- Email: [email protected]
Study on high-precision temperature measurement of infrared thermal imager
Infrared Physics & Technology 53 (2010) 396–398
Contents lists available at ScienceDirect
Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Study on high-precision temperature measurement of infrared thermal imager Shao-sheng Dai *, Xiao-hui Yan, Tian-qi Zhang Chongqing Key Laboratory of Signal and Information Processing, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
a r t i c l e
i n f o
Article history: Received 22 November 2009 Available online 18 July 2010 Keywords: Infrared thermal imager Temperature measurement algorithm IRFPA Calculation model
a b s t r a c t The objective of this paper is to improve the precision and reliability of algorithms for temperature measurement using an IRFPA. A high-precision infrared temperature measurement algorithm based on the nonlinear response of each pixel in the IRFPA is proposed. The results show that the error variance of the algorithm is about one-sixth of traditional algorithms under identical conditions. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Compared with general temperature measurement methods, infrared thermal imaging temperature measurement has the advantage of high speed, large area, high resolution, non-contact and so on, so it can be real-time, effective and fast to measure the surface temperature of an object. However, infrared temperature measurement precision is influenced by many factors, including emissivity and reflectivity of an object surface, ambient temperature, atmospheric temperature, measuring distance, etc. [1,2], and these factors limit range of the application of infrared thermal imaging temperature measurement. By analyzing the factors which influences infrared thermal imaging temperature measurement, a high-precision infrared temperature measurement algorithm is proposed in this paper. This algorithm is based on the nonlinear response of individual pixels. Experimental results demonstrate the algorithm we propose can reduce the impact caused by environmental factors and can effectively improve temperature measurement precision by an infrared thermal imager.
where Ek is the blackbody radiation flux density (unit: W/m2); c1 is the first radiation constant; c2 is the second radiation constant; k is the wavelength of the radiation spectrum (unit: lm); T is the absolute temperature of the blackbody (unit: K). In real temperature measurements, the infrared thermal imager can receive radiation energy which includes: the object’s own radiation, object’s reflection from the surrounding environment and atmospheric radiation. The infrared radiation Lk (unit: W) of the target object is given by
Lk ¼ ek Lbk ðT 0 Þ þ qk Lbk ðT u Þ ¼ ek Lbk ðT 0 Þ þ ð1 ak ÞLbk ðT u Þ
ð2Þ
In Eq. (2), the first term is the infrared radiation of the object’s surface; the second term is infrared radiation from the surrounding environment. T0 is the surface temperature of the object (unit: °C); Tu is ambient temperature (unit: °C); ek is the target surface emissivity; qk is target surface reflectivity; ak is the absorption of the target surface. Infrared radiation Lk of a target object will be absorbed and scattered when it passes through the atmosphere to reach the infrared thermal imager. The receiving radiation energy is given by 2
E ¼ A0 d ½sak ek Lbk ðT 0 Þ þ sak ð1 ak ÞLbk ðT u Þ þ eak Lbk ðT a Þ
2. Temperature measurement principle of infrared object The relation between energy and wavelength for blackbody radiation is given by the Planck Radiation Law. The relation can be expressed through the following equation.
