Response Nonlinear Calibration of Solar Blind Phototube Detection System Using Indirect Method

Hanhui Cao; Hongyao Chen; Wenxin Huang; Jiawei Li

doi:10.3788/AOS231501

Acta Optica Sinica, Volume. 44, Issue 3, 0304001(2024)

Response Nonlinear Calibration of Solar Blind Phototube Detection System Using Indirect Method

Hanhui Cao^1,2, Hongyao Chen^2、*, Wenxin Huang², and Jiawei Li²

Author Affiliations

¹University of Science and Technology of China, Hefei 230026, Anhui, China

²Key Laboratory of Optical Calibration and Characterization, Anhui Institute of Optics and Fine Mechanics, HFIPS, Chinese Academy of Sciences, Hefei 230031, Anhui, China

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Figures & Tables(15)

Fig. 1. Linear measurement device of solar blind phototube detection system

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Fig. 2. Response nonlinear calibration results of solar blind phototube detection system

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Fig. 3. Change of relative spectral radiance of xenon lamp light source with time

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Fig. 4. Linear fitting results of response photocurrents of reference detector and detector to be tested

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Fig. 5. Correlated coefficient, original response photocurrent, and relative error of response photocurrents of detector to be tested and reference detector. (a) Correlated coefficient; (b) original response photocurrent values; (c) relative error

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Fig. 6. Experimental results of reference detector and light source current changes. (a) Linear fitting result; (b) response nonlinear calibration results; (c) current change of light source over time

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Table 1. Parameters of Si photodiode S2281 and phototube R6800U-11^[25-26]

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Table 1. Parameters of Si photodiode S2281 and phototube R6800U-11^[25-26]

Parameter	S2281	R6800U-11
Spectral response range /nm	190 to 1100	160 to 350
Photocathode material	Si	Cs-Te
Dark current /pA	50@V_R=10 mV and 25 ℃	1
Recommended operating voltage /V	—	15
Ambient temperature /℃	-10 to 60	-80 to 50
Radiant sensitivity /（A/W）	0.12@200 nm and 25 ℃	0.02@254 nm and 25 ℃
Input window material	Quartz	Quartz
Active area size /mm	11.3	8

Table 2. Characteristic parameters of 6485 picoammeter (Keithley)^[27]

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Table 2. Characteristic parameters of 6485 picoammeter (Keithley)^[27]

Range	5¹/₂ digit default resolution	Accuracy（1YR）±（% RDG.+ offset）18-28 °C，0-70% RH	Typical RMS noise	Analog rise time （10% to 90%）
2 nA	10 fA	0.4%+400 fA	20 fA	8 ms
20 nA	100 fA	0.4%+1 pA	100 fA	8 ms
200 nA	1 pA	0.2%+10 pA	1 pA	500 μs
2 μA	10 pA	0.15%+100 pA	10 pA	500 μs
20 μA	100 pA	0.1%+1 nA	100 pA	500 μs
200 μA	1 nA	0.1%+10 nA	1 nA	500 μs
2 mA	10 nA	0.1%+100 nA	10 nA	500 μs
20 mA	100 nA	0.1%+1 μA	100 nA	500 μs

Table 3. Relative response values and relative error at each measurement point

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Table 3. Relative response values and relative error at each measurement point

Measurement point	Response photocurrent of S2281 /A	Response photocurrent of R6800U-11 /A	Relative responsivity	Relative error /%
1	9.314×10^-12	1.384×10^-12	0.149	-1.056
2	4.641×10^-11	6.374×10^-12	0.137	6.591
3	2.053×10^-10	2.806×10^-11	0.137	7.062
4	2.128×10^-9	2.965×10^-10	0.139	5.268
5	1.207×10^-8	1.718×10^-9	0.142	3.210
6	4.863×10^-8	7.034×10^-9	0.145	1.639
7	1.369×10^-7	1.979×10^-8	0.145	1.676
8	2.662×10^-7	3.934×10^-8	0.148	-0.505
9	3.719×10^-7	5.484×10^-8	0.147	-0.270
10	4.308×10^-7	6.330×10^-8	0.147	0.073
11	4.500×10^-7	6.610×10^-8	0.147	0.122

Table 4. Influence of dark background noise on measured values of each measurement point

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Table 4. Influence of dark background noise on measured values of each measurement point

Measurement point	Measured value of R6800U-11 /%	Measured value of S2281 /%
1	180.9796	1.7538
2	39.2955	0.3520
3	8.9255	0.0795
4	0.8448	0.0070
5	0.1458	0.0012
6	0.0328	0.0012
7	0.0117	0.0004
8	0.0067	0.0002
9	0.0048	0.0002
10	0.0042	0.0001
11	0.0040	0.0001

