Acta Optica Sinica, Volume. 39, Issue 6, 0626001(2019)
Phase Recovery Algorithm Based on Pupil Diversity
Figures & Tables(16)
Fig. 1. Principle diagram of NRM-GS algorithm. (a) Original wavefront; (b) I (ξ,η); (c) wavefront after mask; (d) INRM(ξ,η); (e) fMT of INRM(ξ,η); (f) principle of NRM-GS algorithm
Fig. 3. Iteration processes for NRM-GS algorithm with and without phase constraints or ordinary GS algorithm. (a) S curves; (b) ERMS curves
Fig. 4. Recovery of astigmatism aberration. (a) Original wavefront; (d) wavefront after mask; (b)(e) recovered wavefronts by NRM-GS algorithm and GS algorithm; (c)(f) recovered residual wavefronts by NRM-GS algorithm and GS algorithm
Fig. 5. Iteration processes for NRM-GS algorithms with and without phase constraints or ordinary GS algorithm. (a) S curves; (b) ERMS curves
Fig. 6. Recovery of randomly combined wavefront (first 15 terms). (a) Original wavefront; (d) wavefront after mask; (b)(e) recovered wavefronts by NRM-GS algorithm and GS algorithm; (c)(f) recovered residual wavefronts by NRM-GS algorithm and GS algorithm
Fig. 7. Comparison of Zernike polynomial coefficients (first 15 items) of original wavefront with those by NRM-GS algorithm and GS algorithm
Fig. 8. Recovery results of co-phase errors on synthetic aperture telescope. (a) Original wavefront; (b) recovered wavefront by NRM-GS algorithm; (c) recovered residual wavefront by NRM-GS algorithm; (d) wavefront after mask; (e) recovered wavefront by GS algorithm; (f) recovered residual wavefront by GS algorithm
Fig. 9. Iteration processes for NRM-GS algorithms with and without phase constraints or ordinary GS algorithm when co-phase errors on synthetic aperture telescope are detected. (a) S curves; (b) ERMS curves of residual wavefronts on three sub-telescopes
Table 1. Original wavefront phases, initial phases of NRM-GS and ordinary GS algorithms and their errors for six-sub-aperture centers
View tableTable 1. Original wavefront phases, initial phases of NRM-GS and ordinary GS algorithms and their errors for six-sub-aperture centers
Sub-aperture Original phase Initial phase Initial phase error NRM-GS piston component GS random initial phase NRM-GS piston component GS random initial phase 1 0.1789 λ 0.1787 λ 0.1261 λ -0.0002 λ 0.0526 λ 2 0.0439 λ 0.0437 λ 0.1197 λ -0.0002 λ -0.0757 λ 3 0.2589 λ 0.2587 λ 0.1248 λ -0.0002 λ -0.1341 λ 4 -0.0870 λ -0.0872 λ 0.1265 λ -0.0002 λ -0.2135 λ 5 -0.3021 λ -0.3023 λ 0.0278 λ -0.0002 λ -0.3229 λ
Table 2. Six groups of recovery results of single order Zernike polynomial by NRM-GS algorithm and GS algorithm
View tableTable 2. Six groups of recovery results of single order Zernike polynomial by NRM-GS algorithm and GS algorithm
Single order Zernike term NRM-GS algorithm GS algorithm Residual wavefront E RMSNumber of iteration Residual wavefront E RMSNumber of iteration 3 0.0040 λ 91 0.1523 λ 105 5 0.0031 λ 112 0.1167 λ 191 9 0.0145 λ 125 0.1096 λ 212 11 0.0056 λ 97 0.1244 λ 129 12 0.0080 λ 109 0.1241 λ 136 13 0.0123 λ 103 0.1248 λ 117 Average 0.0079 λ 0.1253 λ