Ek ¼ c1 k5 ½expðc2 =kTÞ 11
ð1Þ
ð3Þ
where A0 is the visual area of the object, d is the distance between the object and the imager, Ta is the atmospheric temperature. A0d2 is a constant, sak is the spectral transmittance of the atmosphere, eak is the atmospheric emissivity. The infrared radiation power Pk (unit: W) absorbed by IRFPA of the imager is given by
P k ¼ E k AR
ð4Þ 2
* Corresponding author. E-mail address: [email protected] (S.-s. Dai). 1350-4495/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2010.07.005
where AR is lens area of the infrared thermal imager (unit: m ). The infrared thermal imager is usually used in two wave bands: 2–6 lm and 8–14 lm. In the two wave bands, the conversion
397
S.-s. Dai et al. / Infrared Physics & Technology 53 (2010) 396–398
between infrared radiation energy and voltage signal can be expressed as follows:
V s ¼ AR
Z
Ek gdk
ð5Þ
Dk
where g is the detector spectral responsivity. An infrared thermal imager usually operates at certain narrow wave band, so the parameters ek, ak, eak and sak are independent of wavelength k. Eq. (5) can be simplified:
Z Z 2 V s ¼ AR A0 d sa e Lbk ðT 0 Þgdk þ sa ð1 aÞ Lbk ðT u Þgdk Dk Dk Z Lbk ðT a Þgdk þ ea
ð6Þ
where sa is the spectral transmittance of the atmosphere, e is target surface emissivity, a is the absorption of target surface, ea is the atmospheric emissivity. R When expression K = ARA0d2 and Dk Lbk ðtÞgdp ¼ f ðtÞ are brought into Eq. (6), we obtain:
ð7Þ
When expression Vs/K = f(T0 ) is brought into Eq. (7), Eq. (8) can be obtained:
f ðT 0 Þ ¼ sa ½ef ðT 0 Þ þ ð1 aÞf ðT u Þ þ ea f ðT a Þ
ð8Þ
where T0 is the temperature measured by infrared thermal imager. When an object is regarded as gray, the e equals a and the ea equals aa (ea = aa = 1 sa). Eq. (8) is also written as:
f ðT 0 Þ ¼ sa ½ef ðT 0 Þ þ ð1 eÞf ðT u Þ þ ð1 sa Þf ðT a Þ
Theoretical and experimental research shows that every detector response in an IRFPA is S-mode nonlinear relation with its received infrared radiation energy [5]. During the course of real temperature measurement, the nonlinear response coefficients can be obtained by blackbody radiation calibration. In Eq. (14), we establish the S-mode nonlinear function expression between temperature and response output value of infrared detector:
H¼
Dk
V s ¼ Kfsa ½ef ðT 0 Þ þ ð1 aÞf ðT u Þ þ ea f ðT a Þg
3. Establishment of high-precision infrared temperature measurement model
A þD 1 þ exp½BðT CÞ
ð14Þ
where A–D are the response coefficients of each detector. The inverse function expression of Eq. (14) is:
T¼
1 ½lnðA þ D HÞ lnðH DÞ þ C B
First-order derivative of Eq. (15) is written as:
T 0 ¼ A ½BðA þ D HÞðH DÞ1
1 H0 ¼ ½BðA þ D TÞðT DÞ A
gk Lbk ðTÞdk ¼
Dk
gk
Dk
c1
pk5
2
H ¼ aT 3 þ bT þ cT þ d
ð18Þ
where T is object’s radiation temperature, H is detection unit response output value of IRFPA, a–d are the response coefficients of
ð9Þ A
½expðc2 =kTÞ 11 dk
ð10Þ
n
180
1
sa
1 T na
80 20
e sa
T 0n ð1 eÞT nu
1
sa
1=n 1 T na
40
60
80
100
120
140
160
180
200
Temperature (ºC) Fig. 1. Diagram of IRFRA non-uniformity correction.
ð12Þ
220 200
ð13Þ
From Eq. (13), we know environmental temperature can affect temperature measurements of infrared thermal imager under certain conditions. When using the different wave bands imager, the value of n is different. For the HgCdTe (8–14 lm) IRFPA, the value of n is 4.09 and for the InSb (2–6 lm) IRFPA the value of n is 8.68 (n parameter can be found from The Sadtler Handbook of Infrared Spectra [4]). Therefore, if IRFPA temperature, ambient temperature, atmospheric temperature, as well as the target object emissivity and atmospheric transmission conditions are given, the target surface temperature can be calculated accurately by Eq. (13).
