High-Precision Phase Retrieval for Shack-Hartmann Wavefront Sensors Using Modal Reconstruction and an Improved Adaptive Stochastic Parallel Gradient Descent Algorithm

Feikuai Fang; Changwei Li; Min Lai

doi:10.3788/LOP242411

Laser & Optoelectronics Progress, Volume. 62, Issue 12, 1212004(2025)

High-Precision Phase Retrieval for Shack-Hartmann Wavefront Sensors Using Modal Reconstruction and an Improved Adaptive Stochastic Parallel Gradient Descent Algorithm

Feikuai Fang^1,2,3, Changwei Li^2,3,4、*, and Min Lai¹

Author Affiliations

¹School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, Jiangsu , China

²Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, Jiangsu , China

³Key Laboratory of Astronomical Optics & Technology, Nanjing Institute of Astronomical Optics & Technology, Chinese Academy of Sciences, Nanjing 210042, Jiangsu , China

⁴School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(16)

Fig. 1. Geometric relationship of the local slope for a single lens

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Fig. 2. Flow chart of ASPGD

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$Schematic diagram of the optical path of the iterative diffraction process$

Fig. 3. Schematic diagram of the optical path of the iterative diffraction process

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Fig. 4. Schematic diagrams of the simulated optical path. (a) Pupil plane image; (b) microlens arrays; (c) focal plane imaging

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Fig. 5. Results of phase recovery. (a) Input phase; (b) (c) phase recovery results reconstructed by the modal algorithm and the corresponding residual; (d) (e) phase recovery results by the proposed algorithm and the corresponding residual

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Fig. 6. Comparison of the Zernike coefficients between the input phase and the recovery phase

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Fig. 7. Evaluation of the cost function

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Fig. 8. Evaluation function of different learning rates

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Fig. 9. Evaluation function of different disturbance coefficients

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Fig. 10. Evaluation function variation curves

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Fig. 11. Results of phase recovery. (a) Input phase; (b) (c) phase recovery results reconstructed by the SPGD algorithm and the corresponding residual; (d) (e) phase recovery results by the proposed algorithm and the corresponding residual

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Fig. 12. Results of phase recovery at a Gaussian noise signal-to-noise ratio of 5 dB. (a) Input phase; (b) (c) phase recovery results reconstructed by the modal algorithm and the corresponding residual; (d) (e) phase recovery results by the proposed algorithm and the corresponding residual

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Fig. 13. Zernike coefficients recovered at a Gaussian noise signal-to-noise ratio of 5 dB

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Table 1. The residuals of ASPGD and SPGD under different values of $Δ a$
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Table 1. The residuals of ASPGD and SPGD under different values of $Δ a$
$Δ a$ PV / $λ$ RMS / $λ$
modal + ASPGD modal + SPGD modal + ASPGD modal + SPGD
0.001 0.02 0.24 0.003 0.017
0.005 0.02 0.02 0.003 0.003
0.010 0.02 0.13 0.003 0.011
0.020 0.03 0.72 0.004 0.091
0.050 0.09 13.91 0.008 0.742

Table 2. The residuals of the partial random input phase

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Table 2. The residuals of the partial random input phase

No.	PV / $λ$	PV / $λ$		RMS / $λ$
No.	PV / $λ$	modal	modal + ASPGD	modal	modal + ASPGD
1	1.36	0.12	0.02	0.009	0.002
2	0.94	0.09	0.02	0.006	0.003
3	1.27	0.13	0.02	0.009	0.003
4	0.98	0.08	0.02	0.007	0.002
5	1.19	0.11	0.02	0.010	0.002
6	1.98	0.14	0.02	0.012	0.003
7	2.53	0.19	0.04	0.014	0.007
8	1.40	0.16	0.03	0.012	0.005
9	2.39	0.20	0.03	0.016	0.005
10	1.36	0.27	0.03	0.016	0.003

Table 3. The residuals with different noise types under different SNR

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Table 3. The residuals with different noise types under different SNR

Noise type	SNR /dB	PV / $λ$		RMS / $λ$
Noise type	SNR /dB	modal	modal+ASPGD	modal	modal+ASPGD
Gaussian	30	0.15	0.02	0.009	0.003
	25	0.16	0.02	0.009	0.005
	20	0.18	0.02	0.009	0.002
	15	0.21	0.02	0.011	0.005
	10	0.27	0.04	0.015	0.006
	5	0.39	0.07	0.024	0.009
Poisson	30	0.14	0.01	0.009	0.002
	25	0.12	0.01	0.008	0.002
	20	0.13	0.04	0.010	0.003
	15	0.17	0.04	0.009	0.004
	10	0.34	0.06	0.019	0.009
	5	0.58	0.09	0.037	0.012

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Feikuai Fang, Changwei Li, Min Lai. High-Precision Phase Retrieval for Shack-Hartmann Wavefront Sensors Using Modal Reconstruction and an Improved Adaptive Stochastic Parallel Gradient Descent Algorithm[J]. Laser & Optoelectronics Progress, 2025, 62(12): 1212004

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