MINISTRY OF EDUCATION

AND TRAINING

VIETNAM ACADEMY

OF SCIENCE AND TECHNOLOGY

GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY

……..….***…………

Nguyen Quang Minh

Study on Design and Fabrication of Blackbody Simulator for Image

Non-Uniformity Correction of Long-Wave Infrared (8-12 m) Thermal

Cameras

Major: Optics

Code: 9440110

SUMMARY OF DOCTORAL THESIS IN PHYSICS

Hanoi – 2018

The doctoral thesis was completed at Institute of Physics, Graduate University of

Science and Technology, Vietnam Academy of Science and Technology

Supervisors: 1. Prof. Dr. Nguyen Dai Hung

2. Dr. Ta Van Tuan

Reviewer 1: ..........................................................................

Reviewer 2: ..........................................................................

Reviewer 3: ..........................................................................

This doctoral thesis will be defensed at Graduate University of Science and Technology,

Vietnam Academy of Science and Technology on .....hour....., date .....month.....year.....

This doctoral thesis can be found at:

- Library of the Graduate University of Science and Technology

- National Library of Vietnam

25

LIST OF PUBLICATIONS

1. Nguyen Quang Minh, Nguyen Van Thanh, and Nguyen Ba Thi, "Non-Uniformity

of Infrared Imaging Systems using FPA and some Its Correction Techniques," in Hội

nghị Hội nghị Quang học, Quang phổ Toàn quốc lần thứ VII, Session C: Optics,

Laser and Applications, C-24, HCMC, Vietnam, 2012.

2. Nguyen Quang Minh, Ta Van Tuan, and Nguyen Van Binh, "Design

Considerations of a Simple Optical LWIR Imaging System," in Hội nghị Quang học,

Quang phổ Toàn quốc lần thứ VII, Session C: Lasers, Optics and Applications, C-32,

HCMC, Vietnam, 2012.

3. Nguyễn Quang Minh and Tạ Văn Tuân, "Thiết kế ống kính tạo ảnh hồng ngoại xa

cho một camera ảnh nhiệt không làm lạnh," Tạp chí Nghiên cứu khoa học và công

nghệ quân sự, ISSN 1859-1043, (2013) pp. 104-112.

4. Tạ Văn Tuân and Nguyễn Quang Minh, "Phân tích một hệ quang vô tiêu vùng

hồng ngoại xa," Tạp chí Nghiên cứu khoa học và công nghệ quân sự, ISSN 1859-

1403, (2013) pp. 96-103.

5. Nguyen Quang Minh and Ta Van Tuan, "Evaluation of the Emissivity of an

Isothermal Diffuse Cylindro-Inner-Cone Blackbody Simulator Cavity" in

Proceedings of The 3rd Academic Conference on Natural Science for Master and

PhD Students from ASEAN Countries, CASEAN, Phnompenh, Cambodia, (2014) pp.

397-405. ISBN 978-604-913-088-5.

6. Nguyen Quang Minh and Ta Van Tuan, "Design of a Cylinder-Inner-Cone

Blackbody Simulator Cavity based on Absorption of Reflected Radiation Model," in

Proceedings of The 3rd Academic Conference on Natural Science for Master and

PhD Students from Asean Countries, CASEAN, Phnompenh, Cambodia, (2014),

pp.111-121. ISBN 978-604-913-088-5.

7. Ta Van Tuan and Nguyen Quang Minh, "Calculation of Effective Emissivity of

the Conical Base of Isotherrmal Diffuse Cylindrical-Inner-Cone Cavity using

Polynomial Interpolation Technique" Communications in Physics, vol. 26, no. 4, pp.

335-343, (2016). ISSN 0868-3166, Viện Hàn lâm KH&CN VN.

8. Nguyen Quang Minh and Nguyen Van Binh, "Evaluation of Average Directional

Effective Emissivity of Isotherrmal Cylindrical-inner-cone Cavities Using Monte-

Carlo Method", Communications in Physics, vol.27, no.4, pp.357-367, (2017). ISSN

0868-3166, Viện Hàn lâm KH&CN VN.

24

CONCLUSIONS

From the requirements arising in practice of thermal imaging cameras research

and development in Vietnam, we have chosen the topic " Study on design and

fabrication of blackbody simulator for image non-uniformity correction of long -

wave infrared (8-12 m) thermal cameras".

The main results and new points of this thesis are:

- The effective emissivity of the diffuse and isothermal cylindrical - inner -

cone cavity has been calculated using the polynomial interpolation technique for the

angle factor integrals describing the radiation exchange inside the cavity. The

interpolation - calculated results are approximately accurate in comparison with those

obtained by the analytical methods. This approach is a rather new in the practice of

cavity effective emissivity calculation.

- The Monte Carlo radiation absorption simulation algorithm using the 2 -

dimentional, directional - diffuse surface reflection model has been developed for the

system design of the cylindrical - inner - cone blackbody cavity. It can calculate the

normal effective emissivity of the isothermal cavity with any system parameters. The

developed algorithm is light, simple in computation and helpful in practice of

radiation cavity design.

- The research on system design of the cylindrical - inner - cone cavity has

been implemented using the developed Monte Carlo algorithm. The system

parameters of the cavity have been determined through the simulation - based

optimization method. The simulation - calculated values have been verified by the

polynomial interpolation technique to prove their reliability.

- The blackbody simulator based on the cylindrical - inner- cone cavity with

determined system design has been fabricated. It has been experimentally

characterized to meet all the requirements. This blackbody simulator has been used in

two-point calibration - based image non-uniformity correction (NUC) for thermal

cameras in the room and field conditions.

Further research direction

- Study of design and fabrication of blackbody simulators for image NUC of

Mid-Wave Infrared (MWIR) thermal cameras.

- Research on development of efficient 2-point calibration NUC algorithm for

thermal cameras developed in Nacentech.