180
Gray
1 1
140
100
Finally, the formula for calculating real temperature of object surface is given out by
T0 ¼
160
120
ð11Þ
eT n0 þ ð1 eÞT nu þ
C
200
where C is constant. When Eq. (11) is substituted into Eq. (9), Eq. (12) can be got:
T 0n ¼ sa
B
220
For IRFPA with different responding wave bands, they have different spectral responsivity with wavelength variation. According to the relation of gk and k, we can obtain Eq. (11) by applying integral operator for Eq. (10):
f ðTÞ CT
ð17Þ
The indefinite integral expression of Eq. (17) is:
Gray
f ðTÞ ¼
Z
ð16Þ
Similarly, first-order derivative of Eq. (14) is also written as:
According to Planck’s Law [3]:
Z
ð15Þ
160 140 120 100 80 20
40
60
80
100
120
140
160
Temperature (ºC) Fig. 2. Diagram of corrected curves.
180
200
398
S.-s. Dai et al. / Infrared Physics & Technology 53 (2010) 396–398
Table 1 Form of temperature comparison between two algorithms.
4. Experimental results and comparison
Real temperature (°C)
Traditional algorithm (°C)
Proposed algorithm (°C)
21 26 35 40 50 60 70 80 110 120 140 160 180 200 Error variance
27.27 30.79 33.43 38.70 45.73 55.40 65.07 76.50 112.53 125.72 146.81 161.756 178.02 194.28 20.59
23.15 28.35 32.12 39.31 48.26 59.49 69.66 80.59 110.92 121.90 141.20 157.15 177.62 202.28 3.66
The experiment is carried out with a rate of 25 frames per minute by an IRFPA detector with the 320 240 pixel. The non-uniformity of IRFPA is calibrated using a blackbody working range of 0– 200 °C. Table 1 lists the temperature error variance of comparison results between the proposed algorithms and the traditional algorithm [6,7], and the curve of comparison is also drawn in Fig. 3. From Table 1, it is clear that the temperature error variance between the temperature value obtained by the proposed algorithm and the real temperature value is 3.66, however, that between the temperature values obtained by the traditional algorithm and the real temperature value is 20.59. Fig. 3 shows the measurement temperatures of the proposed algorithm are much nearer to real temperatures than that of the traditional algorithm. 5. Conclusion
Traditional Algorithm
In this paper, a high-precision infrared temperature measurement algorithm is proposed, which adopts error compensation of some influence factors to ensure high-precision temperature measurement. Finally, Table 1 shows that the error variance of proposed algorithm is less than that of traditional algorithm, and Fig. 3 curves also show the temperature measurement error range of the proposed algorithm is narrower than that of the traditional algorithm. Also the experimental results show that the higher temperature measurement precision can be obtained by using the proposed algorithm. It is very suitable for engineering application.
Proposed Algorithm
8 6
T (ºC)
4 2 0 -2
20
40
60
80
100
120
140
160
180
200
Temperature (ºC)
-4 -6
Acknowledgements
-8 Fig. 3. Diagram of the temperature difference between two algorithms.
every detector among which the differences which cause the nonuniformity response in IRFPA. In order to improve the temperature measurement precision of infrared thermal imager, the non-uniformity response of an IRFPA must be corrected and then temperature measurement can then be implemented. After non-uniformity correction, the detector response equation can be written as: 0
0
H0 ¼ a0 T 3 þ b T 2 þ c0 T þ d
ð19Þ
Generally, the progress of non-uniformity correction is to establish the mapping relation between H and H0 . The mapping function expressions from the coefficients a–d to the coefficients a0 –d0 are also found. Through the mapping relation between Eqs. (18) and (19), the non-uniformity response of IRFPA is corrected. Any two nonlinear response curves A and B of detectors in IRFPA and the standard response curve C are drawn in Fig. 1. Corrected curves are drawn in Fig. 2. The symmetry curve of Eq. (19) about y = x is expressed as 0
0
T 0 ¼ a0 H3 þ b H2 þ c0 H þ d
ð20Þ
Under given conditions such as the target emissivity, ambient temperature, atmospheric temperature and the operating wave band of IRFPA, combining Eqs. (13) and (20) we can calculate object surface temperature.
