Đang tải... (xem toàn văn)
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 25 The doctoral thesis was completed at Institute of Physics, Graduate University of Science and Technology, Vietnam Academy of Science and Technology Supervisors: Prof Dr Nguyen Dai Hung Dr Ta Van Tuan LIST OF PUBLICATIONS 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 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 Nguyễn Quang Minh and Tạ Văn Tuân, "Thiết kế ống kính tạo ảnh hồng ngoại xa cho camera ảnh nhiệt khơng làm lạnh," Tạp chí Nghiên cứu khoa học công nghệ quân sự, ISSN 1859-1043, (2013) pp 104-112 Tạ Văn Tuân and Nguyễn Quang Minh, "Phân tích hệ quang vơ tiêu vùng hồng ngoại xa," Tạp chí Nghiên cứu khoa học cơng nghệ qn sự, ISSN 18591403, (2013) pp 96-103 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 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 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 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 Nguyen Quang Minh and Nguyen Van Binh, "Evaluation of Average Directional Effective Emissivity of Isotherrmal Cylindrical-inner-cone Cavities Using MonteCarlo Method", Communications in Physics, vol.27, no.4, pp.357-367, (2017) ISSN 0868-3166, Viện Hàn lâm KH&CN VN This doctoral thesis can be found at: - Library of the Graduate University of Science and Technology - National Library of Vietnam 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 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 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-innercone 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 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 cylindricalinner-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: 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 2 23 - Calculation of the effective emissivity of the isothermal diffuse cylindricalinner-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 cylindricalinner-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 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-innercone 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 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: 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 (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) 27 25 22 20 18 15 12 Average NU NU(/mean),(%) Before NUC After NUC 28,6 1,9 29,1 1,9 29,8 1,7 30,3 1,5 30,9 1,9 31,7 1,8 32,6 1,9 30,4 1,8 4.6 Conclusions for Chapter 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]: 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]: (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 (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) (a) (b) Fig 4.29: The blackbody radiation images at 20C before (a) and after (b) NUC (a) (b) 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 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 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 Bidirectional Reflectance Distribution Function (BRDF) [26,28,54-56], is the 21 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] The IT-545 (Horiba) portable infrared thermometer is used to measure the temperature distribution on 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 A1 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]: 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: (1.30) Commonly, the term radiation temperature rather than radiance temperature is used and is defined as follows [28]: (1.31) (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 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 In Chapter 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 Table 4.6: Effective emissivity of radiation cavity (L/R =3; R/r =1,08; = 55) with various values of Wall emissivity 0,7 0,8 0,9 0,92 e,n calculated by Monte Carlo simulation (D = 1) 0,971202 (=3,34E-05) 0,9823652(=2,74889E-05) 0,9919636 ((=1,2063E-05) 0.9936954 (=1.05001E-05) (y0)tb calculated by 2nd order polynomial interpolation 0,971476 0,982244 0,991752 0,993502 4.3 Heat supply and temperature control The working temperature of the radiation source is set within the range 1050C 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 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) 28 26 24 22 20 18 16 14 12 10 TP1 (C) 28,5 (+0,3/-0,1) 26,5 (+0,1/-0,2) 24,5 (+0,1/-0,2) 22,4 (± 0,2) 20,5 (+0/-0,1) 18,7 (± 0,2) 16,7 (+0,2/-0,1) 14,8 (± 0,2) 13,0 (+0,1/-0,2) 11,2 (+0,1/-0,2) TP2 (C) 28,4 (+0,1/-0,2) 26,5 (+0,1/-0,2) 24,5 (+0,2/-0,1) 22,3 (± 0,2) 20,4 (± 0,2) 18,6 (+0,2/-0,1) 16,6 (± 0,1) 14,7 (+0,3/-0,1) 12,9 (± 0,2) 11,1(± 0,2) TP3 (C) 28,4 (+0,3/-0,2) 26,4 (± 0,2) 24,3 (± 0,2) 22,3 (± 0,1) 20,4 (± 0,2) 18,5(± 0,2) 16,5 (± 0,2) 14,6 (+0,3/-0,2) 12,7 (± 0,2) 10,9 (+0,1/-0,3) TTB (C) 28,4 26,5 24,4 22,3 20,4 18,6 16,6 14,7 12,9 11,1 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 19 radiation properties (intrinsic emissivity and surface reflectivity) Note that the approximate expressions 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 Fig.4.5: Distribution of e,n as function of L/R (R/r=1) : (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.4.7: 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 selfdeveloped 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 to (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.) 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 y ds=rdrd r O R0 R 1.0 X = 2R/tan x L 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) 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 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) 17 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 perfect reflection components This model is most popular in radiation simulation but remains some disadvantages [21,57,58,81]: results obtained by our algorithm and by other author using STEEP 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 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 cylindricalinner-cone cavity in particular and of the blackbody simulator in general (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 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 Fig.2.4.: Bi-directional Reflectance Distribution Function (BRDF) [77] specular component 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 Fig.2.8: Specular reflection model proposed by Phong [86] No Technical specifications Cavity geometry Emission spectral range Aperture diameter, Normal effective emissivity Working temperature Power supply 4.2 Research in cavity system design Unit m mm C VDC Required Cylindrical-inner-cone 8-12 110 0,9650,005 10 50 ( 1C) 12 16 i Diffuse reflection s g 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) directional - diffuse reflection r 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 - 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 -4