Infrared and Laser Engineering, Volume. 52, Issue 12, 20230351(2023)
The construction method of space-based digital imaging link mathematical model
Figures & Tables(20)
Fig. 1. Technical diagram of the space-based digital imaging system for planar targets
Fig. 4. Partitioning of geometric surface mesh based on different distance functions. (a) Square; (b) Sphere; (c) Circular ring; (d) Cube
Fig. 5. Schematic diagram of light source importance sampling for radiative transfer path
Fig. 6. Illustration of the number of bounding boxes for different layer depths. (a) Layer depth 1; (b) Layer depth 2; (c) Layer depth 4; (d) Layer depth 6
Fig. 7. Modulation transfer function and mathematical representation of noise in imaging process
Fig. 8. (a), (b) Represent the position error values between the calculated results of the camera and target for 24 hours and 15 days, respectively, using the mathematical model, and the simulated results from STK
Fig. 9. Results of target visibility time periods within 15 days. (a) Visibility model calculation result; (b) STK simulation result
Fig. 10. Imaging results at different distances within the visible time period
Fig. 11. Imaging results under different poses and lighting directions
Fig. 12. (a) Three-dimensional schematic of the high-frequency vibration transfer function MTF for the imaging platform; (b) Spectrum plot within the cutoff frequency
Fig. 13. The influence of different amplitudes of high-frequency vibrations on MTF
Fig. 14. (a) Target radiance image; (b) Image with added high-frequency platform vibrations; (c) Image with added photon noise; (d) Image with the combined effects of high-frequency vibrations and photon noise
Table 1. Average orbital elements of the Sun
View tableView in ArticleTable 1. Average orbital elements of the Sun
Parameter Method of calculation T is the Julian century number calculated from January 1, 2000, 12:00. Semimajor axis/km a= 149597870 Eccentricity e= 0.01670862 − 0.0004204T− 0.00000124T2 Inclination/(°) i = 23°26'21''.448 − 46''.8150− 0''.00059T2 + 0''.001813T3 RAAN/(°) $\varOmega = 0$ Argument of perigee/(°) ω= 282°56'14''.45 + 6190''.32T + 1''.655T2 + 0''.012T3 Mean anomaly/(°) M= 357°31'44''.76 + 129596581''.04T− 0''.562T2− 0''.012T3
Table 2. Methods for solving the visible area
View tableView in ArticleTable 2. Methods for solving the visible area
Area Solution method GEarth $\begin{gathered} \left\{ {\left. { { {\boldsymbol{r} }_c},{R_E},{ {\boldsymbol{r} }_o},{h_0},{ {\boldsymbol{r} }_{co} } } \right|\beta > {\beta _0} {\text{or}} (\beta < {\beta _0}\; {\rm{and} } \; \alpha < {\alpha _0})} \right\} \\ = \left\{ \begin{gathered} \left. { { {\boldsymbol{r} }_c},{R_E},{ {\boldsymbol{r} }_o},{h_0},{ {\boldsymbol{r} }_{co} } } \right| \arccos \left( {\frac{ { - { {\boldsymbol{r} }_c} \cdot { {\boldsymbol{r} }_{co} } } }{ {\left| { { {\boldsymbol{r} }_c} } \right| \cdot \left| { { {\boldsymbol{r} }_{co} } } \right|} } } \right) > \arccos \frac{ {\sqrt { { {\left| { { {\boldsymbol{r} }_c} } \right|}^2} - { {({h_0} + {R_E})}^2} } } }{ {\left| { { {\boldsymbol{r} }_c} } \right|} }or \\ \left( {\left( {\arccos \left( {\frac{ { - { {\boldsymbol{r} }_c} \cdot { {\boldsymbol{r} }_{co} } } }{ {\left| { { {\boldsymbol{r} }_c} } \right| \cdot \left| { { {\boldsymbol{r} }_{co} } } \right|} } } \right) < \arccos \frac{ {\sqrt { { {\left| { { {\boldsymbol{r} }_c} } \right|}^2} - { {({h_0} + {R_E})}^2} } } }{ {\left| { { {\boldsymbol{r} }_c} } \right|} } } \right)\;{\rm{and} }\; \left( {\arccos \left( {\frac{ { { {\boldsymbol{r} }_o} \cdot { {\boldsymbol{r} }_c} } }{ {\left| { { {\boldsymbol{r} }_o} } \right| \cdot \left| { { {\boldsymbol{r} }_c} } \right|} } } \right) < \arccos \frac{ {\sqrt { { {\left| { { {\boldsymbol{r} }_c} } \right|}^2} - { {({h_0} + {R_E})}^2} } } }{ {\left| { { {\boldsymbol{r} }_c} } \right|} } } \right)} \right) \\ \end{gathered} \right\} \\ \end{gathered}$ $ \begin{gathered} {{\boldsymbol{r}}_c},{{\boldsymbol{r}}_o}{\text{ and }}{{\boldsymbol{r}}_s}{\text{ are the distances from the camera, target, and sun to the center of the earth, respectively;}}\;{R_E}{\text{ is the Earth radius}};{h_0}{\text{ is the height of the critical line of sight}} \\ {\text{ from the ground; }}{{\boldsymbol{r}}_{co}}{\text{ is the distance from