This work is supported by the NSAF Foundation (No. 10776040) of National Natural Science Foundation of China, the National Natural Science Foundation of China (No. 60602057), the Project of Key Laboratory of Signal and Information Processing of Chongqing (No. CSTC2009 CA2003), the Natural Science Foundation of Chongqing Science and Technology Commission (CSTC2006BB2373, CSTC2009BB2287), the Natural Science Foundation of Chongqing Municipal Education Commission (No. KJ060509, KJ080517), the Program for New Century Excellent Talents in University (No. NCET-10-0927) and the Natural Science Foundation of Chongqing University of Posts and Telecommunications (CQUPT) (A2006-04, A2006-86). References [1] Y.-H. Li, X.-G. Sun, G.-B. Yuan, Accurate measuring temperature with infrared thermal imager, Options and Precision Engineering 15 (9) (2007) 1336–1341. [2] L. Yang, Calculation and error analysis of temperature measurement using thermal imager, Infrared Technology 21 (4) (1999) 20–24. [3] H.-K. Liu, L. Yang, Effect of radiation of the sun on infrared temperature measurement, Infrared Technology 24 (1) (2002) 34–37. [4] W.S. William, Sadtler Handbook of Standard Infrared Grating Spectra [M], Sadtler Research Laboratories Inc., Philadelphia, 1980. [5] G.-H. Hu, Q. Chen, X.-Y. Shen, Research on the nonlinearity of Infrared Focal Plane Arrays, Journal of Optoelectronics Laser 14 (5) (2003) 489–492. [6] Z.-F. Lu, Y.-L. Pan, X.-J. Wang, Q. Sun, L.-S. Gu, Z.-W. Lu, Y.-C. Liu, Influence of object-system distance on accuracy of temperature measurement with IR system, Infrared Technology 30 (5) (2008) 271–274. [7] G. Liu, Z.-J. Huang, H. Zhou, Y.-X. He, S.-H. Chen, X.-J. Yi, IRFPA no-uniformity correction using the DSP image processing system, Infrared Technology 26 (6) (2004) 34–37.
Contents lists available at ScienceDirect
Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Study on high-precision temperature measurement of infrared thermal imager Shao-sheng Dai *, Xiao-hui Yan, Tian-qi Zhang Chongqing Key Laboratory of Signal and Information Processing, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
a r t i c l e
i n f o
Article history: Received 22 November 2009 Available online 18 July 2010 Keywords: Infrared thermal imager Temperature measurement algorithm IRFPA Calculation model
a b s t r a c t The objective of this paper is to improve the precision and reliability of algorithms for temperature measurement using an IRFPA. A high-precision infrared temperature measurement algorithm based on the nonlinear response of each pixel in the IRFPA is proposed. The results show that the error variance of the algorithm is about one-sixth of traditional algorithms under identical conditions. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Compared with general temperature measurement methods, infrared thermal imaging temperature measurement has the advantage of high speed, large area, high resolution, non-contact and so on, so it can be real-time, effective and fast to measure the surface temperature of an object. However, infrared temperature measurement precision is influenced by many factors, including emissivity and reflectivity of an object surface, ambient temperature, atmospheric temperature, measuring distance, etc. [1,2], and these factors limit range of the application of infrared thermal imaging temperature measurement. By analyzing the factors which influences infrared thermal imaging temperature measurement, a high-precision infrared temperature measurement algorithm is proposed in this paper. This algorithm is based on the nonlinear response of individual pixels. Experimental results demonstrate the algorithm we propose can reduce the impact caused by environmental factors and can effectively improve temperature measurement precision by an infrared thermal imager.
