Relative Radiometric Calibration for Space Camera with Optical Focal Plane Assembly

Fig. 9. Calibration images before and after radiometric correction. (a) Vignetting image before relative radiometric correction; (b) image after relative radiometric correction

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Fig. 10. Scene images before and after radiometric correction. (a) Original vignetting image before relative radiometric correction; (b) image after relative radiometric correction

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Table 1. Parameters and expressions of average radiometric responsivity

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Table 1. Parameters and expressions of average radiometric responsivity

Parameter	Expression
Zeroth moment M₀	M₀= $\begin{matrix} \overset{λ = \infty}{\int_{λ = 0}} \end{matrix}$ R(λ)dλ
First moment M₁	M₁= $\begin{matrix} \overset{λ = \infty}{\int_{λ = 0}} \end{matrix}$ λR(λ)dλ
Second moment M₂	M₂= $\begin{matrix} \overset{λ = \infty}{\int_{λ = 0}} \end{matrix}$ λ²R(λ)dλ
Center wavelength λ_C	λ_C=M₁/M₀
Variance σ²	σ²=M₂/M₀- $\begin{matrix} λ_{C}^{2} \end{matrix}$
Short wavelength limit λ₁	λ₁=λ_C- $\begin{matrix} \sqrt[]{3} \end{matrix}$ σ
Long wavelength limit λ₂	λ₂=λ_C+ $\begin{matrix} \sqrt[]{3} \end{matrix}$ σ
Bandwidth Δλ	Δλ=2 $\begin{matrix} \sqrt[]{3} \end{matrix}$ σ
Average radiometric responsivity R_n	R_n=M₀/Δλ

Table 2. Calibration results of image sensors
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Table 2. Calibration results of image sensors
CCD number CCD serial number Radiometric responsivity /(DN·W^-1·m²) Saturation irradiance /(W·m^-2)
CCD 1 8652 1538.9 0.5078
CCD 2 8644 1535.5 0.5083
CCD 3 8657 1527.9 0.5051
Relative deviation 0.30% 0.27%

Table 3. Calibration results of focal plane components

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Table 3. Calibration results of focal plane components

CCD number	CCD serial number	Saturation irradiance before circuit adjustment /(W·m^-2)	Saturation irradiance after circuit adjustment /(W·m^-2)
CCD 1	8652	0.4822	0.5054
CCD 2	8644	0.5082	0.5046
CCD 3	8657	0.4917	0.5051
Relative deviation		2.2%	0.7%

Table 4. Spectral calibration results of camera
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Table 4. Spectral calibration results of camera
Spectrum band number Short wavelength /nm Center wavelength /nm Long wavelength /nm Out-of-band responsivity
B 448 494 528 1.01%
G 511 563 614 0.47%
R 625 662 700 0.67%
IR 765 831 895 0.06%
P 523 708 896 0.01%

Table 5. Radiometric calibration parameters of panchromatic camera

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Table 5. Radiometric calibration parameters of panchromatic camera

Parameter	Pixel 1	Pixel 2	Pixel 3	Pixel 4
Responsivity /(DN·W^-1·m²·sr)	14.5	14.6	14.7	14.7
Gray level of dark noise /DN	1.51	1.51	1.52	1.51
Linear correlation coefficient	0.9997	0.9995	0.9995	0.9995
Saturation radiance /(W·m^-2·sr^-1)	70.5	70.1	69.6	69.6
Dynamic range	677	677	673	677
Saturation irradiance /(W·m^-2)	0.506	0.503	0.499	0.499

Table 6. PRNU before and after radiometric correction
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Table 6. PRNU before and after radiometric correction
Image Average gray value Standard deviation of gray value PRNU
Before correction 447.5 63.0 14.1%
After correction 507.3 2.1 0.4%

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Xiansheng Li, Hongxing Liu, Jingxu Sun, Changxi Xue, Jianyue Ren, Liguo Zhang, Changzheng Chen, Jianwei Ren. Relative Radiometric Calibration for Space Camera with Optical Focal Plane Assembly[J]. Acta Optica Sinica, 2017, 37(8): 0828006

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