Analysis of Solar Diffuser BRDF Characteristics and Their Effect on On-Board Calibration

Zhiyuan Zhang; Hongyao Chen; Wenxin Huang; Xiaolong Si; Shiwei Bao; Xiaobing Zheng

doi:10.3788/AOS250565

Acta Optica Sinica, Volume. 45, Issue 12, 1228013(2025)

Analysis of Solar Diffuser BRDF Characteristics and Their Effect on On-Board Calibration

Zhiyuan Zhang^1,2, Hongyao Chen^2、*, Wenxin Huang², Xiaolong Si², Shiwei Bao², and Xiaobing Zheng²

Author Affiliations

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

²Key Laboratory of Optical Calibration and Characterization, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, Anhui , China

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Figures & Tables(16)

Fig. 1. Relative geometric relationship between incident vector and reflected vector

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Fig. 2. BRDF absolute measurement facility

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Fig. 3. Surface scattering characteristic of the solar diffuser

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Fig. 4. Test sample

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Fig. 5. BRDF of a perfect Lambertian surface at any incident angle

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Fig. 6. Solar diffuser BRDF at different incident zenith angles (radial direction is θ_r, with a range of 45° to 70° and an interval of 15°)

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Fig. 7. Solar diffuser BRDF for different incident zenith angles and reflected azimuth angles at the same reflected zenith angle

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Fig. 8. Relationship between the measurement uncertainty of reflected signals and energy level

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Fig. 9. Test sample after 100 h of irradiation and sample that have not undergone irradiation

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Fig. 10. Decay result of the solar diffuser with different angles after 100 h irradiation

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Fig. 11. Relative solar diffuser BRDF at different incident zenith angles

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Table 1. Measurement uncertainty (k=2) of the solar diffuser BRDF
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Table 1. Measurement uncertainty (k=2) of the solar diffuser BRDF
Spectral band /nm Relative uncertainty （k=2） /%
350‒410 1.04
410‒480 0.60
480‒1000 0.43
1000‒2400 0.86

Table 2. Measurement plan of the solar diffuser (the text in parentheses indicates the angular interval)

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Table 2. Measurement plan of the solar diffuser (the text in parentheses indicates the angular interval)

Incident zenith angle /（°）	Incident azimuth angle /（°）	Reflected zenith angle /（°）	Reflected azimuth angle /（°）	Wavelength /nm
0‒25 （5）	0	15‒75 （5）	60‒300 （60）	650
30‒40 （5）			60‒300 （30）
45‒55 （5）			60‒300 （15）
60‒75 （5）			60‒300 （10）

Table 3. Rise in solar diffuser BRDF measurement uncertainty for each 1% decrease in BRDF at different incident zenith angles
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Table 3. Rise in solar diffuser BRDF measurement uncertainty for each 1% decrease in BRDF at different incident zenith angles
Incident zenith angle /（°） Measurement uncertainty increases /%
0 0.00145
20 0.00145
45 0.00204
65 0.00351
75 0.00577

Table 4. Effect of placement errors on the accuracy of on-board calibrations at different incident zenith angles

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Table 4. Effect of placement errors on the accuracy of on-board calibrations at different incident zenith angles

Incident zenith angle /（°）	BRDF relative change /%
Incident zenith angle /（°）	$θ_{i} + 0.2 °$	$θ_{i} - 0.2 °$	$θ_{r} + 0.2 °$	$θ_{r} - 0.2 °$	$φ + 0.2 °$
0	0.063	0.063	0.044	0.044	0
20	0.123	0.121	0.014	0.014	2.39×10^-5
45	0.276	0.304	0.043	0.073	0.016
65	0.702	0.691	0.162	0.161	8.17×10^-5
75	1.002	0.983	0.248	0.246	2.30×10^-5

Table 5. Influence of the on-board calibration angle design on the calibration accuracy

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Table 5. Influence of the on-board calibration angle design on the calibration accuracy

Factor	Relative uncertainty /%
Factor	Reasonable design	Unreasonable design
Total	3.49	4.60
SD BRDF measurement	1.00	1.12
SD cosine error of incidence	0.54	0.54
SD radiance non-uniformity	0.9	0.9
Earth-sun distance correction factor	0.2	0.2
SD stability monitor	0.86	0.86
Attenuation varies with observation angle	0.8	2.9
Measurement of SDH factor before launch	0.5	0.5
Solar spectral irradiance	1	1
SD BRDF variation due to the placement error	0.1	1.0
Stray light	2.72	2.72

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Zhiyuan Zhang, Hongyao Chen, Wenxin Huang, Xiaolong Si, Shiwei Bao, Xiaobing Zheng. Analysis of Solar Diffuser BRDF Characteristics and Their Effect on On-Board Calibration[J]. Acta Optica Sinica, 2025, 45(12): 1228013

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Paper Information

Category: Remote Sensing and Sensors

Received: Feb. 5, 2025

Accepted: Mar. 10, 2025

Published Online: Jun. 23, 2025

The Author Email: Hongyao Chen (hychen@aiofm.ac.cn)

DOI:10.3788/AOS250565

CSTR:32393.14.AOS250565

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Measurement uncertainty (k=2) of the solar diffuser BRDF

Table 1. Measurement uncertainty (k=2) of the solar diffuser BRDF

Table 2. Measurement plan of the solar diffuser (the text in parentheses indicates the angular interval)

Table 2. Measurement plan of the solar diffuser (the text in parentheses indicates the angular interval)

Table 3. Rise in solar diffuser BRDF measurement uncertainty for each 1% decrease in BRDF at different incident zenith angles

Table 3. Rise in solar diffuser BRDF measurement uncertainty for each 1% decrease in BRDF at different incident zenith angles

Table 4. Effect of placement errors on the accuracy of on-board calibrations at different incident zenith angles

Table 4. Effect of placement errors on the accuracy of on-board calibrations at different incident zenith angles

Table 5. Influence of the on-board calibration angle design on the calibration accuracy

Table 5. Influence of the on-board calibration angle design on the calibration accuracy