where Ek is the blackbody radiation flux density (unit: W/m2); c1 is the first radiation constant; c2 is the second radiation constant; k is the wavelength of the radiation spectrum (unit: lm); T is the absolute temperature of the blackbody (unit: K). In real temperature measurements, the infrared thermal imager can receive radiation energy which includes: the object’s own radiation, object’s reflection from the surrounding environment and atmospheric radiation. The infrared radiation Lk (unit: W) of the target object is given by
Lk ¼ ek Lbk ðT 0 Þ þ qk Lbk ðT u Þ ¼ ek Lbk ðT 0 Þ þ ð1 ak ÞLbk ðT u Þ
ð2Þ
In Eq. (2), the first term is the infrared radiation of the object’s surface; the second term is infrared radiation from the surrounding environment. T0 is the surface temperature of the object (unit: °C); Tu is ambient temperature (unit: °C); ek is the target surface emissivity; qk is target surface reflectivity; ak is the absorption of the target surface. Infrared radiation Lk of a target object will be absorbed and scattered when it passes through the atmosphere to reach the infrared thermal imager. The receiving radiation energy is given by 2
E ¼ A0 d ½sak ek Lbk ðT 0 Þ þ sak ð1 ak ÞLbk ðT u Þ þ eak Lbk ðT a Þ
2. Temperature measurement principle of infrared object The relation between energy and wavelength for blackbody radiation is given by the Planck Radiation Law. The relation can be expressed through the following equation.
Ek ¼ c1 k5 ½expðc2 =kTÞ 11
ð1Þ
ð3Þ
where A0 is the visual area of the object, d is the distance between the object and the imager, Ta is the atmospheric temperature. A0d2 is a constant, sak is the spectral transmittance of the atmosphere, eak is the atmospheric emissivity. The infrared radiation power Pk (unit: W) absorbed by IRFPA of the imager is given by
P k ¼ E k AR
ð4Þ 2
* Corresponding author. E-mail address: [email protected] (S.-s. Dai). 1350-4495/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2010.07.005
where AR is lens area of the infrared thermal imager (unit: m ). The infrared thermal imager is usually used in two wave bands: 2–6 lm and 8–14 lm. In the two wave bands, the conversion
397
S.-s. Dai et al. / Infrared Physics & Technology 53 (2010) 396–398
between infrared radiation energy and voltage signal can be expressed as follows:
V s ¼ AR
Z
Ek gdk
ð5Þ
Dk
where g is the detector spectral responsivity. An infrared thermal imager usually operates at certain narrow wave band, so the parameters ek, ak, eak and sak are independent of wavelength k. Eq. (5) can be simplified:
Z Z 2 V s ¼ AR A0 d sa e Lbk ðT 0 Þgdk þ sa ð1 aÞ Lbk ðT u Þgdk Dk Dk Z Lbk ðT a Þgdk þ ea
ð6Þ
where sa is the spectral transmittance of the atmosphere, e is target surface emissivity, a is the absorption of target surface, ea is the atmospheric emissivity. R When expression K = ARA0d2 and Dk Lbk ðtÞgdp ¼ f ðtÞ are brought into Eq. (6), we obtain:
ð7Þ
When expression Vs/K = f(T0 ) is brought into Eq. (7), Eq. (8) can be obtained:
f ðT 0 Þ ¼ sa ½ef ðT 0 Þ þ ð1 aÞf ðT u Þ þ ea f ðT a Þ
ð8Þ
where T0 is the temperature measured by infrared thermal imager. When an object is regarded as gray, the e equals a and the ea equals aa (ea = aa = 1 sa). Eq. (8) is also written as:
f ðT 0 Þ ¼ sa ½ef ðT 0 Þ þ ð1 eÞf ðT u Þ þ ð1 sa Þf ðT a Þ
Theoretical and experimental research shows that every detector response in an IRFPA is S-mode nonlinear relation with its received infrared radiation energy [5]. During the course of real temperature measurement, the nonlinear response coefficients can be obtained by blackbody radiation calibration. In Eq. (14), we establish the S-mode nonlinear function expression between temperature and response output value of infrared detector:
H¼
Dk
V s ¼ Kfsa ½ef ðT 0 Þ þ ð1 aÞf ðT u Þ þ ea f ðT a Þg
3. Establishment of high-precision infrared temperature measurement model
A þD 1 þ exp½BðT CÞ
ð14Þ
where A–D are the response coefficients of each detector. The inverse function expression of Eq. (14) is:
T¼
1 ½lnðA þ D HÞ lnðH DÞ þ C B
First-order derivative of Eq. (15) is written as:
T 0 ¼ A ½BðA þ D HÞðH DÞ1
1 H0 ¼ ½BðA þ D TÞðT DÞ A
gk Lbk ðTÞdk ¼
Dk
gk
Dk
c1
pk5
2
H ¼ aT 3 þ bT þ cT þ d
ð18Þ
where T is object’s radiation temperature, H is detection unit response output value of IRFPA, a–d are the response coefficients of
ð9Þ A
½expðc2 =kTÞ 11 dk
ð10Þ
n
180
1
sa
1 T na
80 20
e sa
T 0n ð1 eÞT nu
1
sa
1=n 1 T na
40
60
80
100
120
140
160
180
200
Temperature (ºC) Fig. 1. Diagram of IRFRA non-uniformity correction.
