sCorRef 0.40 17.792sSid 0.49 27.012sCor 0.54 33.61

3 Detectors3sSid 0.34 10.113sCor 0.37 15.68

4 Detectors4sSid 0.32 7.134sCor 0.30 8.48

we found that ranking the geometries was some-what different from using quantitative statistics.The geometries that had extra rays ~1sRefE and1sRef4CorE! reconstructed maps with as many as sixpeaks with the most accurate peak shapes, heights,and locations and the fewest artifacts @see Figs. 2~b!–2~f ! and 3~b!–3~f !#. In contrast with the similarity ofthe nearness and peak exposure error measures, vi-sually the 1sRef4CorE geometry was far superior tothe 1sRef. The use of extra rays adjacent to thereflected rays greatly improved reconstruction qual-ity and removed many artifacts. All the geometriescould reconstruct the relative locations of as many asthree peaks fairly well without many artifacts, unlessthe peaks were located near the detector. Peaks inthe center of the grid created artifacts that resem-bled smearing of concentration distributions. The1sRef4Cor and 1sRef4Sid geometries, which hadlarge, poorly sampled areas of the grid, had consid-erably shortened peak heights and a great number ofartifacts that resembled additional peaks and smearsalong the ray paths. Reconstructions of test mapsthat had multiple peaks with widely different concen-trations resulted in overestimated peak concentra-tions.

2. Geometries With Two Optical Remote SensingDetectorsWithin the geometries using two detectors, based onnearness, peak exposure error, peak location error,and visual evaluation, the geometries that used re-

Fig. 2. Static original and reconstructed test maps with six peaks.~a! Original map. Reconstructed maps: ~b! 1sRef, ~c! 1sRefE, ~d!1sRef4Cor, ~e! 1sRef4Sid, ~f ! 1sRef4CorE, ~g! 2sCor, ~h! 2sCorRef,~i! 2sSid, ~j! 2sSidRef, ~k! 3sCor, ~l! 3sSid, ~m! 4sCor, and ~n! 4sSid.

flected rays ~2sSidRef and 2sCorRef ! resulted in bet-ter reconstructions than the geometries that usedstraight rays ~2sSid and 2sCor! ~Table 1!. Peak ex-posure error was more sensitive than nearness to thecomplexity of the maps ~number of peaks!. Meanpeak exposure errors ranged from 15 to 34%. Thegeometries that used reflections reconstructed peakswithin a mean location error of 1.25 pixels of theactual peak locations; geometries without reflectionsreconstructed peaks within a mean location error of1.5 pixels. Geometries that used 180° fanlike beamswere superior to geometries that used 90° fanlikebeams ~side versus corner placement of detectors!.

Visually the relative locations and shapes of asmany as two peaks were reconstructed fairly wellusing all four geometries; however, peak height ac-curacy varied widely and was poorest for the geome-tries without reflections. Maps with three to sixpeaks were reconstructed with only fair success;peaks were smeared, false peaks were present, andpeak height accuracy was highly dependent on peaksize and location @see Figs. 2~g!–2~j! and 3~g!–3~j!#.The addition of reflections primarily improved thereconstruction of peak concentrations and did not sig-nificantly eliminate artifacts; however, the intensityof the artifacts decreased. For the geometries withdetectors in the corners, peaks were smeared alongthe rays coming from the detectors.

3. Geometries With Three Optical Remote SensingDetectorsWithin the geometries using three detectors, basedon nearness, peak exposure error, peak location er-

Fig. 3. Static original and reconstructed test maps with five peaks.~a! Original map. Reconstructed maps: ~b! 1sRef, ~c! 1sRefE, ~d!1sRef4Cor, ~e! 1sRef4Sid, ~f ! 1sRef4CorE, ~g! 2sCor, ~h! 2sCorRef, ~i!2sSid, ~j! 2sSidRef, ~k! 3sCor, ~l! 3sSid, ~m! 4sCor, and ~n! 4sSid.


ror, and visual evaluation, the geometry that used180° fanlike beams ~3sSid! gave the best reconstruc-tions ~Table 1!. Both geometries reconstructedpeaks within a mean location error of 1.0 pixel of theactual peak location. The mean peak exposure er-rors ranged from 10 to 16%. Visually the relativelocations and shapes of the peaks were reconstructedfairly well using both geometries for maps with asmany as four peaks. The more complicated the map~number of peaks!, the more artifacts were present;peaks were usually spread along the rays of the ge-ometry. The 3sCor geometry spread the concentra-tions radially from the corners, and the 3sSidgeometry spread them radially from the middle of thesides of the grid @see Figs. 2~k!, 2~l!, 3~k!, and 3~l!#.Overall, the 3sSid geometry produced maps withmore accurate peak heights and shapes and fewerartifacts than the 3sCor geometry.