the target to the camera;}}\;\beta {\text{ is the angle between - }}{{\boldsymbol{r}}_c}{\text{ and }}{{\boldsymbol{r}}_{co}};\;{\beta _0}{\text{ is the angle between thecritical axis of view and - }}{{\boldsymbol{r}}_c}; \\ \alpha {\text{ is the angle between }}{{\boldsymbol{r}}_c}{\text{ and }}{{\boldsymbol{r}}_o};\;{\alpha _0}{\text{ is the angle between the perpendicular of the critical axis of view and the center of the earth and }}{{\boldsymbol{r}}_c}. \\ \end{gathered} $ GEclipse $\left\{ { { {\boldsymbol{r} }_o},{ {\boldsymbol{r} }_s}|\gamma \leqslant \pi /2{\text{or } }\left| { { {\boldsymbol{r} }_o} } \right|\sin \gamma > {R_E} } \right\} = \left\{ { { {\boldsymbol{r} }_o},{ {\boldsymbol{r} }_s}|\dfrac{ { { {\boldsymbol{r} }_o} \cdot { {\boldsymbol{r} }_s} } }{ {\left| { { {\boldsymbol{r} }_o} } \right| \cdot \left| { { {\boldsymbol{r} }_s} } \right|} } \geqslant 0{\text{ or } }\left| { { {\boldsymbol{r} }_o} } \right|\sin (\arccos (\dfrac{ { { {\boldsymbol{r} }_o} \cdot { {\boldsymbol{r} }_s} } }{ {\left| { { {\boldsymbol{r} }_o} } \right| \cdot \left| { { {\boldsymbol{r} }_s} } \right|} })) \geqslant {R_E} } \right\}{\text{ } }\gamma {\text{ is the angle between } }{ {\boldsymbol{r} }_o}{\text{ and } }{ {\boldsymbol{r} }_s}.$ Gsun $\left\{ { { {\boldsymbol{r} }_{co} },{ {\boldsymbol{r} }_{cs} }|\varUpsilon > {\varUpsilon _0} } \right\} = \left\{ { { {\boldsymbol{r} }_{co} },{ {\boldsymbol{r} }_{cs} }|\dfrac{ { { {\boldsymbol{r} }_{co} } \cdot { {\boldsymbol{r} }_{cs} } } }{ {\left| { { {\boldsymbol{r} }_{co} } } \right| \cdot \left| { { {\boldsymbol{r} }_{cs} } } \right|} } < \cos {\varUpsilon _0} } \right\}$ ${{\boldsymbol{r}}_{cs}}{\text{ is the distance from the sun to the camera;}}{\Upsilon _0}{\text{ is the critical angle of the solar apparent circular plane}}.$ Gp ${\text{Determined by factors such as the field of view angle,detection distance, and signal-to-noise ratio of the detector} }{\text{.} }$
Table 3. Fitted parameter values for satellite surface material BRDF
View tableView in ArticleTable 3. Fitted parameter values for satellite surface material BRDF
Material ar br kb kd kr Silicon solar panel 0.557 −261.6 15.42 0.047 0.717 Polyimide 0.458 −51.90 28.38 0.077 1.865
Table 4. Parameters for lens and detector imaging simulation
View tableView in ArticleTable 4. Parameters for lens and detector imaging simulation
Item Value Item Value Focal length 4.5 m Number of pixels 1024×1024 Simulation band 450-850 nm Pixel size 6.5 μm× 6.5 μm Camera aperture 0.36 m Quantum efficiency 55% Lens transmission efficiency $ \geqslant 0.7$ Full well charge 30 K Quantization bits 11 Readout noise 2e- Number of pixel samples 50 Dark current noise 35 e-/s
Table 5. On orbit camera and target orbit parameters
View tableView in ArticleTable 5. On orbit camera and target orbit parameters
Orbital $a$ $e$ $i$ Camera 6868.8546 0.0066917 97.4154 Satellite 6796.7142 0.0006096 51.6417 Orbital $\omega $ ${\varOmega }$ M Camera 140.0776 200.0074 183.0867 Satellite 117.6201 40.2943 7.3764
Table 6. Calculation and reference table for the position of the Sun at 00:00 on January 1st to June 1st, 2022
View tableView in ArticleTable 6. Calculation and reference table for the position of the Sun at 00:00 on January 1st to June 1st, 2022
Date Calculation results Solar apparent right ascension/ h m s Solar apparent declination/ (°)(′)(″) Jan. 1st 18 45 52 −23 01 03 Feb. 1st 20 58 15 −17 09 46 Mar. 1st 22 47 34 −07 40 21 Apr. 1st 00 41 24 04 27 11 May 1st 02 32 49 15 00 32 Jun. 1st 04 35 39 22 01 18 Date Astronomical calendar query results Solar geocentric right ascension/ h m s Solar geocentric declination/ (°)(′)(″) Jan. 1st 18 45 48 −23 01 13 Feb. 1st 20 58 12 −17 10 07 Mar. 1st 22 47 31 −07 40 25 Apr. 1st 00 41 21 04 26 54 May 1st 02 32 47 15 00 24 Jun. 1st 04 35 38 22 01 20
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Yaru Li, Liang Zhou, Zhaohui Liu, Wenji She. The construction method of space-based digital imaging link mathematical model[J]. Infrared and Laser Engineering, 2023, 52(12): 20230351
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Received: Jun. 8, 2023
Accepted: --
Published Online: Feb. 23, 2024
The Author Email: Zhou Liang (zhouliang@opt.ac.cn)
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