ð12Þ
220 200
ð13Þ
From Eq. (13), we know environmental temperature can affect temperature measurements of infrared thermal imager under certain conditions. When using the different wave bands imager, the value of n is different. For the HgCdTe (8–14 lm) IRFPA, the value of n is 4.09 and for the InSb (2–6 lm) IRFPA the value of n is 8.68 (n parameter can be found from The Sadtler Handbook of Infrared Spectra [4]). Therefore, if IRFPA temperature, ambient temperature, atmospheric temperature, as well as the target object emissivity and atmospheric transmission conditions are given, the target surface temperature can be calculated accurately by Eq. (13).
180
Gray
1 1
140
100
Finally, the formula for calculating real temperature of object surface is given out by
T0 ¼
160
120
ð11Þ
eT n0 þ ð1 eÞT nu þ
C
200
where C is constant. When Eq. (11) is substituted into Eq. (9), Eq. (12) can be got:
T 0n ¼ sa
B
220
For IRFPA with different responding wave bands, they have different spectral responsivity with wavelength variation. According to the relation of gk and k, we can obtain Eq. (11) by applying integral operator for Eq. (10):
f ðTÞ CT
ð17Þ
The indefinite integral expression of Eq. (17) is:
Gray
f ðTÞ ¼
Z
ð16Þ
Similarly, first-order derivative of Eq. (14) is also written as:
According to Planck’s Law [3]:
Z
ð15Þ
160 140 120 100 80 20
40
60
80
100
120
140
160
Temperature (ºC) Fig. 2. Diagram of corrected curves.
180
200
398
S.-s. Dai et al. / Infrared Physics & Technology 53 (2010) 396–398
Table 1 Form of temperature comparison between two algorithms.
4. Experimental results and comparison
Real temperature (°C)
Traditional algorithm (°C)
Proposed algorithm (°C)
21 26 35 40 50 60 70 80 110 120 140 160 180 200 Error variance
27.27 30.79 33.43 38.70 45.73 55.40 65.07 76.50 112.53 125.72 146.81 161.756 178.02 194.28 20.59
23.15 28.35 32.12 39.31 48.26 59.49 69.66 80.59 110.92 121.90 141.20 157.15 177.62 202.28 3.66
The experiment is carried out with a rate of 25 frames per minute by an IRFPA detector with the 320 240 pixel. The non-uniformity of IRFPA is calibrated using a blackbody working range of 0– 200 °C. Table 1 lists the temperature error variance of comparison results between the proposed algorithms and the traditional algorithm [6,7], and the curve of comparison is also drawn in Fig. 3. From Table 1, it is clear that the temperature error variance between the temperature value obtained by the proposed algorithm and the real temperature value is 3.66, however, that between the temperature values obtained by the traditional algorithm and the real temperature value is 20.59. Fig. 3 shows the measurement temperatures of the proposed algorithm are much nearer to real temperatures than that of the traditional algorithm. 5. Conclusion
Traditional Algorithm
In this paper, a high-precision infrared temperature measurement algorithm is proposed, which adopts error compensation of some influence factors to ensure high-precision temperature measurement. Finally, Table 1 shows that the error variance of proposed algorithm is less than that of traditional algorithm, and Fig. 3 curves also show the temperature measurement error range of the proposed algorithm is narrower than that of the traditional algorithm. Also the experimental results show that the higher temperature measurement precision can be obtained by using the proposed algorithm. It is very suitable for engineering application.
