Analytical method for calculating internal stray radiation from an IR spectrometer based on the view factor

Zhi-Nan Zhang; Zhi-Nan Zhang; Li-Bo Li; Bing-Liang Hu; Peng-Chong Wang; Ying Yang; Shan-Liang Ke; Shuang Wang; Si-Yuan Li

doi:10.1364/AO.478330

Applied Optics
Vol. 62,
Issue 3,
pp. 725-734
(2023)
•https://doi.org/10.1364/AO.478330

Analytical method for calculating internal stray radiation from an IR spectrometer based on the view factor

Zhi-Nan Zhang, Li-Bo Li, Bing-Liang Hu, Peng-Chong Wang, Ying Yang, Shan-Liang Ke, Shuang Wang, and Si-Yuan Li

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Zhi-Nan Zhang, Li-Bo Li, Bing-Liang Hu, Peng-Chong Wang, Ying Yang, Shan-Liang Ke, Shuang Wang, and Si-Yuan Li, "Analytical method for calculating internal stray radiation from an IR spectrometer based on the view factor," Appl. Opt. 62, 725-734 (2023)

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Abstract

Optomechanical components such as the lens barrels and frames of IR spectrometers produce strong internal stray radiation, which reduces the instrument’s SNR and dynamic range. An IR internal stray radiation calculation method based on an analytical model of the view factor is proposed. The mathematical model of the view factor calculation method of typical optomechanical components is established. For any IR optical systems, the internal stray radiation can be quickly and accurately calculated by adjusting the coordinate systems in the calculation method. Based on the proposed method, the internal stray radiation of a double-pass long-wave IR spectrometer was calculated. The calculation results are consistent with the simulation results. The RMS value of the relative error between the calculated value and the simulated value is around 11%. To verify the proposed method, an experiment was conducted to test the internal stray radiation of the long-wave IR spectrometer. The internal stray radiation test results agree with the calculated and simulated results, and the relative error between the test results and the calculation results is within 9%.

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Parameter	Specification
Spectral range	8–11 µm
Spectral resolution	40 nm
Numerical aperture	0.133
Field of view	91.44 mm

		Irradiance of Internal Radiation (W/m²)
Source	View Factor	300 K	230 K	200 K	180 K	153 K	133 K	113 K	100 K
1	0.1032	10.5619	2.4161	0.9526	0.4378	0.0928	0.0228	0.0035	0.0010
2	0.0431	4.4097	1.0087	0.3977	0.1828	0.0388	0.0095	0.0014	0.0004
3	0.2009	20.5607	4.7033	1.8544	0.8523	0.1807	0.0444	0.0068	0.0020
4	0.0767	7.8570	1.7973	0.7086	0.3257	0.0690	0.0170	0.0026	0.0008
5	0.0975	9.9778	2.2824	0.8999	0.4136	0.0877	0.0216	0.0033	0.0010
6	0.0143	1.4655	0.3352	0.1322	0.0607	0.0129	0.0032	0.0005	0.0001
7	0.0261	2.6701	0.6108	0.2408	0.1107	0.0235	0.0058	0.0009	0.0003
8	0.0590	6.0358	1.3807	0.5444	0.2502	0.0530	0.0130	0.0020	0.0006
9	0.0108	1.1046	0.2527	0.0996	0.0458	0.0097	0.0024	0.0004	0.0001
Total	0.6315	64.6429	14.7873	5.8301	2.6796	0.5681	0.1396	0.0212	0.0064

No.	Surface Type	Transmittance	Absorptance	Specular Reflectivity	Integrated BRDF
1	Lens surface	97.8%	1%	1%	0.2%
2	Mirror surface	–	2.9%	97%	0.1%
3	Mechanical surface	–	85%	1%	14%

	Irradiance of Internal Radiation (W/m²)
Source	300 K	230 K	200 K	180 K	153 K	133 K	113 K	100 K
1	10.2510	2.3507	0.9282	0.4243	0.0908	0.0224	0.0034	0.0010
2	3.5045	0.8042	0.3176	0.1453	0.0311	0.0077	0.0012	0.0004
3	21.8436	5.0336	1.9933	0.9134	0.1960	0.0484	0.0074	0.0022
4	7.3957	1.7110	0.6785	0.3113	0.0669	0.0166	0.0025	0.0008
5	10.0520	2.3119	0.9149	0.4190	0.0898	0.0222	0.0034	0.0010
6	1.5185	0.3480	0.1372	0.0627	0.0134	0.0033	0.0005	0.0002
7	3.0006	0.6878	0.2715	0.1241	0.0265	0.0065	0.0010	0.0003
8	5.4145	1.2559	0.4991	0.2293	0.0494	0.0122	0.0019	0.0006
9	1.2384	0.2885	0.1149	0.0528	0.0113	0.0028	0.0004	0.0001
Total	64.2188	14.7915	5.8551	2.6821	0.5753	0.1421	0.0217	0.0065

