Summary of doctoral thesis in physics: Study on design and fabrication of blackbody simulator for image non uniformity correction of long wave infrared (8-12 um) 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.

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

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

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

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:

- 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

simulator Suppose that at the temperatures T 1  T 2 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 20C 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)

temperature TPV (C)

NU(/mean),(%)

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

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 20C before (a) and after (b) NUC

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

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

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 c 1 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

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)

A 1

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 0,1C 0,3C 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 ((1K [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 = 290K, max = 10 m In the spectral ranges of 5,5m    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 =10m 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)

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

4.3 Heat supply and temperature control

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

10-50C 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

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

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)

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

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

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

R 0 R 1.0

O 

ds=rdrd

r

X = 2R/tan

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

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

4 Normal effective emissivity  0,9650,005

5 Working temperature C 10 50 ( 1C)

4.2 Research in cavity system design