1

INTRODUCTION

Thermal imaging cameras based on infrared focal plane arrays (IR FPA) are

increasingly used for day/night electro-optical observation systems. Thermal images

captured by such cameras are generally degraded by fixed pattern noises (FPN). The

most used Non-Uniformity Correction (NUC) technique to minimize the influence of

FPN and improve the infrared image quality of thermal cameras is the linear

calibration using the radiation sources such as blackbody simulators.

The image NUC should be implemented regularly or instantly in field

conditions when required. The blackbody simulators for this purpose are not popular

and generally customized by specific needs. Thus, the topic "Study on design and

fabrication of blackbody simulator for image non-uniformity correction of long-wave

infrared (8-12 m) thermal cameras" is chosen and performed in this thesis to

contribute an effort in solving such practical need. It is a new problem in the research

and development activity of Vietnam.

Purpose of thesis is to research on the efficient calculation methods and the

computational tools usable for designing and fabricating the compact and portable

blackbody simulator based on cylindrical-inner-cone cavity for NUC technique of

LWIR (8-12 m spectral band) thermal cameras in the field conditions.

Research scope of thesis:

- Study on processes of thermal radiation exchange inside real cavity and

cavity radiation characteristics.

- Study on methods of cavity effective emissivity calculation and blackbody

radiation sources characterization.

- Research in development of computational tools and techniques for

calculation of effective emissivity of cylindrical-inner-cone cavity.

- Design and fabrication of blackbody simulator based on cylindrical-inner-

cone cavity. Practical applications of created blackbody in image NUC of thermal

cameras.

Structure of thesis:

Except the introduction and the conclusion parts, the thesis contents of 4

chapters as following:

Chapter 1: Theoretical basics of blackbody radiation.

Chapter 2: Methods of determination of blackbody cavity radiation characteristics.

Chapter 3: Study of calculation of directional effective emissivity of cylindrical-

inner-cone cavity.

Chapter 4: Research in design, fabrication and characterization of blackbody

simulator based on cylindrical-inner-cone cavity for image non-uniformity correction

of thermal cameras.

Methodology of research: the research in thesis is carried out by theoretical

calculation combined with experimental methods. The main scientific and practical

contributions of thesis are:

2

- Calculation of the effective emissivity of the isothermal diffuse cylindrical-

inner-cone cavity using polynomial interpolation technique for the integral equations

describing radiation exchanges inside cavity. This approach is almost not found in

published scientific literature concerning blackbody cavity calculation till 2016.

- Calculation of the normal effective emissivity of the isothermal cylindrical-

inner-cone cavity using self - developed algorithm based on Monte Carlo simulation

of cavity radiation. In this algorithm the interaction of radiation is modelled by a 2 -

dimensional, directional - diffuse reflectance distribution function of surface. Thus, it

is considerably new contribution in Monte Carlo simulation methods applied in

blackbody cavity system designing.

- Design and fabrication of the blackbody simulator based on cylindrical-inner-

cone cavity working in 8-12 m spectral band. Achievements in this thesis are useful

for image NUC of thermal cameras in room and field conditions and have meaningful

contributions in practice of R&D activity, application and technical service of

thermal cameras developed for special uses in Vietnam.

- The research results of thesis were presented and published in scientific

journals /periodicals and in proceedings of Vietnam and international conferences.

CHAPTER 1: THEORETICAL BASICS OF BLACKBODY

RADIATION

1.1. Radiometric quantities

The therrmal radiation emitting by a surface has continuous spectrum and its

energy distribution depends on radiation wavelength and direction [26,28,43]. The

thermal radiation travels in space and interacts with the optical materials in

compliance with the optical laws. The characteristic radiometric quantities such as

radiant power (flux) , radiance L, exitance M, radiant intensity I and irradiance E

are introduced. Among them, the spectral radiance in spherical coordinate system is

defined as follows [26,43-45,47]:

(1.3)

where is the power emitted by a surface area unit into a solid angle unit

around the direction , is the radiation wavelength, and are the angular

coordinates in the spherical coordinate system.

1.2. Radiation absorption, reflection and transmission

Assume that the radiation interacts with the optical material in the thermal

equilibrium conditions. According to the energy conservation law, we have [44,45]:

(1.12)

where , , and are the radiant powers of irradiation, reflection,

absorption and transmission, respectively; are the spectral reflectivity,

absorptivity and transmissivity of material , respectively.

1.3. Absolute blackbody radiation

23

simulator. Suppose that at the temperatures T1 T2 the source emits the radiations

and . If were the calibrated grey values of image

pixels, than and can be found by solving the system of equations:

(4.13)

The image affected by FPN at 20C and its grey level histogram are presented

in Fig. 4.29(a) and Fig. 4.30(a). The NUC results are shown in Fig. 4.29(b),

Fig.4.30(b) and in the Table 4.10. The fabricated blackbody simulator also has been

used to perform NUC for the thermal cameras in the field operation, independent of

the weather conditions.

Table 4.10: Evaluation of image non-uniformity (NU)

No Blackbody

temperature TPV (C)

NU(/mean),(%)

Before NUC After NUC

1 27 28,6 1,9

2 25 29,1 1,9

3 22 29,8 1,7

4 20 30,3 1,5

5 18 30,9 1,9

6 15 31,7 1,8

7 12 32,6 1,9

Average NU 30,4 1,8

4.6. Conclusions for Chapter 4

The system design parameters of the cavity are determined by the simulation -

based optimization method through evaluating the distribution of of the cavity

depending on those parameters. The results obtained by the simulation algorithm are

then evaluated by the polynomial interpolation technique, which shows that their

reliability is satisfactory. The fabricated blackbody simulator consists of the designed

cavity, the TE heat source AC-027 which is controlled by the Yamatake SDC15

temperature controller with the Omron E52-CA1DY temperature sensor.