Table 5. Influence of noise on measured values of each measurement point
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Table 5. Influence of noise on measured values of each measurement point
Measurement point Measured value of R6800U-11 /% Measured value of S2281 /%
1 146.804 1.850
2 20.055 0.700
3 5.131 0.573
4 1.073 0.473
5 0.464 0.418
6 0.360 0.361
7 0.313 0.285
8 0.208 0.205
9 0.170 0.165
10 0.162 0.158
11 0.157 0.152

Table 6. Root mean square values of noise at each measuring point

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Table 6. Root mean square values of noise at each measuring point

Measurement point	Root mean square value of R6800U-11 /A	Root mean square value of S2281 /A
1	2.032×10^-12	1.723×10^-13
2	1.278×10^-12	3.246×10^-13
3	1.440×10^-12	1.176×10^-12
4	3.181×10^-12	1.006×10^-11
5	7.967×10^-12	5.043×10^-11
6	2.534×10^-11	1.754×10^-10
7	6.184×10^-11	3.896×10^-10
8	8.168×10^-11	5.457×10^-10
9	9.301×10^-11	6.147×10^-10
10	1.027×10^-10	6.812×10^-10
11	1.036×10^-10	6.853×10^-10

Table 7. Data of nonlinear correction factor for various response photo current

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Table 7. Data of nonlinear correction factor for various response photo current

Photo current /A	Nonlinear correction factor								Relative standard deviation /%
Photo current /A	Group 1	Group 2	Group 3	Group 4	Group 5	Group 6	Group 7	Group 8	Relative standard deviation /%
1.239×10^-9	0.993	0.993	0.990	0.997	0.993	0.994	0.990	0.995	0.222
7.087×10^-9	1.000	0.997	0.995	0.998	0.997	1.008	0.994	0.997	0.422
2.873×10^-8	1.001	0.998	1.002	0.998	1.000	1.001	1.005	0.995	0.296
7.833×10^-8	1.001	1.000	1.002	0.998	1.000	1.003	1.003	1.001	0.158
1.527×10^-7	1.003	1.001	1.001	1.001	1.003	1.001	1.000	1.001	0.108
2.140×10^-7	0.998	1.000	1.002	1.000	1.002	0.999	0.999	1.001	0.151
2.494×10^-7	1.001	0.998	1.001	0.999	1.001	1.002	1.000	1.000	0.127
2.647×10^-7	0.997	1.001	0.999	0.999	0.999	1.001	1.003	0.997	0.212

Table 8. Data of nonlinear correction factor for each measurement point

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Table 8. Data of nonlinear correction factor for each measurement point

Measurement point	Nonlinear correction factor								Relative standard deviation /%
Measurement point	Group 1	Group 2	Group 3	Group 4	Group 5	Group 6	Group 7	Group 8	Relative standard deviation /%
1	1.180	0.934	0.752	1.148	0.670	1.425	0.928	1.049	24.107
2	0.978	0.913	0.898	0.971	0.933	—	0.901	0.949	3.471
3	0.930	0.927	0.927	0.934	0.920	0.946	0.927	0.929	0.826
4	0.949	0.946	0.946	0.949	0.948	0.949	0.948	0.948	0.139
5	0.968	0.967	0.968	0.970	0.969	0.969	0.969	0.968	0.098
6	0.982	0.983	0.984	0.986	0.985	0.985	0.985	0.984	0.123
7	0.981	0.984	0.985	0.985	0.984	0.985	0.984	0.984	0.129
8	1.001	1.004	1.006	1.007	1.007	1.008	1.007	1.007	0.242
9	0.998	1.001	1.003	1.004	1.005	1.005	1.005	1.005	0.256
10	0.995	0.998	1.000	1.001	1.002	1.002	1.002	1.001	0.259
11	0.994	0.998	0.999	1.000	1.001	1.001	1.001	1.001	0.241

Table 9. Combined uncertainty of measurement system

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Table 9. Combined uncertainty of measurement system

Influence factor	Uncertainty /%
Surface nonuniformity（integrating sphere）	0.800
Angle nonuniformity（integrating sphere）	0.500
Standard detector	0.422
Repeatability	0.259
Dark background	0.845
Standard transfer process	0.473
Detection system to be tested（phototube，picoammeter，source meter）	1.073
Combined uncertainty	1.795
Expanded uncertainty（confidence factor k=2）	3.591

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Hanhui Cao, Hongyao Chen, Wenxin Huang, Jiawei Li. Response Nonlinear Calibration of Solar Blind Phototube Detection System Using Indirect Method[J]. Acta Optica Sinica, 2024, 44(3): 0304001

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