Performance analysis of multiplexed phase computer-generated hologram for modal wavefront sensing

Liu Changhai; Xi Fengjie; Huang Shengyang; Jiang Zongfu

doi:10.1364/AO.50.001631

Applied Optics
Vol. 50,
Issue 11,
pp. 1631-1639
(2011)
•https://doi.org/10.1364/AO.50.001631

Performance analysis of multiplexed phase computer-generated hologram for modal wavefront sensing

Liu Changhai, Xi Fengjie, Huang Shengyang, and Jiang Zongfu

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Liu Changhai, Xi Fengjie, Huang Shengyang, and Jiang Zongfu, "Performance analysis of multiplexed phase computer-generated hologram for modal wavefront sensing," Appl. Opt. 50, 1631-1639 (2011)

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Abstract

We investigate the performance and capability of a holographic modal wavefront sensor (HMWS) that is based on a multiplexed phase computer-generated hologram (MPCGH). The theoretical treatments of the HMWS are presented with scalar diffraction approximations and Fourier analysis. Several MPCGHs have been designed with different linear carrier frequencies, by using of the multiplexed coding scheme we have proposed, and by coding some common Zernike modes. The numerical simulation is carried out to investigate the performance of the HMWS to detect particular aberration mode(s), by considering the effect of different carrier frequency selections and the capability of coding a large number of modes. The results exhibit the expected characteristics of a corresponding symmetric spot pair, and indicate that the wavefront distorted by a particular Zernike mode(s) can be retrieved immediately through solving the amplitude of each mode coded in MPCGHs through the response curves of the HMWS.

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Single Index k	Double Indices n, m	$Z_{k} (ρ, θ)$ or $Z_{n}^{m} (ρ, θ)$	Name
4	2, 0	$2 ρ^{2} - 1$	Defocus
6	2, 2	$ρ^{2} \sin 2 θ$	Astigmatism at $45 °$
8	3, 1	$(3 ρ^{3} - 2 ρ) \sin θ$	Primary y coma
11	4, 0	$6 ρ^{4} - 6 ρ^{2} + 1$	Primary spherical aberration

Input Zernike Mode		Retrieved Zernike Modes
$Z_{2}^{0}$		$Z_{2}^{0}$	$Z_{2}^{2}$	$Z_{3}^{1}$	$Z_{4}^{0}$
Zernike mode amplitude (rad)	0.20	0.21	$- 0.01$	0.01	$- 0.03$
	0.25	0.27	$- 0.01$	0.00	$- 0.03$
	0.56	0.58	$- 0.01$	0.00	$- 0.08$
	0.81	0.82	$- 0.06$	$- 0.05$	$- 0.10$
	0.91	0.91	$- 0.07$	$- 0.05$	$- 0.12$
	1.09	1.06	$- 0.01$	0.00	$- 0.19$
	1.26	1.18	$- 0.01$	0.01	$- 0.24$
	1.83	1.45	$- 0.02$	0.01	$- 0.47$
	2.00	1.49	$- 0.02$	0.01	$- 0.58$

Single Index k	Double Indices n, m	$Z_{k} (ρ, θ)$ or $Z_{n}^{m} (ρ, θ)$	Name
4	2, 0	$2 ρ^{2} - 1$	Defocus
6	2, 2	$ρ^{2} \sin 2 θ$	Astigmatism at $45 °$
8	3, 1	$(3 ρ^{3} - 2 ρ) \sin θ$	Primary y coma
11	4, 0	$6 ρ^{4} - 6 ρ^{2} + 1$	Primary spherical aberration

Input Zernike Mode		Retrieved Zernike Modes
$Z_{2}^{0}$		$Z_{2}^{0}$	$Z_{2}^{2}$	$Z_{3}^{1}$	$Z_{4}^{0}$
Zernike mode amplitude (rad)	0.20	0.21	$- 0.01$	0.01	$- 0.03$
	0.25	0.27	$- 0.01$	0.00	$- 0.03$
	0.56	0.58	$- 0.01$	0.00	$- 0.08$
	0.81	0.82	$- 0.06$	$- 0.05$	$- 0.10$
	0.91	0.91	$- 0.07$	$- 0.05$	$- 0.12$
	1.09	1.06	$- 0.01$	0.00	$- 0.19$
	1.26	1.18	$- 0.01$	0.01	$- 0.24$
	1.83	1.45	$- 0.02$	0.01	$- 0.47$
	2.00	1.49	$- 0.02$	0.01	$- 0.58$

Abstract

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Equations (12)

Applied Optics