The experimental results show that the designed and fabricated blackbody

simulator meets all the technical and user requirements. It has been used to perform

NUC for the LWIR thermal cameras in the room conditions with the image NU after

NUC is 1,8% or is 17 times lower than those before NUC. This blackbody simulator

also has been used to perform NUC for thermal cameras in the field, independent of

the weather conditions.

22

4.5. Image non-uniformity correction for thermal cameras

The digitalized image pixel value of the thermal camera can be represented by

the linear expression [5,18,20,29,122,123]:

(4.10)

where is the data of position (r,c) of the input image, are the

multiplicative and additive coefficients, respectively. The image non-uniformity

correction includes the update of the coefficients in the Eq. (4.10) to calibrate the

value of the output image.

Fig. 4.29: The blackbody radiation images at 20C before (a) and after (b) NUC.

Fig.4.30: The grey level histograms of the blackbody radiation images at 20C

before (a) and after (b) NUC.

We have set up a model of thermal camera that consists of the IR118 uncooled

module based on 384x288 a-Si microbolometer FPA, the unfocal IR lens [35], the iris

(aperture from 1,0...41,3 mm), and the image-forming IR lens [36]. The image

uniformity of this camera is evaluated by the NU criteria. The video image of IR118

module is captured by the PX610 (Cyber Optics) frame grabber and the grey value of

image pixels can be represented by the linear expression:

(4.12)

The image non-uniformity correction based on two-point calibration technique

for this thermal camera is implemented by exposing the camera to the blackbody

(a) (b)

(a) (b)

3

Absolute (perfect) blackbody can absorb all incident electromagnetic radiation

at any temperature, regardless of its wavelength or direction (angle of incidence). The

blackbody radiation is described according to the Plank's law and its spectrum is

determined by the temperature only [26,50]:

(1.15)

where c1 and c2 are the radiation coefficients, and are the blackbody spectral

exitance and radiance at the temperature T. Blackbody radiation also is described by

the Stefan-Boltzmann's and the Wien's laws.

1.4. Blackbody simulator radiation theory

1.4.1. Real body radiation

The radiation capability of real body is characterized by a physical quantity -

emissivity . It is defined as the ratio between radiation quantities of real body

at temperature T and those of absolute blackbody at same temperature describing

"blackness" of real body in comparison with absolute one [26,28,47]:

(1.20)

The radiation characteristics of the real body are just approximate of those of

the perfect blackbody at certain temperatures and spectral ranges [51,52].

1.4.2. Blackbody simulator cavity

In practice, there are 2 kind of popular radiation sources: (i) Blackbody

simulators based on cavities, and (ii) Flat plate radiation sources [26,28,30,43,50].

1.4.2.1. Cavity shapes

The radiation of isothermal cavity has the characteristics nearly like those of the

perfect blackbody [26,30,47]. The radiation flux at aperture of the cylindrical-inner-cone

cavity is relatively collimated and distributed similarly to those of the cylindrical one, but

with smaller divergence and higher emissivity. Its uniformity is better than that of the

conical shaped cavity. Even more, the cylindrical-inner-cone cavity can be fabricated in

affordable, lightweight and compact forms, with large aperture and shorten cylinder length

[26,41,53].., that satisfy requirements stated in this thesis.

1.4.2.2. Radiant flux from cavity surface

The outgoing radiant flux from a surface in the direction (Fig.1.6) has the

spectral radiance , which can be represented as the sum of the intrinsic surface

radiance and the radiance of surface reflection portion [26]:

(1.21)

(1.22)

(1.23)

where is the intrinsic surface emissivity, is the surface Bi-

directional Reflectance Distribution Function (BRDF) [26,28,54-56], is the

4

perfect blackbody spectral radiance at temperature T, is the spectral irradiance,

and are the incident angle and solid angle, respectively. If the cavity surfaces were

diffuse, the irradiation onto the surface can be represented by the angle factors

describing the solid angles, under which this surface is "seeing" other ones inside the

cavity [26,28,39,40,45,50]. Evidently, radiant flux of cavity surface is always greater

than that of flat radiation source at same conditions (cavity effect) [26,28].

Fig.1.6: Radiant flux of blackbody cavity surface.

1.4.2.3. Effective emissivity of cavity

A blackbody simulator based on cavity is characterized by the effective

emissivity, , that is disimilar to the emissivity of the material, . The local spectral

directional effective emissivity is primary radiation characteristic of the blackbody

simulator that can be defined as [26,28,47]:

(1.25)

where is the local spectral radiance of surface area unit of cavity at

coordinate in direction ; is the spectral radiance of absolute

blackbody at reference temperature .

Other effective quantity such as the total local directional , local

spectral hemispherical , and total hemispherical effective

emissivity can be also defined from Eq.(1.25).

1.4.2.4. Radiation temperature

The cavity radiance temperature is defined as [28]:

(1.30)

Commonly, the term radiation temperature rather than radiance temperature is

used and is defined as follows [28]:

(1.31)

A1

21

The IT-545 (Horiba) portable infrared thermometer is used to measure the

temperature distribution on 3 areas of the conical surface: around the apex of the cone

(P1), in the middle of the cone (P2) and nearby the base of the cone (P3). As

presented in Table 4.7. the temperature differences between areas are in the range of

0,1C...0,3C and the temperature distribution on the conical surface can be

considered quite uniform. The values TTB are a bit higher than TSV due to the

temperature gradient depending on the thermal conductivity density of the cone. The

differences between them become larger as the temperature offsets of the opposite

surfaces increase. However, these deviations are within the acceptable range ((1K

[16]). As the cylinder of cavity is short enough, so the contribution of its radiation in

the normal directional radiation of the cavity is negligible.

Fig.4.22: The spectral radiance of blackbody simulator measured

experimentally.

