Multi-Field-of-View Sparse Aperture Imaging Based on Double Zernike Polynomials

Fig. 3. MTFs of Golay3 optical system under different field coordinates calculated by DZP. (a) (0°, 0°); (b) (0.05°, 0°); (c) (0°, 0.05°); (d) (-0.05°, 0°); (e) (0°, -0.05°); (f) (0.1°, 0°); (g) (0°, 0.1°); (h) (-0.1°, 0°); (i) (0°, -0.1°)

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Fig. 4. MTFs of Golay3 optical system under different field coordinates calculated by ZEMAX software. (a) (0°, 0°); (b) (0.05°, 0°); (c) (0°, 0.05°); (d) (-0.05°, 0°); (e) (0°, -0.05°); (f) (0.1°, 0°); (g) (0°, 0.1°); (h) (-0.1°, 0°); (i) (0°, -0.1°)

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Fig. 5. Simulated imaging results under different field coordinates of sparse aperture optical system. (a) (0°, 0°); (b) (0.05°, 0°); (c) (0°, 0.05°); (d) (-0.05°, 0°); (e) (0°, -0.05°); (f) (0.1°, 0°); (g) (0°, 0.1°); (h) (-0.1°, 0°); (i) (0°, -0.1°)

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Fig. 6. Simulated imaging results under different field coordinates of full aperture optical system. (a) (0°, 0°); (b) (0.05°, 0°); (c) (0°, 0.05°); (d) (-0.05°, 0°); (e) (0°, -0.05°); (f) (0.1°, 0°); (g) (0°, 0.1°); (h) (-0.1°, 0°); (i) (0°, -0.1°)

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Fig. 7. Results of image restoration using Wiener filters under different field coordinates for sparse aperture optical system. (a) (0°, 0°); (b) (0.05°, 0°); (c) (0°, 0.05°); (d) (-0.05°, 0°); (e) (0°, -0.05°); (f) (0.1°, 0°); (g) (0°, 0.1°); (h) (-0.1°, 0°); (i) (0°, -0.1°)

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Fig. 8. Results of image restoration using Wiener filters under different field coordinates for full aperture optical system. (a) (0°, 0°); (b) (0.05°, 0°); (c) (0°, 0.05°); (d) (-0.05°, 0°); (e) (0°, -0.05°); (f) (0.1°, 0°); (g) (0°, 0.1°); (h) (-0.1°, 0°); (i) (0°, -0.1°)

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Fig. 9. Contrast curves before and after Wiener filtering under different field of view coordinates. (a) Field coordinate is (0°,0°); (b) field coordinate is (0.05°,0°); (c) field coordinate is (0°,0.05°); (d) field coordinate is (0.1°,0°)

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Table 1. Field coordinates of Golay3 sparse aperture imaging system

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Table 1. Field coordinates of Golay3 sparse aperture imaging system

Number	Field of view	Number	Field of view
1	（0°，0°）	10	（0.1°，0°）
2	（0.05°，0°）	11	（0.071°，0.071°）
3	（0.035°，0.035°）	12	（0°，0.1°）
4	（0°，0.05°）	13	（-0.071°，0.071°）
5	（-0.035°，0.035°）	14	（-0.1°，0°）
6	（-0.05°，0°）	15	（-0.071°，-0.071°）
7	（-0.035°，-0.035°）	16	（0°，-0.1°）
8	（0°，-0.05°）	17	（0.071°，-0.071°）
9	（-0.035°，0.035°）

