Simplified Calibration Method for Radiation Temperature Measurement System with Wide Dynamic Range

Fig. 5. Error between actual and theoretical calculation values. (a) Attenuator with transmittance of 0.0740%; (b) attenuator with transmittance of 0.8193%

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Fig. 6. Relative errors of inversion temperature and radiance of calibration models for different attenuators. (a) 0.8 ms; (b) 1 ms; (c) radiance (τf=0.0740%); (d) temperature (τf=0.0740%); (e) radiance(τf=0.8193%); (f) temperature (τf=0. 0.8193%)

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Table 1. 2 Inversion results and relative error of calibration model at integration time of 0.2 ms after placing attenuator with transmittance of 0.8193%

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Table 1. 2 Inversion results and relative error of calibration model at integration time of 0.2 ms after placing attenuator with transmittance of 0.8193%

Gray value	Relative error /%(gray value)	Inversion radiance L /(W·m^-2·Sr^-1)	Relative error of inversion radiance /%	Inversion temperature T /℃	Relative error of inversion temperature /%
923.28	-1.41	259.22	-2.21	302.11	-0.70
1288.62	-3.25	426.72	-4.49	355.61	-1.60
1773.38	-4.50	649.10	-5.76	408.52	-2.13
2385.87	-4.38	919.45	-5.30	459.34	-2.07
3130.61	-4.49	1251.02	-5.24	510.71	-2.14
4008.92	-4.15	1634.27	-4.71	561.19	-2.03
5019.64	-3.89	2074.93	-4.32	611.80	-1.97
6159.72	-3.41	2563.92	-3.72	661.76	-1.81
7424.77	-3.02	3105.85	-3.26	711.83	-1.69

Table 1. 0 Inversion results of calibration model at different integration time after placing attenuator with transmittance of 0.0740%

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Table 1. 0 Inversion results of calibration model at different integration time after placing attenuator with transmittance of 0.0740%

Gray value		L(0.8 ms) /(W·m^-2·Sr^-1)	T(0.8 ms) /℃	L(1 ms) /(W·m^-2·Sr^-1)	T(1 ms) /℃
0.8 ms	1 ms	L(0.8 ms) /(W·m^-2·Sr^-1)	T(0.8 ms) /℃	L(1 ms) /(W·m^-2·Sr^-1)	T(1 ms) /℃
1499.72	1847.79	607.51	398.65	612.36	399.70
1990.44	2461.21	1199.81	501.61	1204.73	502.32
2673.44	3314.98	2008.67	602.16	2013.38	602.67
3543.04	4402.00	3034.78	702.40	3038.53	702.73
4585.58	5705.20	4238.37	800.69	4244.03	801.12
5784.06	7203.34	5610.39	898.45	5614.45	898.72

Table 1. 1 Relative error of inversion radiance and inversion temperature

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Table 1. 1 Relative error of inversion radiance and inversion temperature

Temperature /℃	L_b /(W·m^-2·Sr^-1)	Relative error of inversion radiance /%		Relative error of inversion temperature /%
Temperature /℃	L_b /(W·m^-2·Sr^-1)	0.8 ms	1.0 ms	0.8 ms	1.0 ms
400	613.74	1.01		0.22		0.34	0.07
500	1188.69	-0.94		-1.35		-0.32	-0.46
600	1988.92	-0.99		-1.23		-0.36	-0.45
700	3007.78	-0.90		-1.02		-0.34	-0.39
800	4229.26	-0.22		-0.35		-0.09	-0.14
900	5633.46	0.41		0.34		0.17	0.14

Table 1. Gray value responses of attenuator with transmittance of 0.0278% at different integration time

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Table 1. Gray value responses of attenuator with transmittance of 0.0278% at different integration time

Temperature /℃	L_b /(W·m^-2·Sr^-1)	G_N(0.8 ms)	G_N(1 ms)
300	253.61	1045.78	1281.57
400	613.74	1169.13	1436.49
500	1188.69	1359.49	1673.39
600	1988.92	1621.32	2001.71
700	3007.78	1949.87	2413.85
800	4229.26	2335.99	2865.68
900	5633.46	2781.38	3450.40
1000	7199.81	3277.95	4072.91

Table 2. Fitting model of attenuator with transmission of 0.0278% at different integration time
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Table 2. Fitting model of attenuator with transmission of 0.0278% at different integration time
Temperature /℃ Integration time /ms Fitting equation R-square
From 300 ℃ to 1000℃ with a gradient of 100 ℃ 0.8 G_N=0.3207L_b+975.9 0.9999
1.0 G_N=0.4001L_b+1193 0.9999

Table 3. Linear coefficients of calibration model for attenuator with transmittance of 0.0740% at integration time of 0.8 ms and 1.0 ms

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Table 3. Linear coefficients of calibration model for attenuator with transmittance of 0.0740% at integration time of 0.8 ms and 1.0 ms

Integration time /ms	A₁	t_int1 /ms	t_int2 /ms	t_int2/t_int1	τ_f2/τ_f1	A₂	Average value
0.8	0.3207	0.8	0.8	1.00	2.664	0.8543	0.8535
	0.4001	1.0	0.8	0.80	2.664	0.8527
1.0	0.3207	0.8	1.0	1.25	2.664	1.0679	1.0669
	0.4001	1.0	1.0	1.00	2.664	1.0659