The radiation characteristics of the fabricated blackbody simulator are

evaluated by using the SR-5000 (CI Systems) spectroradiometer. The output data of

SR-5000 are the values of the spectral radiance of the measured sample source

(Fig 4.22) at TSV =16, maximum wavelength =10,2 m, corresponding to the

reference temperature of the perfect blackbody T = 290K, max = 10 m. In the

spectral ranges of 5,5m 8,0 m and 12,0 m, the experimental spectral

radiance decreases sharply, possibly related to the absorption caused of water vapor

during the measurements. The average normal effective emissivity of the cavity is

defined as:

(4.8)

Around the wavelength =10m the effective emissivity is up to 0,999 that

matched with the theoretical calculation result. In the spectral range of

, is 0,973 that satisfies the requirements

(Table 4.1).

20

intrinsic emissivity is ensured by coating the metallic inner walls of the cavity with

the black paint having = 0,90…0,95.

Table 4.6: Effective emissivity of radiation cavity (L/R =3; R/r =1,08; = 55)

with various values of .

Wall

emissivity

e,n calculated by Monte Carlo

simulation (D = 1)

(y0)tb calculated by 2nd

order

polynomial interpolation

0,7 0,971202 (=3,34E-05) 0,971476

0,8 0,9823652(=2,74889E-05) 0,982244

0,9 0,9919636 ((=1,2063E-05) 0,991752

0,92 0.9936954 (=1.05001E-05) 0,993502

4.3. Heat supply and temperature control

The working temperature of the radiation source is set within the range 10-

50C corresponding to that the maximum wavelength of cavity radiation should be in

the LWIR spectral range as stated in the technical requirements (Table 4.1). In order

to set the temperature of the inner cone lower than the environmental one, the

thermoelectric (TE) generator based on Peltier effect is chosen. The working

parameters of the TE generator are determined using the finite element method [112]

and the TE Technology AC-027 [114] module with the suitable specifications is used

as the heat supply source. The inner cone temperature is controlled automatically by

using the popular temperature controller (Yamatake SDC15) and the type K

thermocouple (Omron E52-CA1DY).

4.4. Evaluation of characteristics of blackbody simulator

The fabricated blackbody simulator consists of 2 units: 1) The control unit

including the power supply, the SDC15 temperature controller and the control panel;

and 2) The radiation source block including the blackbody cavity, the AC-027 TE

module, the E52-CA1DY temperature sensor, the mechanical construction and outer

cover.

Table 4.7: Temperature distribution of conical surface

TSV (C) TP1 (C) TP2 (C) TP3 (C) TTB (C)

28 28,5 (+0,3/-0,1) 28,4 (+0,1/-0,2) 28,4 (+0,3/-0,2) 28,4

26 26,5 (+0,1/-0,2) 26,5 (+0,1/-0,2) 26,4 (± 0,2) 26,5

24 24,5 (+0,1/-0,2) 24,5 (+0,2/-0,1) 24,3 (± 0,2) 24,4

22 22,4 (± 0,2) 22,3 (± 0,2) 22,3 (± 0,1) 22,3

20 20,5 (+0/-0,1) 20,4 (± 0,2) 20,4 (± 0,2) 20,4

18 18,7 (± 0,2) 18,6 (+0,2/-0,1) 18,5(± 0,2) 18,6

16 16,7 (+0,2/-0,1) 16,6 (± 0,1) 16,5 (± 0,2) 16,6

14 14,8 (± 0,2) 14,7 (+0,3/-0,1) 14,6 (+0,3/-0,2) 14,7

12 13,0 (+0,1/-0,2) 12,9 (± 0,2) 12,7 (± 0,2) 12,9

10 11,2 (+0,1/-0,2) 11,1(± 0,2) 10,9 (+0,1/-0,3) 11,1

5

1.4.2.5. Non-isothermal cavity

Real cavity is non-isothermal in nature and its local spectral directional

effective emissivity can be defined as a sum [28,57,58]:

(1.32)

where is the cavity local spectral directional effective emissivity in isothermal

conditions, is the non-isothermal addition in total value of the local

spectral directional effective emissivity, which depends on the cavity wall temperature.

Thus, cavity effective emissivity depends on cavity geometry, wall intrinsic

emissivity and temperature. To design a blackbody cavity, one must evaluate its

radiation characteristics in the isothermal conditions firstly.

1.5. Conclusion for Chapter 1

In Chapter 1 an overview of theoretical basics of the thermal radiation, the

perfect blackbody and the blackbody simulator cavity radiation is presented.

Radiation of the blackbody simulator based on cylindrrical - inner - cone cavity

is collimated and uniformly distributed with high emissivity, that is suitable for

thermal camera image NUC.

The outgoing radiant flux of cavity surface consists of the intrinsic emission

and the portion of multiple reflection. Due to this effect, a cavity is characterized by

the effective emissivity. The local spectral directional effective emissivity is primary

radiation characteristic of a cavity. Its value depends on the cavity geometry, wall

emissivity and temperature. At the cavity system design stage, the calculation of the

cavity spectral directional effective emissivity in the isothermal conditions is

necessary. By creating a cavity having the proper geometry and reasonable

temperature distribution, one can get its radiation closely similar to those of perfect

blackbody and usable for practical applications.

CHAPTER 2: METHODS OF DETERMINATION OF BLACKBODY

CAVITY RADIATION CHARACTERISTICS

The cavity spectral directional effective emissivity can be determined by the

calculation and experimental methods [26,28]. The experimental methods require

complicated equipment and systems for the measurement of the radiation

characteristics of the blackbody simulator [28,63]. The calculation methods are

commonly used in the design stage and also in the characterization of the blackbody

simulator. They are: i) Deterministic calculation methods, and ii) Non-deterministic

calculation methods based on Monte Carlo simulation

[26,28,31,39,40,43,56,60,61,64].

2.1. Deterministic methods

2.1.1. Approximate expressions

The approximate methods are simple and convenient to quickly evaluate the

effective emissivity of a cavity through its geometrical parameters such as: the

aperture diameter, the ratio between aperture and the cavity wall surface areas, the

ratio between cylinder length and aperture radius...as well as through the wall

6

radiation properties (intrinsic emissivity and surface reflectivity). Note that the

approximate expressions do not provide exact results and take into account for a few

standard cavity shapes only.

2.1.2. Analytical methods

2.1.2.1. Basic integral equation

In the case of the isothermal - diffuse cavity, the Kirchhoff's law is applied for

its surface radiation characteristics and the thermal radiation exchange between its

surfaces can be described by the integral equations. By solving them, the cavity

effective emissivity can be determined exactly [48]. Following Eq.(1.21), the radiant

flux from surface at position can be defined as [68]:

(2.8)

Assume that the radiation characteristics are temperature and spectral

independent, from Eq.(2.8) we get:

(2.9)

Note that the irradiance can be represented by the angle factor :

(2.11)

Replacing Eq.(2.11) into Eq.(2.9), using (Kirchhoff's law), and

dividing both terms by (Stefan-Boltzmann law), we have:

(2.13)

In the isothermal conditions, the Eq. (2.13) becomes:

(2.14)

The Eq. (2.14) is referred as the basic equation of the local effective emissivity

of the cavity. It has the form of type II of the Fredholm's integral equation.

2.1.2.2. Equations for effective emissivity of cylindrical-inner-cone cavity

Assume that a cavity is completely closed, totally diffuse and isothermal, then

all its surfaces will emit radiation like that of perfect blackbody with intensity .

According to De Vos [70], the reflection flux from an area does not consist

of: i) the irradiation from the aperture onto it, and ii) the radiation from

reflected by the rest area of the cavity surface then onto [60]:

(2.16)

19

Fig.4.5: Distribution of e,n as function of L/R (R/r=1).

Fig.4.7: Distribution of e,n as function of (L/R=3, R/r = 1).

The cavity parameters must be chosen so as to satisfy the condition e,n ≥ 0,97,

as well as the requirement of cavity compactness. The optimization for cavity

parameters is processed under the considerations:

- As the required aperture is 110mm, the ratio R/r must be not large;

- The value of inner cylinder radius R must be small enough, so that the ratio

L/R is as small as possible;

- The angle must be chosen so as the inner cone mass is as light as possible;

- The intrinsic emissivity should be chosen as high as good.

The cavity system parameters obtained by the optimization are:

The values of e,n of such cavity calculated by the polynomial interpolation and

Monte Carlo simulation techniques have the difference in the range of 10-4

. Note that

the results obtained by the two calculations are equal by rounding them to 10-3

(Table

4.6.). The system parameters listed above satisfy the design requirements. The high

18

The system design parameters of the interested cavity (Fig.3.2)

are determined by the simulation - based optimization technique [107,108]. The self-

developed Monte Carlo simulation algorithm is used to investigate the distribution of

depending on , and . The main criteria used for the optimization

during the simulation are: i) The requirement for compactness of the blackbody

simulator to be designed, and ii) The requirement for the expected value of e,n of this

blackbody cavity.

All of the system parameters should be determined according to the required

value of the aperture radius, r. With the remained constant, the value of

increases gradually to approximate unity when the ratio increases and

the largest increase is in the range R/r from 1 to 2 (Fig.4.2). The simulation also

shows that the greater the parameters or , the higher value and the

value of does not depend linearly on .

With the constant value of and with the certain values of , the value of

increases when the ratio increases (Fig.4.5). There are "crtical" values

of , where approaches the maximum possible value. The variation of

depends on the ratio , the angle and the value of . The small value

of can be established if was an acute angle. The greater value, the the higher

even when small value of is chosen (Fig.4.5.).

Fig.4.2: Distribution of e,n as function of R/r (L/R= 6, = 60).

For each certain set of the cavity geometrical parameters, if the angle is

within the ranges of = 33... 40 or = 50...60 then the value of was assured

to be highest (Fig.4.7.). Note that the angle > 60 lowers the in general and

when = 90 the cavity simply becomes a cylinder. In the case of , the

has a minimum nearby = 45. The function depends on the parameters

and : the smaller the , the more e,n dependent on . In contrary, the

larger the , the less e,nchanges in a wide range of values. The higher ,

the larger e,n .

7

The right term inside the bracket of Eq.(2.16) is the cavity effective emissivity as

defined by Eq.(1.25), where and are the angle factors.

Fig. 2.3: Geometry of cylindrical-inner-con cavity [39].

Considering a diffuse and isothermal cylindrical-inner-cone cavity, where

(Fig.2.3), Z.Chu in [39] had rewritten Eq.(2.16) in the terms of the angle

factors and proposed the equations for the distribution of the effective emissivity of

three parts of this cavity. In particular, the equation for the local effective emissivity

of the inner conical base has a form [39]:

(2.17)

To solve this equation, one has to derive all of the angle factors

in the Eq.(2.17). It is a difficult and complicated

computational process. The calculation results of Z.Chu [39] show that:

- The cylindrical-inner-cone cavity provides high effective emissivity with

shortened cylinder combined with lower temperature gradient along its length.

- The effective emissivity along the cone base is quite uniform and can

approach unity easily with the practical values of parameters, i.e. for high values of

wall emissivity, small aperture diameter and long cylinder length.

Note that the analytical calculation of the cavity effective emissivity can be

used in the case of non-completely diffuse cavities with difficulties [39,40,56,60,61].

2.2. Monte Carlo simulation method

The Monte Carlo simulation method as the probabilistic treatment of radiation

phenomena can be used in studying on optical radiation processes [73,75,76].