Proposed Algorithm
8 6
T (ºC)
4 2 0 -2
20
40
60
80
100
120
140
160
180
200
Temperature (ºC)
-4 -6
Acknowledgements
-8 Fig. 3. Diagram of the temperature difference between two algorithms.
every detector among which the differences which cause the nonuniformity response in IRFPA. In order to improve the temperature measurement precision of infrared thermal imager, the non-uniformity response of an IRFPA must be corrected and then temperature measurement can then be implemented. After non-uniformity correction, the detector response equation can be written as: 0
0
H0 ¼ a0 T 3 þ b T 2 þ c0 T þ d
ð19Þ
Generally, the progress of non-uniformity correction is to establish the mapping relation between H and H0 . The mapping function expressions from the coefficients a–d to the coefficients a0 –d0 are also found. Through the mapping relation between Eqs. (18) and (19), the non-uniformity response of IRFPA is corrected. Any two nonlinear response curves A and B of detectors in IRFPA and the standard response curve C are drawn in Fig. 1. Corrected curves are drawn in Fig. 2. The symmetry curve of Eq. (19) about y = x is expressed as 0
0
T 0 ¼ a0 H3 þ b H2 þ c0 H þ d
ð20Þ
Under given conditions such as the target emissivity, ambient temperature, atmospheric temperature and the operating wave band of IRFPA, combining Eqs. (13) and (20) we can calculate object surface temperature.
This work is supported by the NSAF Foundation (No. 10776040) of National Natural Science Foundation of China, the National Natural Science Foundation of China (No. 60602057), the Project of Key Laboratory of Signal and Information Processing of Chongqing (No. CSTC2009 CA2003), the Natural Science Foundation of Chongqing Science and Technology Commission (CSTC2006BB2373, CSTC2009BB2287), the Natural Science Foundation of Chongqing Municipal Education Commission (No. KJ060509, KJ080517), the Program for New Century Excellent Talents in University (No. NCET-10-0927) and the Natural Science Foundation of Chongqing University of Posts and Telecommunications (CQUPT) (A2006-04, A2006-86). References [1] Y.-H. Li, X.-G. Sun, G.-B. Yuan, Accurate measuring temperature with infrared thermal imager, Options and Precision Engineering 15 (9) (2007) 1336–1341. [2] L. Yang, Calculation and error analysis of temperature measurement using thermal imager, Infrared Technology 21 (4) (1999) 20–24. [3] H.-K. Liu, L. Yang, Effect of radiation of the sun on infrared temperature measurement, Infrared Technology 24 (1) (2002) 34–37. [4] W.S. William, Sadtler Handbook of Standard Infrared Grating Spectra [M], Sadtler Research Laboratories Inc., Philadelphia, 1980. [5] G.-H. Hu, Q. Chen, X.-Y. Shen, Research on the nonlinearity of Infrared Focal Plane Arrays, Journal of Optoelectronics Laser 14 (5) (2003) 489–492. [6] Z.-F. Lu, Y.-L. Pan, X.-J. Wang, Q. Sun, L.-S. Gu, Z.-W. Lu, Y.-C. Liu, Influence of object-system distance on accuracy of temperature measurement with IR system, Infrared Technology 30 (5) (2008) 271–274. [7] G. Liu, Z.-J. Huang, H. Zhou, Y.-X. He, S.-H. Chen, X.-J. Yi, IRFPA no-uniformity correction using the DSP image processing system, Infrared Technology 26 (6) (2004) 34–37.