Algorithm 2: Description of the relative calibration of the LJ1-01 nighttime sensor

Input: dark current calibration results $C_i$, i = 1, 2, 3, … N Input: dark current correction reference $\overline{C}$

Input: daytime low-gain calibration data $D{N}_{i,j}{}^{org}$, j = 1, 2, 3, … M Input: model relationship between low- and high-gain DNs of LJ1-01 in HDR mode, $\mathit{P}\mathbf{1}\left[D{N}_{low},D{N}_{high}\right]$, $\mathit{P}\mathbf{2}\left[\overline{D{N}_{low}},\overline{D{N}_{high}}\right]$

Output: relative calibration coefficients $a_{i,low}$ and $b_{i,low}$ for low-gain images and relative correction model for high-gain images $\mathit{P}\mathbf{3}\left[\overline{D{N}_{high}},D{N}_{high}\right]$

for each j = 1 to M do for each i = 1 to N do

Correct the dark current:

$D{N}_{i,j}=D{N}_{i,j}{}^{org}-C_i+\overline{C}$

end for

end for

Compute the average values of all detectors for the uniform daytime calibration data (j = 1):

$\overline{DN}={\displaystyle \sum _i^N}D{N}_{i,1}$

for each i = 1 to N do

Compute the response difference coefficient $g_i$:

$g_i=\frac{\overline{DN}}{D{N}_{i,1}}$

end for

Compute the average value of the interest zone (9 × 9) of each frame: ${\overline{DN}}_j$ Compute the reference detector relative calibration coefficients: $a_{ref}$ and $b_{ref}$

${\overline{DN}}_j=a_{ref}\ast D{N}_{ref,j}+b_{ref}$

for each i = 1 to N do

Compute the relative calibration coefficients of the other detectors for low-gain images:

$a_{i,low}=\frac{g_i}{g_{ref}}\ast a_{ref}$

$b_{i,low}=b_{ref}$

end for

Based on the $\mathit{P}\mathbf{1}\left[D{N}_{low},D{N}_{high}\right]$, $\mathit{P}\mathbf{2}\left[\overline{D{N}_{low}},\overline{D{N}_{high}}\right]$, and the correction model of the low-gain images:

$\mathit{P}\mathbf{1}\left[D{N}_{low},D{N}_{high}\right]: D{N}_{high}=B_0+B_1\ast D{N}_{low}+B_2\ast D{N}_{low}{}^2+\dots +B_n\ast D{N}_{low}{}^n$ $\mathit{P}\mathbf{2}\left[\overline{D{N}_{low}},\overline{D{N}_{high}}\right]:\overline{D{N}_{high}}=B_0+B_1\ast \overline{D{N}_{low}}+B_2\ast {\overline{D{N}_{low}}}^2+\dots +B_n\ast {\overline{D{N}_{low}}}^n$ $\overline{D{N}_{low}}=a_{i,low}\ast D{N}_{i,low}+b_{i,low}$

When the polynomial is of order n = 2, the relative correction model for high-gain images $\mathit{P}\mathbf{3}\left[\overline{D{N}_{high}},D{N}_{high}\right]$ is:

$\begin{array}{c}\overline{D{N}_{high}}=\frac{{\left(B_1\pm \sqrt{-4B_2{B}_0+B_1^2+4B_{2}D{N}_{high}}\right)}^2{a}_{low}^2}{4B_2}\hfill \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-\frac{\left(2B_2{b}_{low}{a}_{low}+B_1{a}_{low}\right)\left(B_1\pm \sqrt{-4B_2{B}_0+B_1^2+4B_{2}D{N}_{high}}\right)}{2B_2}+B_2{b}_{low}^2+B_1{b}_{low}+B_0\hfill \end{array}$

return $a_{i,low}$, $b_{i,low}$, and $\mathit{P}\mathbf{3}\left[\overline{D{N}_{high}},D{N}_{high}\right]$.