Phase retrieval from subdivision of the focal plane with a lenslet array

Richard M. Clare; Richard G. Lane

doi:10.1364/AO.43.004080

Applied Optics
Vol. 43,
Issue 20,
pp. 4080-4087
(2004)
•https://doi.org/10.1364/AO.43.004080

Phase retrieval from subdivision of the focal plane with a lenslet array

Richard M. Clare and Richard G. Lane

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Richard M. Clare and Richard G. Lane, "Phase retrieval from subdivision of the focal plane with a lenslet array," Appl. Opt. 43, 4080-4087 (2004)

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Abstract

A phase retrieval algorithm derived from subdivision of the complex field at the focal plane is proposed. This subdivision is achieved with a lenslet array at the focal plane in a manner similar to the pyramid wave-front sensor. The phase retrieval algorithm significantly improves the wave-front estimate that can be attained as a linear combination of the aperture images. This phase retrieval algorithm also avoids the twin-image stagnation problem inherent in phase retrieval and phase retrieval in conjunction with the Shack-Hartmann sensor.

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Array	Iteration	Starting Phase
Array	Iteration	Zero	Pyramid Estimate	True
2× 2	Initial	0.013 ± 0.001	0.168 ± 0.004	1.000 ± 0.000
	After 200	0.085 ± 0.003	0.371 ± 0.007	0.696 ± 0.002
4 × 4	Initial	0.013 ± 0.001	0.223 ± 0.004	1.000 ± 0.000
	After 200	0.190 ± 0.006	0.654 ± 0.006	0.777 ± 0.001
8 × 8	Initial	0.013 ± 0.001	0.337 ± 0.004	1.000 ± 0.000
	After 200	0.271 ± 0.003	0.697 ± 0.007	0.722 ± 0.001
16 × 16	Initial	0.013 ± 0.001	0.160 ± 0.005	1.000 ± 0.000
	After 200	0.277 ± 0.015	0.519 ± 0.014	0.608 ± 0.006

Array	Iteration	Starting Phase
Array	Iteration	Zero	Pyramid Estimate	True
2× 2	Initial	0.013 ± 0.001	0.168 ± 0.004	1.000 ± 0.000
	After 200	0.032 ± 0.001	0.166 ± 0.004	0.490 ± 0.002
4 × 4	Initial	0.013 ± 0.001	0.223 ± 0.004	1.000 ± 0.000
	After 200	0.080 ± 0.003	0.388 ± 0.006	0.655 ± 0.002
8 × 8	Initial	0.013 ± 0.001	0.339 ± 0.003	1.000 ± 0.000
	After 200	0.206 ± 0.005	0.613 ± 0.003	0.690 ± 0.001
16 × 16	Initial	0.013 ± 0.001	0.161 ± 0.005	1.000 ± 0.000
	After 200	0.310 ± 0.013	0.531 ± 0.010	0.640 ± 0.004

Array	Iteration	Starting Phase
Array	Iteration	Zero	Pyramid Estimate	True
2× 2	Initial	0.013 ± 0.001	0.168 ± 0.004	1.000 ± 0.000
	After 200	0.085 ± 0.003	0.371 ± 0.007	0.696 ± 0.002
4 × 4	Initial	0.013 ± 0.001	0.223 ± 0.004	1.000 ± 0.000
	After 200	0.190 ± 0.006	0.654 ± 0.006	0.777 ± 0.001
8 × 8	Initial	0.013 ± 0.001	0.337 ± 0.004	1.000 ± 0.000
	After 200	0.271 ± 0.003	0.697 ± 0.007	0.722 ± 0.001
16 × 16	Initial	0.013 ± 0.001	0.160 ± 0.005	1.000 ± 0.000
	After 200	0.277 ± 0.015	0.519 ± 0.014	0.608 ± 0.006

Array	Iteration	Starting Phase
Array	Iteration	Zero	Pyramid Estimate	True
2× 2	Initial	0.013 ± 0.001	0.168 ± 0.004	1.000 ± 0.000
	After 200	0.032 ± 0.001	0.166 ± 0.004	0.490 ± 0.002
4 × 4	Initial	0.013 ± 0.001	0.223 ± 0.004	1.000 ± 0.000
	After 200	0.080 ± 0.003	0.388 ± 0.006	0.655 ± 0.002
8 × 8	Initial	0.013 ± 0.001	0.339 ± 0.003	1.000 ± 0.000
	After 200	0.206 ± 0.005	0.613 ± 0.003	0.690 ± 0.001
16 × 16	Initial	0.013 ± 0.001	0.161 ± 0.005	1.000 ± 0.000
	After 200	0.310 ± 0.013	0.531 ± 0.010	0.640 ± 0.004

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Equations (12)

Applied Optics