Table 3. Original wavefront phases, initial phases and their errors for six-sub-aperture centers
View tableTable 3. Original wavefront phases, initial phases and their errors for six-sub-aperture centers
Sub-aperture Original phase Initial phase Initial phase error NRM-GS piston component GS random initial phase NRM-GS piston component GS random initial phase 1 -0.164 λ -0.1521 λ 0.1051 λ -0.0119 λ -0.2791 λ 2 -0.1284 λ -0.1086 λ 0.091 λ -0.0198 λ -0.2194 λ 3 0.0907 λ 0.0861 λ 0.1259 λ 0.0046 λ -0.0352 λ 4 0.1995 λ 0.1924 λ 0.1245 λ 0.0071 λ 0.075 λ 5 -0.1301 λ -0.1212 λ 0.0051 λ -0.0089 λ -0.1361 λ 6 0.0887 λ 0.1027 λ 0.1244 λ -0.014 λ -0.0357 λ
Table 4. Five groups of recovery results of randomly combined wavefronts by NRM-GS algorithm and GS algorithm
View tableTable 4. Five groups of recovery results of randomly combined wavefronts by NRM-GS algorithm and GS algorithm
Number of terms of Zernike polynominals RMS of original wavefront ϕ 0NRM-GS GS Residual wavefront E RMSNumber of iterations Residual wavefront E RMSNumber of iterations 1(first 15 terms) 0.1156 λ 0.0088 λ 95 0.1241 λ 98 2(first 20 terms) 0.1919 λ 0.0140 λ 112 0.1027 λ 127 3(first 25 terms) 0.1048 λ 0.0240 λ 108 0.1556 λ 145 4(first 30 terms) 0.1301 λ 0.0099 λ 99 0.1342 λ 165 5(first 37 terms) 0.0800 λ 0.0141 λ 110 0.1258 λ 128
Table 5. Added co-phase errors on each sub-telescope
View tableTable 5. Added co-phase errors on each sub-telescope
Sub-telescope Piston error Tip error Tilt error 1 2 3 0.0000 λ 0.2000 λ 0.0500 λ 0.2000 λ 0.1254 λ 0.0752 λ 0.0752 λ 0.0627 λ 0.1254 λ
Table 6. Original wavefront phases, initial phases and their errors
View tableTable 6. Original wavefront phases, initial phases and their errors
Sub-aperture Original phase Initial phase Initial phase error NRM-GS piston component GS random initial phase NRM-GS piston component GS random initial phase 1 0.0000 λ 0.0000 λ 0.0235 λ 0.0000 λ -0.0235 λ 2 0.0112 λ 0.0011 λ 0.0453 λ 0.0101 λ -0.0341 λ 3 0.3734 λ 0.3707 λ 0.1305 λ 0.0027 λ 0.2132 λ 4 0.0384 λ 0.0289 λ 0.0973 λ 0.0095 λ -0.0589 λ 5 0.0461 λ 0.0378 λ 0.0542 λ 0.0083 λ -0.0081 λ
Table 7. Recovery results of multigroup co-phase errors
View tableTable 7. Recovery results of multigroup co-phase errors
Co-phase error Maximum E RMSMinimum E RMSAverage E RMSAverage number of iteration NRM-GS GS NRM-GS GS NRM-GS GS NRM-GS GS Piston(10 groups) 0.0078 λ 0.0741 λ 0.0045 λ 0.0424 λ 0.0056 λ 0.0533 λ 37 43 Tip/tilt(10 groups) 0.0100 λ 0.1327 λ 0.0037 λ 0.1240 λ 0.0071 λ 0.1267 λ 38 49 Piston, tip/tilt (10 groups) 0.0064 λ 0.0860 λ 0.0022 λ 0.0423 λ 0.0045 λ 0.0651 λ 40 47
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Qian Li, Zhen Wu, Jiesu Xu, Honglan Li. Phase Recovery Algorithm Based on Pupil Diversity[J]. Acta Optica Sinica, 2019, 39(6): 0626001
Paper Information
Category: Physical Optics
Received: Jan. 9, 2019
Accepted: Mar. 21, 2019
Published Online: Jun. 17, 2019
The Author Email: Wu Zhen (zhenwu@niaot.ac.cn)
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