2.2.1. Monte Carlo methods in optical radiometry

2.2.1.1. Stochastic models for surface optical properties

The reflection characteristics of a surface can be modelled by the BRDF as in

Eq.(1.23) which obeys the optical reciprocal principle [57,58,64,68,72,77] and in the

spherical coordinate system (Fig.2.4.) it has the form [28,54,55]:

(2.21)

y

x

L

R0 R 1.0 O

ds=rdrd

r

X = 2R/tan

8

In practice, real surface is specular-diffuse rather than perfectly specular or

diffuse [26]. The reflection properties of real surface can be determined by its

roughness [54,77-80] and its BRDF can be represented by the linear combination of

reflection components. In the Uniform Specular-Diffuse (USD) model, the surface

BRDF contains 2 perfect reflection components. This model is most popular in

radiation simulation but remains some disadvantages [21,57,58,81]:

(2.25)

Recently, the three components (3C BRDF) model as better approximation of

real rough surface is used, but its calculation is more complicated [64,77]:

(2.26)

where are diffuse, specular, quasi-specular, and ghost reflection

BRDF components.

Fig.2.4.: Bi-directional Reflectance Distribution Function (BRDF) [77].

Fig.2.8: Specular reflection model proposed by Phong [86].

specular

component

17

results obtained by our algorithm and by other author using STEEP 3 program from

Virial Inc. in [41] are compared with the differences in the range of 10-4

(Table 3.4).

This means that our algorithm is quite reliable in the design calculation of the

blackbody cavity. The notable advantage of this computational tool is time saving,

visual in calculation and efficient in the practice of designing the blackbody cavity.

3.3. Conclusion for Chapter 3

In this chapter the 2nd - order polynomial interpolation technique is applied for

the angle factors expressions rewritten in the explicit forms to calculate the normal

effective emissivity of the cylindrical-inner-cone cavity. The calculated results are

agreed with those obtained by the numerical analytical methods with the average

differences within the range of 10-4

.

The important content of this chapter is the study of development of a

computational algorithm based on the Monte Carlo absorption simulation method for

calculation of the normal effective emissivity of the isothermal cylindrical-inner-cone

cavity. In this algorithm, the corrected simplified Phong's reflection model is used to

describe the directional reflection property of the cavity wall surfaces and the

propagation of radiation inside cavity is simulated on 2-dimenson plane. Such

technique reduces the complexity and the volume of calculation during the ray

tracing process. The results obtained by using this algorithm are agreed with those of

other author [41] with the differences in the range of 10-4

.

The techniques studied and developed in this chapter are time - saving,

accurate and reliable. They are quite suitable for the system design of the cylindrical-

inner-cone cavity in particular and of the blackbody simulator in general.

CHAPTER 4: RESEARCH IN DESIGN, FABRICATION AND

CHARACTERIZATION OF BLACKBODY SIMULATOR BASED ON

CYLINDRICAL-INNER-CONE CAVITY FOR IMAGE NON-UNIFORMITY

CORRECTION OF THERMAL CAMERAS.

4.1. Blackbody simulator system requirements

The blackbody simulator to be designed can be used as the standard radiation

source for the thermal image non-uniformity correction. It must be portable in use

and can operate in the field conditions.

Table 4.1: Blackbody simulator system requirements

No. Technical specifications Unit Required

1 Cavity geometry Cylindrical-inner-cone

2 Emission spectral range m 8-12

3 Aperture diameter, mm 110

4 Normal effective emissivity 0,9650,005

5 Working temperature C 10 ...50 ( 1C)

6 Power supply VDC 12

4.2. Research in cavity system design

16

Fig.3.3: The directional - diffuse reflection model [101].

The cavity normal effective absorptivity can be calculated by simulating N

random radiation rays with the initial statistical weights :

(3.30)

where k = 1,2,...,m is the number of reflections of i-th radiation ray. After k-times of

reflection the statistical weight of a ray, , will be as :

(3.31)

where are the surface diffuse and specular

probability density functions, respectively. Consequently, we can obtain the normal

effective emissivity by using Eq.(3.22). The simulation and investigation of

the radiation propagation in the cavity were implemented using 2 - step inverse ray

tracing technique: i) finding out the intersection points between ray trajectory and

cavity surfaces, and ii) determining the reflection direction of traced ray. The number

of the simulated rays must be large enough ( ) to ensure the statistical error

<10-4

[28,90]. The probability of the reflection events (diffuse or specular) is defined

by the ratio . The direction of the reflected ray is determined by

the appropriate PDF. The trajectory of the traced ray ended if its statistical weight

after k –times of reflections becomes negligible ( , where is the pre-

specified uncertainty of calculation) and/or if its trajectory intersects the cavity

aperture. Our simulation algorithm was developed in the LabView environments.

Table 3.4: Average normal effective emissivity for a cylindrical-inner-cone

cavity with L/R = 6, R/r =1, = 60.

Wall

emissivity,

( )

Average normal effective emissivity,

J.Wang results in [41] Our results

0.7 0.99125 0.991084 ( = 2.62E-05)

0.8 0.99475 0.994903 ( = 1.79E-05)

0.9 0.99757 0.997723 ( = 1.44E-05)

For each set of cavity parameters , the value of was

calculated by using our Monte Carlo algorithm and the Eqs. (3.30) and (3.31). The

directional

- diffuse

reflection

i s

r

Diffuse

reflection

g

9

B.T.Phong (1975) had presented an empirical surface reflection model

(Fig.2.8). Its specular component in Eq.(2.25) is described in the form [83]:

(2.29)

where is the ratio between specular reflection portion and irradiation, k models

the beam dimension of quasi-specular reflection and that is chosen to match the

experimental data [54,79,83-85]. The reflection energy depends on the angles of

radiation observation. The Phong's model is very popular in computer graphic

applications because of its simplicity and efficiency. Space and/or angular distribution of

radiation flux can be represented by probability density functions (PDF) with respective

random variables [28].