4. Geometries With Four Optical RemoteSensing DetectorsNone of the four-detector geometries was obviouslysuperior to the other. Based on peak exposure error,the 4sSid geometry that used 180° fanlike beamsgave better reconstructions than the 4sCor geometry;based on nearness, the results were reversed ~seeTable 1!. Both geometries reconstructed peakswithin a mean location error of 0.8 pixels of the actualpeak locations. The mean peak exposure errorsranged from 7 to 9%. Visually the relative locationsand shapes of as many as six peaks were recon-structed reasonably well using both geometries; how-ever, artifacts with relatively low concentrationswere present in many maps @see Figs. 2~m!, 2~n!,3~m!, and 3~n!#. There were only small differencesin the reconstructions, primarily in the location andshape of artifacts. When peaks were near the cor-ners, the 4sCor geometry smeared the peaks alongthe lines of the rays. The 4sSid geometry had re-constructions with irregular artifacts that resemblednoise in many maps; when there were multiple peakswith large differences in concentrations, concentra-tions were overestimated. In contrast, concentra-tions were usually underestimated using the 4sCorgeometry.

B. Time-Series Maps: Comparison of the BestGeometries

Based on the results using the static maps, we fur-ther evaluated five geometries with two sets of time-series maps. Time-series maps provide a morerealistic representation of the flow of air contami-nants over time and space. Besides evaluating thespatial distribution of rays in the geometries, time-series maps also evaluate the effect of overall sam-pling time. Given the same number of rays, thegreater the number of detectors, the shorter the timerequired to sample an entire area once. With thestatic maps used, based on statistical measures andvisual evaluation, the ranking of the geometries wasthe following: 1sRefE and 4sCor, 3sSid, and 1sRefand 2sSidRef.


With the time-series maps used, based on nearness,the two-, three- and four-detector geometries that used120 rays and the single-detector geometry that used240 rays were similar to each other @see Figs. 4 and 5!.Mean nearness values for the geometries with two tofour detectors were also similar to the mean nearnessvalues obtained using the static maps. For the single-detector geometries nearness values were higher usingthe time-series maps than using the static maps.With the time-series maps used for geometries withthe same number of rays, average peak exposure er-rors were similar to errors found using the static mapsfor geometries with two or more detectors, and theywere at least three times higher for the geometry withone detector ~see Table 2!. For the geometry withdouble the number of rays ~1sRefE!, peak exposureerrors were similar to the static maps using themultiple-source time series and were significantlyhigher using the moving-peak time series. Peak lo-cation errors were highly variable for all the geome-tries and ranged from less than 1 to 4 pixels.

These results compare well with an experimental

Fig. 4. Variation of average nearness values for multiple-sourcetime-series test maps with geometry.

Fig. 5. Variation of average nearness values for moving-sourcetime-series test maps with geometry.

Table 2. Peak Exposure Errors for Time-Series Maps

Multiple-Source Time Series Moving-Source Time Series

120 Rays 144 Rays Same Timea 120 Rays 144 Rays Same Timea

1sRef 49.2 47.9 47.9 40.6 43.9 43.91sRefE 9.8b 12.7b 9.9b 56.6 61.1 29.42sSidRef 19.9 20.2 21.2 24.9 29.1 42.63sSid 7.6 7.6 7.7 10.5 11.1 28.34sCor 15.3 11.1 15.6 12.2 12.9 36.9

aGeometries scanned the entire grid in the same amount of time using 144 rays ~288 for 1sRefE!.bThese were overestimated concentrations; all other concentrations were underestimated.

chamber study in which a prototype CT system withfour detectors and 136 rays was used to reconstructconcentrations of a tracer gas. The system sampledthe chamber slowly because the four detectors did notscan simultaneously. In this case the chemicalpeaks were reconstructed with a mean peak error of27%; this is within the 16–36% error seen in thesesimulations using the four-detector geometry.19

Visually, the greater the number of detectors, themore accurate and smoother the reconstructions.Figures 6 and 7 show original and reconstructed mapsfrom different times in the time series using multipleand moving sources, respectively. The general loca-tions of the peaks can be identified with any of themaps; however, the four-detector geometry gave the

Fig. 6. Two columns of original and reconstructed multiple-source time-series maps. A: Original maps. Reconstructedmaps: B, 1sRef; C, 1sRefE; D, 2sSidRef; E, 3sSid; and F, 4sCor.

best reconstructions of both time-series maps. Withfour detectors the maps were the smoothest in appear-ance and contained the least number of artifacts; how-ever, the peaks heights were usually too short. Thesingle-detector geometry ~1sRef ! gave poor reconstruc-tions: the geometry introduced large streaks into thereconstructions, radiating from the grid center wherethe detector and the peaks were collocated. Althoughthe geometry with extra rays ~1sRefE! reconstructedthe multiple-source time series well, there were manyartifacts when reconstructing the moving-source timeseries. Peaks appeared jagged, and there was streak-ing along some of the ray paths. The 1sRefE geome-

Fig. 7. Original and reconstructed moving-source time-seriesmaps: column 1, 1.25 h; column 2, 1.75 h; column 3, 2.5 h. A:Original maps. Reconstructed maps: B, 1sRef; C, 1sRefE; D,2sSidRef; E, 3sSid; and F, 4sCor.


try poorly located the peaks and significantlyoverestimated concentrations. The difficulty that theone-detector geometries had with reconstructing themoving-source time series compared with themultiple-source time series was due to the increasedtime required to obtain complete sets of rays relative tothe spatial and temporal changes in concentration inthe images.

Unlike results using static maps, increasing thenumber ~density! of rays by 20% in the time seriesdeteriorated reconstruction quality for all the geom-etries; however, the adverse impact was greatest forthe single-detector geometries. Nearness and peaklocation errors were higher ~worse! when we used themoving-source time series rather than the multiple-source time series. Peak location errors were corre-lated with the number of detectors and ranged from amean of 2 to 7 pixels. Visually for any of the geom-etries reconstructions with 144 rays had more irreg-ularities ~appeared noisier! than reconstructionswith 120 rays. The adverse impact of increasing thetime to scan the entire grid by increasing the numberof rays was much greater for the moving-source timeseries than for the multiple-source time series.

With both time-series simulations decreasing scan-ning time was more important than increasing thedensity of rays. Using the time-series data, we de-termined the new ranking of geometries from best toworst to be the following: 4sCor and 3sSid, 2sSid-Ref, 1sRefE, and 1sRef. This is different from theranking with the static maps.

We then evaluated the geometries when the timerequired to scan the room was equivalent; therefore,individual ray measurement times were altered fromthe 15 s used in the previous simulations. This eval-uation then corresponded more closely to use of staticmaps that do not involve scanning time require-ments. For the 4sCor, 3sSid, 2sSidRef, and 1sRefEgeometries, individual ray sampling times werechanged from 15 s to 1 min, 45 s, 30 s, and 7.5 s,respectively. The 1sRef scanning time was kept at15 s. This resulted in an overall scan time for allgeometries of 36 min. When the time required toscan an area was increased to 36 min. for the two-,three-, and four-detector geometries, nearness, peaklocation error, and visual quality deteriorated by useof either time series; peak exposure error increasedonly for the moving-source time series ~see Table 2and Figs. 8 and 9!. This simulation essentially de-creased the scan time by 50% for the 1sRefE geome-try, which significantly improved reconstructionsvisually based on nearness, peak exposure error, andpeak location error. When the overall time to scanthe room was equivalent, the ranking of the geome-tries was the following: 4sCor and 1sRefE, 3srcSid,2sSidRef, and 1sRef. This is similar to the rankingwith the static maps. Using the moving-peak timeseries, we reconstructed false spikes with the three-and four-detector geometries ~see Fig. 5!.

Results with the time-series maps underscored theimportance of having test maps and reconstructionquality measures that are appropriate for the appli-


cation. The geometries were ranked differentlywith the static maps than with the time-series maps.In addition, for the time-series maps there was noconsistent correlation between the numerical evalu-ation measures. Nearness was closest to the overallvisual evaluation of the maps; however, nearness didnot always agree with peak exposure errors.

Fig. 8. Original and multiple-source time-series maps recon-structed by geometries with the same overall scan times. ~a!Original map. Reconstructed maps: ~b! 1sRef, ~c! 1sRefE, ~d!2sSidRef, ~e! 3sSid, and ~f ! 4sCor.

Fig. 9. Original and moving-source time-series maps recon-structed by geometries with the same overall scan times: column1, 1.25 h; column 2, 3 h. A: Original maps. Reconstructedmaps: B, 1sRef; C, 1sRefE; D, 2sSidRef; E, 3sSid; and F, 4sCor.

In air-pollution-source emission monitoring thepurpose of the sampling can be used to drive thegeometry selected. For example, if a 20% mean er-ror were acceptable for evaluating exposures, thethree- or four-detector geometry could be used. Ifthe system were used to help locate a leak in a high-wind-speed area, at least two detectors would beneeded. If the leak were slow and in a relativelylow-wind-speed area, the one-detector geometry withextra rays could also be used; however, this geometrywould likely introduce false peaks and overestimateconcentrations.

4. Conclusion

We have presented an effective way to evaluate ORSgeometries for imaging air pollutants. We evalu-ated 13 different geometries with respect to recon-struction quality using a variety of test maps andreconstruction quality parameters. The use of re-flected rays significantly improved reconstruction ac-curacy by adding orthogonal rays. The ability to usereflected rays to reconstruct air concentrations in-creases the range of possible geometries. However,reflected rays require mirrors, which are difficult toalign and to maintain alignment in field operations.We reconstructed peaks that had a minimum pixeldiameter of 4 on a 40 by 40 grid; in this study thenumber rather than the size of peaks was the limitingfactor in reconstruction accuracy. The greater thenumber of peaks over three, the poorer the recon-structions. For some of the reconstructions the ar-tifacts were as large as the smallest peak in theconcentration maps. The diameter of the concentra-tion peak becomes a limitation when the number ofrays is so sparse that the rays miss the peak. Unlessa peak is high in concentration, at some point a smallpeak may not be relevant to adverse human healtheffects. We are currently developing a dynamic ge-ometry that will help pinpoint peaks and sample re-gions of high concentrations.

Results of this study have underscored the impor-tance of using a variety of images relevant to theapplication; the results changed dramatically whenstatic-test concentration maps were replaced withspatially and temporally varying time-series maps.This is due in part to the fact that the current scan-ning ORS spectrometers take individual ray mea-surements sequentially, not simultaneously. Inaddition, there is a practical limitation to the speedwith which each ray measurement can be taken.The faster the measurement of the chemicals, thelower the signal-to-noise ratio and the higher thelimit of detection. These results have also high-lighted the importance of using a variety of numericalreconstruction quality measures when using simula-tions to evaluate a system before field implementa-tion; the numerical measures were not alwaysconsistent with one another or with the visual eval-uation.

The static maps were useful for evaluating geom-etries that use an equal number of detectors or scanan area in the same time period, for illuminating

artifact patterns, and for determining the best-caseoptimum number of rays. The numerical recon-struction quality parameters were more consistentwith one another using the static maps than with thetime-series maps. The time-series maps were im-portant for testing the limits of each geometry forreconstructing spatially and temporally changingconcentrations.

Visual evaluation of the reconstructed maps wasthe most useful, albeit time-consuming, method forevaluating the geometries. Visual evaluation wasirreplaceable for identifying the location and patternof artifacts, identifying false positives, and discerningdifferences between geometries that were not obviousfrom the numerical measures. Although all the nu-merical measures were useful, for the time-seriesmaps the average exposure error measurement pro-vided information not readily extracted from visualevaluation of time-series reconstructions.

The results of this research, evaluating geometriesfor air pollution monitoring, were highly dependenton the test images used in the simulations. Basedon the images, these results have shown the feasibil-ity of using CT for imaging hazardous pollutants.For locating a leak, if one could live with false posi-tives, geometries with at least two detectors would beacceptable. Evaluating the shape of chemical plumesor using the maps to evaluate human exposures tochemicals would require at least three detectors. Al-though the errors in determining concentrations var-ied widely, the ability to use a tomographic systemover hours, days, and weeks might provide more accu-rate estimates of human exposures than is currentlyavailable using point-sampling measures taken spo-radically. Once installed, a CT system could run con-tinuously at a low cost.

Whether monitoring hazardous pollutants out-doors or indoors, it is likely that non-steady-statemultiple plumes of contaminants are present. Atrade-off exists between the resolution of the projec-tions and the rate at which the projections are ob-tained. We are currently extending this method toinclude nonsquare grid shapes and other resolutions,measurement noise, obstructions ~such as equipmentand buildings!, a larger variety of time-series maps,and additional measures of human exposure. Ulti-mately reconstructed maps will be evaluated in userstudies with defined tasks.

This study was supported by the U.S. Environmen-tal Protection Agency cooperative agreementCR815152 with the University of North Carolina andby the National Science Foundation’s PresidentialFaculty Fellows Award 94-53433. The authorsthank Doug Norton for developing the computer sim-ulation software and Kathleen Mottus for her tech-nical assistance.

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Tomographic reconstruction of air pollutants: evaluation of measurement geometries

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