Fig. 1. Technical diagram of the space-based digital imaging system for planar targets
Fig. 2. Illustration of coordinate position relationships
Fig. 3. Diagram illustrating line-of-sight position relationships
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
| 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 1. Average orbital elements of the Sun
| 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 2. Methods for solving the visible area
| 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 3. Fitted parameter values for satellite surface material BRDF
| 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 4. Parameters for lens and detector imaging simulation
| Orbital | $a$/km
| $e$ | $i$ | | 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 5. On orbit camera and target orbit parameters
| 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 |
|
Table 6. Calculation and reference table for the position of the Sun at 00:00 on January 1st to June 1st, 2022