2.2.1.2. Probability of radiation processes

Based on the conservation law, the interactions between radiation and maters

obey the rule : as described in Eq.(1.12). In the Monte Carlo

simulation, the values of are referred to the probability of relevant

phenomena, such as absorption, reflection, or transmission. If in the Eq.(2.25),

, and in the Eq.(2.26), , so

and could be used as the probabilities of the reflection components

in the aboved models.

2.2.1.3. Ray tracing

The inverse ray tracing technique is often used in the Monte Carlo radiation

simulation to investigate the radiation propagation trajectories in space and the

radiation interactions with the physical surfaces. At every intersection of radiation

and surfaces, kind of reflection depends on known probability and its direction is

determined by proper BRDF. The ray tracing process is continued until the tracked

trajectory ends.

2.2.1.4. Technique of statistical weight

According to the energy conservation rule, after each interaction with surface,

radiation energy will be partially absorbed and reflected [70]. Supposed that the

initial radiation energy is E, after k times of reflections by a surface having

reflectivity , this energy will become [78]:

(2.34)

if then , the initial radiation could be considered completely

absorbed. In the Monte Carlo radiation simulation, a statistical weight is

assigned to each initial radiation ray, after each reflection is multiplied by

reflectivity value . This ray is traced and it ends after k -times of reflections if

(where is small pre-specified uncertainty). Such technique

ensures the convergence of the simulation algorithm.

2.2.2. Calculation of cavity radiation characteristics by Monte Carlo

simulation

2.2.2.1. Emission simulation method

10

This method is based on the definition of radiation flux outgoing from a diffuse

surface as in Eq.(1.17), taking into account the number of multiple reflections [89]:

(2.36)

Assume that and are the radiation energy emitting by the cavity

surface and outgoing from cavity aperture, respectively [53], we have:

(2.38)

where S is the total area of the cavity internal walls, s is the aperture area, N and Nout

are the total amount of radiation "particles" emitting by S and outgoing through

aperture s, respectively.

This method has advantage in direct calculation of the local effective

emissivity of the non-isothermal cavity. It is helpful in considering heat supply to

have the reasonable temperature distribution inside the cavity. In contrary, this

method requires to determine the distribution functions of each surface. Because of

that, the calculation volume of this method is always large and the computation is

complicated.

2.2.2.2. Absorption simulation method

The cavity effective emissivity can be defined through its effective

reflectivity or absorptivity , taking into account of the Kirchhoff's law

. If cavity had the opaque, grey, diffuse and isothermal surfaces,

we have [53]:

(2.40)

where is cavity wall surface reflectivity, is position of surface unit area, and

are angle factors in nature.

Suppose that there are N "particles" irradiated from aperture and Nk of them

escaped the cavity after k - times reflection, the average hemispherical effective

reflectivity of aperture is defined as [53]:

(2.42)

If there are particles totally absorbed, the effective emissivity of the cavity

could be found using its effective absorptivity [90]:

(2.45)

The absorption simulation method is simpler and its calculation volume is less

than that in comparison with the emission one. Its disadvantage is that the

temperature distribution information of the cavity is not derived from the calculation.

15

The average values of the effective emissivity of the conical base obtained by

interpolation technique and calculated by other author [39] were introduced in Table

3.3 with the difference within 10-4

.

The polynomial interpolation technique is efficient in the calculation of the

effective emissivity of the conical base and can be applied in the cylindrical-inner-

cone cavity design stage despite of requiring certain computational skill [98].

3.2. Study of calculation of normal effective emissivity of cylindrical-inner-

cone cavity using Monte Carlo simulation method

We have proposed the algorithm based on the Monte Carlo radiation

absorption simulation to calculate the normal effective emissivity, , of the

isothermal cylindrical-inner-cone cavity.

In Fig.3.2, a cylindrical-inner-cone cavity is presented, where L is the cylinder

length, R is the inner radius of cylinder, r is the aperture radius (r<R), and is the

angle between the conical base and the cylinder. Supposed that the inner surfaces of

the cavity were specular - diffuse, its emissivity was uniformly everywhere inside the

cavity and independent of spectrum, temperature and radiation direction, so that

. The cavity is considered isothermal and its normal radiation

characteristics obey the Kirchhoff's law and the optical reciprocal rule:

(3.22)

Fig.3.2: The investigated cylindrical-inner-cone cavity model.

As the cylindrical-inner-cone cavity is rotationally symmetrical, we can

compute its directional effective emissivity in the plane consisting of the initial ray

and all calculation results obtained in this plane are being true for the rest ones of the

cavity [101]. In our work the corrected Phong’s directional diffuse reflection model

was used to approximate the real surface reflectance property (Fig.3.3.)[101]:

(3.27)

where and , characterizes the size of the directional -

diffuse reflection lobe, is the surface BRDF.

i(,b)

y0

(X’,Y’)

r(,,s)

F(0,-R)

A(0, R)

(0,0)

B(L,R)

E(L,-R)

C(L,r)

D(L,-r)

G(R/tan,0)

x

y

14

Table 3.1: Interpolation polynomials of integral function of d2Fyo,x dFx,ap for a

selection of cavity parameters in the case of =0.7.

L R0

8 0,25 30o 0,00020418 (1-y0 tan)2- 0,00057577 (1-y0 tan)+ 0,00054582

8 0,5 60o - 0,0000502749 (1-y0 tan)2 - 0,000648663 (1-y0 tan) + 0,0017787

12 0,25 20o 0,0000547286 (1-y0 tan)2- 0,000143944 (1-y0 tan) + 0,00013545

12 0,5 45o 0,00001404 (1-y0 tan)2- 0,00018342 (1-y0 tan)+ 0,00044535

Table 3.2: Comparison of the averaged values of first- and second-order terms

of Eq.(2.17) for a selection of cavity parameters( =0.7).