Table 2. Fitting results of DZP coefficients for sub-mirror 1

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Table 2. Fitting results of DZP coefficients for sub-mirror 1

j	C₁_，j，₁	C₁_，j，₂	C₁_，j，₃	C₁_，j，₄	C₁_，j，₅	C₁_，j，₆	C₁_，j，₇	C₁_，j，₈	C₁_，j，₉	C₁_，j，₁₀	C₁_，j，₁₁	C₁_，j，₁₂	C₁_，j，₁₃
j=1	0.853	0.528	0.659	0.650	0.347	0.369	0.110	0.438	0.406	0.635	0.306	0.482	0.515
j=2	0.052	-10.230	0.031	0.065	0.011	0.072	0.074	-3.589	0.009	-0.005	-0.006	0.003	0.018
j=3	0.539	0.003	-10.820	0.3662	0.005	-0.191	-3.723	0.003	0.055	0.000	0.085	-0.051	0.026
j=4	0.150	0.460	-0.259	0.365	0.302	-0.033	-0.225	0.381	0.415	0.553	0.385	0.361	0.448
j=5	0.584	0.236	0.766	0.242	0.775	2.839	2.247	0.643	0.656	0.540	0.348	0.774	0.954
j=6	0.674	0.968	0.463	0.634	0.447	0.936	0.966	0.307	0.607	0.586	0.621	0.227	0.699
j=7	0.017	-0.008	0.011	0.023	0.004	0.026	0.026	0.002	0.003	-0.002	-0.002	0.001	0.006
j=8	0.192	0.001	-0.219	0.130	0.002	-0.068	-0.045	0.001	0.020	0.000	0.030	-0.018	0.009
j=9	0.000	-0.009	0.000	0.000	0.011	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
j=10	-0.084	0.003	0.110	-0.057	0.001	0.044	0.033	0.000	-0.006	0.000	-0.008	0.006	0.000
j=11	-0.592	0.120	-0.067	-0.268	0.079	-0.009	-0.059	0.099	0.109	0.144	0.102	0.095	0.117
j=12	0.147	0.061	0.208	0.060	0.202	0.640	0.590	0.168	0.171	0.141	0.091	0.203	0.250
j=13	0.176	0.253	0.121	0.166	0.011	0.245	0.253	0.081	0.159	0.153	0.163	0.059	0.183
j=14	0.884	0.076	-1.065	0.596	0.120	-0.458	-0.343	0.005	0.069	0.000	0.088	-0.060	0.000
j=15	0.582	0.994	0.696	0.755	0.822	0.834	0.534	0.815	0.121	0.147	0.209	0.738	0.333

Table 3. Fitting results of DZP coefficients for sub-mirror 2

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Table 3. Fitting results of DZP coefficients for sub-mirror 2

j	C₂_，j，₁	C₂_，j，₂	C₂_，j，₃	C₂_，j，₄	C₂_，j，₅	C₂_，j，₆	C₂_，j，₇	C₂_，j，₈	C₂_，j，₉	C₂_，j，₁₀	C₂_，j，₁₁	C₂_，j，₁₂	C₂_，j，₁₃
j=1	0.928	0.279	0.133	0.607	0.295	0.347	0.817	0.354	0.206	0.270	0.475	0.342	0.220
j=2	-0.017	-10.250	-0.007	-0.001	-0.003	-0.018	-0.041	-3.619	-0.014	0.003	0.010	0.008	-0.017
j=3	0.000	-0.003	-10.20	-0.002	-0.003	0.002	-3.582	-0.005	0.006	0.002	-0.002	0.006	-0.004
j=4	0.238	0.994	0.536	0.343	0.569	0.493	0.872	0.594	0.242	0.237	0.534	0.329	0.243
j=5	0.775	0.364	0.762	0.536	0.559	0.855	0.376	0.284	0.687	0.207	0.2780	0.941	0.328
j=6	0.163	1.001	0.693	0.504	1.018	0.361	0.848	0.860	0.587	0.149	0.425	0.491	0.625
j=7	-0.002	-0.013	0.000	0.003	0.001	-0.006	-0.014	-0.007	-0.005	0.001	0.004	0.003	-0.006
j=8	0.002	0.001	0.002	0.001	0.000	0.001	0.005	-0.001	0.002	0.001	-0.001	0.002	-0.001
j=9	0.000	0.006	0.000	0.016	-0.004	-0.006	-0.005	-0.006	0.000	0.001	0.001	0.000	-0.009
j=10	0.000	0.007	0.000	0.007	0.001	0.002	0.011	-0.004	0.000	0.000	-0.001	0.000	-0.003
j=11	-0.569	0.260	0.140	-0.273	0.148	0.128	0.228	0.155	0.063	0.062	0.140	0.086	0.063
j=12	0.203	0.095	0.199	0.140	0.146	0.117	0.098	0.074	0.180	0.054	0.073	0.247	0.085
j=13	0.043	0.261	0.181	0.131	0.160	0.094	0.221	0.225	0.154	0.039	0.111	0.129	0.163
j=14	0.000	0.137	0.002	0.089	0.076	0.078	0.269	0.035	0.000	0.000	0.052	0.000	0.168
j=15	0.746	0.656	0.824	0.276	0.959	0.352	0.130	0.451	0.869	0.853	0.489	0.235	0.184