		View Factor
Source	300 K	230 K	200 K	180 K	153 K	133 K	113 K	100 K	Average	Standard Deviation
1	0.1001	0.1004	0.1005	0.1000	0.1009	0.1011	0.1014	0.1015	0.1007	0.0005
2	0.0342	0.0343	0.0344	0.0342	0.0346	0.0347	0.0348	0.0348	0.0345	0.0002
3	0.2134	0.2149	0.2159	0.2153	0.2179	0.2191	0.2204	0.2208	0.2172	0.0026
4	0.0722	0.0731	0.0735	0.0734	0.0744	0.0749	0.0754	0.0756	0.0741	0.0011
5	0.0982	0.0987	0.0991	0.0987	0.0998	0.1003	0.1007	0.1009	0.0996	0.0009
6	0.0148	0.0149	0.0149	0.0148	0.0149	0.0149	0.0150	0.0150	0.0149	0.0001
7	0.0293	0.0294	0.0294	0.0292	0.0295	0.0295	0.0296	0.0296	0.0294	0.0001
8	0.0529	0.0536	0.0541	0.0540	0.0549	0.0553	0.0559	0.0561	0.0546	0.0011
9	0.0121	0.0123	0.0124	0.0124	0.0126	0.0127	0.0128	0.0129	0.0125	0.0002
Total	0.6273	0.6316	0.6342	0.6321	0.6395	0.6425	0.6461	0.6471	0.6376	0.0068

	Measurement		Relative E
Temperature	View Factor	Internal Stray Radiation (W/m²)	From Calculated Factor	From Simulated Factor
113 K	0.6892	0.0232	0.084	0.075
100 K	0.6491	0.0064	0.027	0.018
Average	0.6692	–	0.056	0.047

		View Factor		Test Error
Temperature Stability		113 K	100 K	113 K	100 K
Temperature fluctuation	$+ 0.1 K$	0.6848	0.6451	−0.6%	−0.6%
Temperature fluctuation	−0.1 K	0.6938	0.6533	0.6%	0.6%
Temperature gradient	$+ 0.4 K$	0.6726	0.6334	−2.4%	−2.4%
Temperature gradient	−0.4 K	0.7061	0.6654	2.5%	2.5%

RMS of Dark	View Factor		Test Error
Current Fluctuation	113 K	100 K	113 K	100 K
1.81DN	0.6981	0.658	1.3%	1.3%

Error Sources of the Experiment	Test Error
Temperature fluctuation of spectrometer	0.6%
Temperature gradient of spectrometer	2.5%
Temperature fluctuation of the blackbody	Negligible
Fluctuation of dark current	1.3%
Summary (SRSS)	2.88%

	Relative Error
Source	300 K	230 K	200 K	180 K	153 K	133 K	113 K	100 K
1	0.03	0.03	0.03	0.03	0.02	0.02	0.02	0.02
2	0.26	0.25	0.25	0.26	0.25	0.24	0.24	0.24
3	−0.06	−0.07	−0.07	−0.07	−0.08	−0.08	−0.09	−0.09
4	0.06	0.05	0.04	0.05	0.03	0.02	0.02	0.01
5	−0.01	−0.01	−0.02	−0.01	−0.02	−0.03	−0.03	−0.03
6	−0.03	−0.04	−0.04	−0.03	−0.04	−0.04	−0.04	−0.04
7	−0.11	−0.11	−0.11	−0.11	−0.12	−0.12	−0.12	−0.12
8	0.11	0.10	0.09	0.09	0.07	0.07	0.05	0.05
9	−0.11	−0.12	−0.13	−0.13	−0.14	−0.15	−0.16	−0.16
Average	0.016	0.009	0.005	0.008	−0.003	−0.007	−0.013	−0.014
RMS	0.112	0.111	0.111	0.112	0.111	0.111	0.111	0.111

	Relative Error
Source	300 K	230 K	200 K	180 K	153 K	133 K	113 K	100 K
1	0.03	0.03	0.03	0.03	0.02	0.02	0.02	0.02
2	0.26	0.25	0.25	0.26	0.25	0.24	0.24	0.24
3	−0.06	−0.07	−0.07	−0.07	−0.08	−0.08	−0.09	−0.09
4	0.06	0.05	0.04	0.05	0.03	0.02	0.02	0.01
5	−0.01	−0.01	−0.02	−0.01	−0.02	−0.03	−0.03	−0.03
6	−0.03	−0.04	−0.04	−0.03	−0.04	−0.04	−0.04	−0.04
7	−0.11	−0.11	−0.11	−0.11	−0.12	−0.12	−0.12	−0.12
8	0.11	0.10	0.09	0.09	0.07	0.07	0.05	0.05
9	−0.11	−0.12	−0.13	−0.13	−0.14	−0.15	−0.16	−0.16
Average	0.016	0.009	0.005	0.008	−0.003	−0.007	−0.013	−0.014
RMS	0.112	0.111	0.111	0.112	0.111	0.111	0.111	0.111

Abstract

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Tables (10)

Equations (20)

Applied Optics