L R0

Our results Z.Chu[39] Our results Z.Chu[39] Integrated Interpolated

8 0,25 30o

0,00054976 0,000549766 0,0006 0,00028397 0,0003

8 0,25 60o

0,00086890 0,000868895 0,0009 0,000396679 0,0004

8 0,5 20o

0,0016611 0,00166115 0,0020 0,0012888 0,0013

8 0,5 60o

0,0034652 0,00346522 0,0035 0,00145737 0,0015

12 0,25 20o

0,00016967 0,000169667 0,0002 0,0000948923 0,0001

12 0,25 30o

0,00023417 0,000234167 0,0003 0,0000941865 0,0001

12 0,5 30o

0,00093534 0,000935335 0,0010 0,00029195 0,0003

12 0,5 60o

0,0015318 0,00153181 0,0016 0,000375528 0,0004

Table 3.3: Average effective emissivity of conical base, (e)ave, of cylindrical-

inner-cone cavity with surface emissivity = 0.7.

L R0 Interpolated using 2nd-

order polynomial

Obtained by Z.Chu's

method[39]

8 0,25 30o

0,99980951470 0,999793

8 0,25 60o

0,99970362889 0,999694

8 0,5 20o

0,99938567800 0,999283

8 0,5 60o

0,99882927670 0,998815

12 0,25 20o

0,99994055869 0,999931

12 0,25 30o

0,99992127221 0,999901

12 0,5 30o

0,99969312250 0,999673

12 0,5 60o

0,99950666248 0,999484

In Table 3.2, the interpolation- and integration-calculated average values of

dFy0,ap in Eq.(3.5) are almost the same with the difference from 10-7

to 10-8

. The

interpolated results of dFyo,ap and of integral of dF2

yo,ap dFx,ap seem to be identical with

the ones obtained by Z.Chu [39] with uncertainty within the range of 4.10-4

.

11

2.3. Experimental methods

There are 2 popular experimental methods used for measurement of radiation

characteristics of blackbody simulators using the reflectometers and the radiometers [63].

The temperature distribution of the wall cavity can be measured by the thermometers.

2.4. Conclusion for Chapter 2

The deterministic and the Monte Carlo calculation methods are generally used

in the design stage and in characterizing blackbody cavities. In Chapter 2 the

approximate and analytical calculations of the cavity effective emissivity are

presented as the deterministic methods. The approximate expressions determine the

average values of effective emissivity of the isothermal - diffuse for conventionally

shaped cavity. The analytical method based on the integral equations can precisely

calculate almost all of the radiation characteristics of cavity, where the main

calculation is determination of the angle factors describing radiation exchange

between cavity wall surfaces. Analytical method is difficult to apply for non-diffuse

cavity having complicated shape. The Monte Carlo simulation method is most

flexible that can be applied for calculation of the effective emissivity of the black

body cavity and offers possibilities to investigate radiation characteristics of the

cavity with any geometry and construction. Nevertheless, the deterministic method is

still meaningful in precise calculation of the radiation characteristics of cavity and

provides theoretical arguments for the Monte Carlo simulation method.

The experimental methods used for characterization of blackbody cavity

require high - cost and complicated equipment and systems in laboratory conditions

only. In practice, it is the most reliable means to measure the characteristics of

physical radiation source.

CHAPTER 3: STUDY OF CALCULATION OF DIRECTIONAL EFFECTIVE

EMISSIVITY OF CYLINDRICAL - INNER - CONE CAVITY

The study of calculation of directional effective emissivity of cylindrical-inner-

cone cavity using polynomial interpolation technique and Monte Carlo simulation

algorithm is presented.

3.1. Study of calculation of directional effective emissivity of cylindrical-

inner-cone cavity using polynomial interpolation technique

Based on the definition of Eq.(1.21) the normal effective emissivity of

a cylindrical-inner-cone cavity can be evaluated by the local effective emissivity

of the conical base [97,98]. Note that the will be found by solving the

Eq.(2.17) with the need to determine all of the angle factors in its.

3.1.1. Determination of the angle factors in the equation for the local

effective emissivity of the conical base

In [39], the angle factors of Eq.(2.17) are expressed as follows:

(3.1)

12

(3.2)

(3.3)

where in the Eq.(3.3), the integral limit is a function which has a form:

x ≥ 2/tanθ

1/tanθ <x< 2/tanθ

0 ≤ x ≤ 1/ tanθ (3.4)

The Eqs. (3.1) - (3.3) can be solved by integrating as stated in [39], but it is

hardly to perform in practice. In our work, we have evaluated these integrals by

implementing the suitable changes or substitutions of variables (See Appendices P.1.-

P.1.3). The results are obtained as follows [97,98]:

(3.5)

(3.6)

(3.7)

13

where the denominators in the Eq. (3.7) are:

(3.8)

There are the singular points in Eqs. (3.5)- (3.7) where the values of are

uncertain. They occur when in Eq.(3.5) and in Eqs.

(3.6) and (3.7). In our work these sigular points have been treated by applying the

L'Hopital's rule [28,98] (see the Appendix P1.4). Finally we got:

(3.9)

(3.10)

(3.11)

By introducing the Eqs. (3.5) - (3.7) and (3.9) - (3.10) to the `Eq.(2.17) we

have the explicit and simpler form of the equation for distribution of the effective

emissivity of the conical base [97,98]. These newly obtained terms can be calculated

inherently by general numerical integration, although it is still tedious, time wasted

and complicated.

3.1.2. Calculation of local effective emissivity of conical base using

polynomial interpolation technique

The second - order integral terms in Eq.(2.7) have a very complicated forms

although they are represented in the explicit expressions as in Eqs. (3.5) and (3.7). In

our work, if set to be a continuous function, where

, there was an unique nth-order Newtonian polynomial

[98]:

(3.12)

This polynomial interpolates the approximate values of between the pre-

defined data points . The order of this polynomial is determined by the interpolation

errors [97.98]. The m = 2 is enough for the required interpolation error < 10-5

. The

coefficients of the polynimial (3.12) are found based on 3 values of

(Table 3.1).