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:

1. Prof. Dr. Nguyen Dai Hung

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

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 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

1

CONCLUSIONS

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 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 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

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

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 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

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 20C before (a) and after (b) NUC.

(a)

(b)

Fig.4.30: The grey level histograms of the blackbody radiation images at 20C
before (a) and after (b) NUC.

[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


4

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 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

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:

(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 =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).


20

5



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 1050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]

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)

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

19

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

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

:

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

7

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 1 to 2 (Fig.4.2). The simulation also
shows that the greater the parameters
or , the higher

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

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]:

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


3
4
5
6

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
 0,9650,005
10 ...50 ( 1C)
12



(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
-4

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




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

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)

(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.

B(L,R)

where
and
diffuse reflection lobe,

,
characterizes the size of the directional is the surface BRDF.


14

11

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.

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.

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:

L

R0



8
8
12
12

0,25
0,5
0,25
0,5

30o
60o
20o
45o

0,00020418 (1-y0 tan)2- 0,00057577 (1-y0 tan)+ 0,00054582
- 0,0000502749 (1-y0 tan)2 - 0,000648663 (1-y0 tan) + 0,0017787
0,0000547286 (1-y0 tan)2- 0,000143944 (1-y0 tan) + 0,00013545
0,00001404 (1-y0 tan)2- 0,00018342 (1-y0 tan)+ 0,00044535

20o
60o
20o
30o
30o
60o

Our results
Integrated
Interpolated
0,00054976
0,00086890
0,0016611
0,0034652
0,00016967
0,00023417
0,00093534
0,0015318

0,000549766
0,000868895
0,00166115
0,00346522
0,000169667
0,000234167
0,000935335
0,00153181

Z.Chu[39]



Table 3.3: Average effective emissivity of conical base, (e)ave, of cylindricalinner-cone cavity with surface emissivity = 0.7.
L

R0



8
8
8
8
12
12
12
12

0,25
0,25
0,5
0,5
0,25
0,25
0,5
0,5

30o
60o
20o
60o


(3.1)


12

13
(3.2)
(3.3)

where the denominators in the Eq. (3.7) are:
(3.8)

where in the Eq.(3.3), the integral limit is a function which has a form:
x ≥ 2/tanθ
1/tanθ
coefficients
of the polynimial (3.12) are found based on 3 values of
(Table 3.1).