Table 4. Linear coefficients of calibration model for attenuator with transmittance of 0.8193% at integration time of 0.2 ms
View table
Table 4. Linear coefficients of calibration model for attenuator with transmittance of 0.8193% at integration time of 0.2 ms
Integration time /ms A₁ t_int1 /ms t_int2 /ms t_int2/t_int1 τ_f2/τ_f1 A₂ Averagevalue
0.2 0.3207 0.8 0.2 0.25 29.472 2.3629 2.3606
0.4001 1.0 0.2 0.20 29.472 2.3583

Table 5. Fitting model of attenuator with transmittance of 0.074% at different integration time
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Table 5. Fitting model of attenuator with transmittance of 0.074% at different integration time
Integration time /ms Fitting equation
0.8 G_N=0.8535L_b+975.9
1.0 G_N=1.0669L_b+1193

Table 6. Theoretical temperature measurement limit of calibration model for attenuator with transmittance of 0.0740%
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Table 6. Theoretical temperature measurement limit of calibration model for attenuator with transmittance of 0.0740%
Integration time /ms Fitting equation Saturated radiance /(W·m^-2·Sr^-1) Saturated temperature /℃
0.8 G_N=0.8535L_b+975.9 10807.38 1203.42
1.0 G_N=1.0669L_b+1193 8442.22 1073.45

Table 7. Theoretical temperature measurement limit of calibration model for attenuator with transmittance of 0.8193%
View table
Table 7. Theoretical temperature measurement limit of calibration model for attenuator with transmittance of 0.8193%
Integration time /ms Fitting equation Saturated radiance /(W·m^-2·Sr^-1) Saturated temperature /℃
0.2 G_N=2.3606L_b+324.6 4183.43 796.51

Table 8. Gray value responses of attenuator with transmittance of 0.0740% at different integration time
View table
Table 8. Gray value responses of attenuator with transmittance of 0.0740% at different integration time
Temperature /℃ L_b /(W·m^-2·Sr^-1) G_N(0.8 ms) G_N(1 ms)
400 613.74 1494.41 1846.33
500 1188.69 1999.94 2478.33
600 1988.92 2690.30 3041.07
700 3007.78 3566.08 4434.81
800 4229.26 4593.35 5720.96
900 5633.46 5764.37 7183.06

Table 9. Gray value responses of attenuator with transmittance of 0.8193% at integration time of 0.2 ms
View table
Table 9. Gray value responses of attenuator with transmittance of 0.8193% at integration time of 0.2 ms
Temperature /℃ L_b /(W·m^-2·Sr^-1) G_N(0.2 ms)
300 253.61 936.50
350 408.38 1331.93
400 613.74 1856.87
450 873.20 2495.05
500 1188.69 3277.75
550 1560.76 4182.47
600 1988.92 5222.68
650 2471.88 6376.99
700 3007.78 7656.27

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Dongxiao Ma, Jiachun Wang, Zongsheng Chen, Bing Wang, Yang Liu. Simplified Calibration Method for Radiation Temperature Measurement System with Wide Dynamic Range[J]. Acta Optica Sinica, 2019, 39(6): 0612003

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Jan. 17, 2019

Accepted: Mar. 11, 2019

Published Online: Jun. 17, 2019

The Author Email: Ma Dongxiao (2864594404@qq.com)

DOI:10.3788/AOS201939.0612003

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. 2 Inversion results and relative error of calibration model at integration time of 0.2 ms after placing attenuator with transmittance of 0.8193%

Table 1. 2 Inversion results and relative error of calibration model at integration time of 0.2 ms after placing attenuator with transmittance of 0.8193%

Table 1. 0 Inversion results of calibration model at different integration time after placing attenuator with transmittance of 0.0740%

Table 1. 0 Inversion results of calibration model at different integration time after placing attenuator with transmittance of 0.0740%

Table 1. 1 Relative error of inversion radiance and inversion temperature

Table 1. 1 Relative error of inversion radiance and inversion temperature

Table 1. Gray value responses of attenuator with transmittance of 0.0278% at different integration time

Table 1. Gray value responses of attenuator with transmittance of 0.0278% at different integration time

Table 2. Fitting model of attenuator with transmission of 0.0278% at different integration time

Table 2. Fitting model of attenuator with transmission of 0.0278% at different integration time

Table 3. Linear coefficients of calibration model for attenuator with transmittance of 0.0740% at integration time of 0.8 ms and 1.0 ms

Table 3. Linear coefficients of calibration model for attenuator with transmittance of 0.0740% at integration time of 0.8 ms and 1.0 ms

Table 4. Linear coefficients of calibration model for attenuator with transmittance of 0.8193% at integration time of 0.2 ms

Table 4. Linear coefficients of calibration model for attenuator with transmittance of 0.8193% at integration time of 0.2 ms

Table 5. Fitting model of attenuator with transmittance of 0.074% at different integration time

Table 5. Fitting model of attenuator with transmittance of 0.074% at different integration time

Table 6. Theoretical temperature measurement limit of calibration model for attenuator with transmittance of 0.0740%

Table 6. Theoretical temperature measurement limit of calibration model for attenuator with transmittance of 0.0740%

Table 7. Theoretical temperature measurement limit of calibration model for attenuator with transmittance of 0.8193%

Table 7. Theoretical temperature measurement limit of calibration model for attenuator with transmittance of 0.8193%

Table 8. Gray value responses of attenuator with transmittance of 0.0740% at different integration time

Table 8. Gray value responses of attenuator with transmittance of 0.0740% at different integration time

Table 9. Gray value responses of attenuator with transmittance of 0.8193% at integration time of 0.2 ms

Table 9. Gray value responses of attenuator with transmittance of 0.8193% at integration time of 0.2 ms