Table 4. Fitting results of DZP coefficients for sub-mirror 3

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Table 4. Fitting results of DZP coefficients for sub-mirror 3

j	C₃_，j，₁	C₃_，j，₂	C₃_，j，₃	C₃_，j，₄	C₃_，j，₅	C₃_，j，₆	C₃_，j，₇	C₃_，j，₈	C₃_，j，₉	C₃_，j，₁₀	C₃_，j，₁₁	C₃_，j，₁₂	C₃_，j，₁₃
j=1	1.055	0.736	0.232	0.619	0.608	0.803	0.417	0.396	0.252	0.610	0.597	0.560	0.1882
j=2	0.012	-10.210	0.004	0.010	-0.011	0.005	0.014	-3.604	-0.003	-0.015	-0.001	0.019	-0.0152
j=3	-0.019	0.005	-10.200	-0.038	0.002	-0.001	-3.590	0.034	-0.000	0.001	0.003	0.011	0.000
j=4	0.350	-0.109	0.622	0.354	0.217	0.890	0.524	0.059	0.282	0.529	0.640	0.519	0.113
j=5	0.330	0.116	0.539	0.536	0.812	0.423	0.292	0.731	0.309	0.348	0.228	0.799	0.151
j=6	0.985	0.047	0.486	1.014	0.403	0.871	0.852	0.600	0.243	0.474	0.828	0.492	0.253
j=7	0.000	0.002	-0.001	0.001	-0.002	0.001	0.004	-0.002	-0.001	-0.005	-0.001	0.007	-0.005
j=8	-0.005	0.000	0.002	-0.012	-0.000	0.000	0.002	0.012	0.000	0.000	0.001	0.004	0.000
j=9	0.021	0.000	-0.003	0.002	-0.006	0.000	0.021	0.007	-0.003	-0.002	0.015	0.007	0.000
j=10	0.012	0.000	-0.001	0.001	0.000	-0.001	0.004	0.002	0.001	0.001	0.005	0.000	0.000
j=11	-0.539	-0.028	0.162	-0.270	0.057	0.233	0.137	0.015	0.074	0.138	0.168	0.135	0.029
j=12	0.086	0.030	0.141	0.140	0.212	0.005	0.076	0.191	0.081	0.091	0.059	0.209	0.040
j=13	0.257	0.012	0.127	0.265	-0.001	0.228	0.222	0.157	0.063	0.124	0.216	0.129	0.067
j=14	0.195	0.000	0.065	0.041	0.087	0.006	0.172	0.074	0.031	0.016	0.085	0.032	0.000
j=15	0.656	0.824	0.276	0.959	0.352	0.130	0.451	0.869	0.730	0.904	0.183	0.173	0.106

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Junliu Fan, Quanying Wu, Baohua Chen, Lei Chen, Jun Wang, Senmiao Wang, Xiaoyi Chen. Multi-Field-of-View Sparse Aperture Imaging Based on Double Zernike Polynomials[J]. Acta Optica Sinica, 2023, 43(10): 1011001

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Paper Information

Category: Imaging Systems

Received: Oct. 21, 2022

Accepted: Dec. 27, 2022

Published Online: May. 9, 2023

The Author Email: Wu Quanying (wqycyh@mail.usts.edu.cn), Chen Lei (chenlei@mail.njust.edu.cn)

DOI:10.3788/AOS221860

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology