Progressive photon mapping algorithm for digital imaging of a space target

Yaru Li; Yaru Li; Yaru Li; Liang Zhou; Liang Zhou; Zhaohui Liu; Zhaohui Liu; Wenji She; Wenji She

doi:10.1364/AO.495869

Applied Optics
Vol. 62,
Issue 26,
pp. 7000-7007
(2023)
•https://doi.org/10.1364/AO.495869

Progressive photon mapping algorithm for digital imaging of a space target

Yaru Li, Liang Zhou, Zhaohui Liu, and Wenji She

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Yaru Li, Liang Zhou, Zhaohui Liu, and Wenji She, "Progressive photon mapping algorithm for digital imaging of a space target," Appl. Opt. 62, 7000-7007 (2023)

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Related Topics
Table of Contents Category
- Imaging Systems, Image Processing, and Displays
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: May 17, 2023
- Revised Manuscript: August 15, 2023
- Manuscript Accepted: August 19, 2023
- Published: September 5, 2023

Abstract

Space target imaging simulation holds great significance for the development of space-based imaging systems and the prediction of imaging tasks. Currently, commonly used rendering algorithms in space target imaging simulation suffer from issues such as radiance calculation results lacking actual physical significance and rendered images containing high-frequency noise. To address these issues, this study proposes a rendering algorithm based on progressive photon mapping in the context of space imaging scenarios, aiming to enhance the accuracy of energy calculations and image rendering for space targets. This algorithm generates multiple photon maps on the target surface through multiple iterations, retrieves photon information near the observation point based on these photon maps, and thus obtains the radiance of the observation direction vector. This study evaluates the quality of rendered images using no-reference image quality assessment algorithms. The results demonstrate that this algorithm can enhance image rendering quality in specific imaging scenarios, consequently improving the accuracy of space target recognition. By comparing the calculated values of this algorithm with the theoretical radiance values for diffuse material, the accuracy of the radiance calculation results of this algorithm is verified, which can provide significant reference values for the selection of backend detectors.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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	Semi Major Axis	Eccentricity	Inclination	Argument of Perigee	Right Ascension of the Ascending node	Mean Anomaly
Orbital	$a (k m)$	$e$	$i$	$w$	$Ω$	$M$
Camera	6868.8546	0.0066917	97.4154	140.0776	200.0074	183.0867
Satellite	6796.7142	0.0006096	51.6417	117.6201	40.2943	7.3764

Coordinate System Conversion	Transformation Matrix
Step1: from satellite body to centroid orbit coordinate system	$[\begin{matrix} \cos ζ \cos ψ - \sin ζ \sin φ \sin ψ & - \sin ψ \cos φ & \sin ζ \cos ψ + \cos ζ \sin φ \sin ψ & 0 \\ \cos ζ \sin ψ + \sin ζ \sin φ \cos ψ & \cos φ \cos ψ & \sin ζ \sin ψ - \cos ζ \sin φ \cos ψ & 0 \\ - \sin ζ \cos φ & \sin φ & \cos ζ \sin φ & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$ $ζ : Pitch angle; φ : Roll angle; ψ : Yaw angle$
Step2: from centroid orbit to J2000.0 coordinate system	$[\begin{matrix} - \sin u \cos Ω - \cos u \cos i \sin Ω & - \sin i \sin Ω & - \cos u \cos Ω + \sin u \cos i \cos Ω & 0 \\ - \sin u \sin Ω + \cos u \cos i \cos Ω & \sin i \cos Ω & - \cos u \sin Ω - \sin u \cos i \cos Ω & 0 \\ \cos u \sin i & - \cos i & - \sin u \sin i & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & - l_{eo} \\ 0 & 0 & 0 & 1 \end{matrix}]$ $\begin{array}{l} Orbital angle : u = w + ξ; w : Argument of perigee; ξ : True anomaly; \\ l_{eo} : The distance between the target centroid and the center of the earth \end{array}$
Step3: from J2000.0 to pixel coordinate system	$[\begin{matrix} \frac{1}{d x} & 0 & u_{0} \\ 0 & \frac{1}{d y} & v_{0} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} \frac{f}{Z^{'}} & 0 & 0 & 0 \\ 0 & \frac{f}{Z^{'}} & 0 & 0 \\ 0 & 0 & \frac{f}{Z^{'}} & 0 \end{matrix}] [\begin{matrix} \cos Θ_{x} \cos Θ_{z} & \sin Θ_{x} \cos Θ_{z} & - \sin Θ_{z} & 0 \\ - \sin Θ_{x} & \cos Θ_{x} & 0 & 0 \\ \cos Θ_{x} \sin Θ_{z} & \sin Θ_{x} \sin Θ_{z} & \cos Θ_{z} & 0 \\ 0 & 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 & 0 & - R_{x} \\ 0 & 1 & 0 & - R_{y} \\ 0 & 0 & 1 & - R_{z} \\ 0 & 0 & 0 & 0 \end{matrix}]$ $\begin{array}{l} (u_{0}, v_{0}) : Pixel coordinate corresponding to the image center point; d x, d y : Pixel size; \\ f : Focal length; Z^{'} : Distance between target and camera; R_{x}, R_{y}, R_{z} : The position of \\ the camera in the J2000.0 coordinate system; θ_{x} = \arccos (\frac{r_{x}}{\sqrt{{r_{x}}^{2} + {r_{y}}^{2}}}); θ_{z} = \arccos (\frac{r_{z}}{\sqrt{{r_{x}}^{2} + {r_{y}}^{2} + {r_{z}}^{2}}}) \\ r : The direction vector of the target relative to the camera \end{array}$

Material	$a$	$b$	$k_{b}$	$k_{d}$	$k_{r}$
Silicon solar panel	0.557	−261.6	15.42	0.047	0.717
Polyimide	0.458	−51.90	28.38	0.077	1.865

Focal length	1.6 m	Number of pixels	$1024 \times 1024$
Simulation band	450–850 nm	Pixel size	$6.5 µ m \times 6.5 µ m$
Camera aperture	0.3 m	Quantum efficiency	55%
Lens transmission efficiency	$\geq 0.7$	Single pixel sampling times	50
Quantization bits	11	Full well charge	30 K

	PATH	PPM	PATH	PPM	PATH	PPM
Figure/Evaluation Method	(a)		(b)		(c)
NIQE	13.6427	8.0977	14.7977	5.2609	22.5662	9.8253
BRISQUE	95.4320	79.2411	52.4796	23.8966	91.9515	80.7213
SSEQ	54.2233	52.7589	51.6675	41.4963	61.1922	54.7742
	PATH	PPM	PATH	PPM	PATH	PPM
Figure/Evaluation Method	(d)		(e)		(f)
NIQE	22.1511	9.0291	24.0971	9.4868	15.9706	7.6131
BRISQUE	76.0916	41.3456	96.3218	55.7313	79.0237	41.2414
SSEQ	40.5509	39.2699	55.2941	41.1703	56.6842	45.9191

Abstract

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Applied Optics