Methods for the characterization of deformable membrane mirrors

Martin Booth; Tony Wilson; Hong-Bo Sun; Taisuke Ota; Satoshi Kawata

doi:10.1364/AO.44.005131

Applied Optics
Vol. 44,
Issue 24,
pp. 5131-5139
(2005)
•https://doi.org/10.1364/AO.44.005131

Methods for the characterization of deformable membrane mirrors

Martin Booth, Tony Wilson, Hong-Bo Sun, Taisuke Ota, and Satoshi Kawata

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Martin Booth, Tony Wilson, Hong-Bo Sun, Taisuke Ota, and Satoshi Kawata, "Methods for the characterization of deformable membrane mirrors," Appl. Opt. 44, 5131-5139 (2005)

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Abstract

We demonstrate two methods for the characterization of deformable membrane mirrors and the training of adaptive optics systems that employ these mirrors. Neither method employs a wave-front sensor. In one case, aberrations produced by a wave-front generator are corrected by the deformable mirror by use of a rapidly converging iterative algorithm based on orthogonal deformation modes of the mirror. In the other case, a simple interferometer is used with fringe analysis and phase-unwrapping algorithms. We discuss how the choice of singular values can be used to control the pseudoinversion of the control matrix.

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Index			Z_i(r, θ)	Aberration Term

i	n	m
1	0	0	1	Piston
2	1	1	2r cos(θ)	Tip
3	1	−1	2r sin(θ)	Tilt
4	2	0	$\sqrt{3} (2 r^{2} - 1)$	Defocus
5	2	2	$\sqrt{6} r^{2} cos (2 θ)$	Astigmatism
6	2	−2	$\sqrt{6} r^{2} sin (2 θ)$	Astigmatism
7	3	1	$2 \sqrt{2} (3 r^{3} - 2 r) cos (θ)$	Coma
8	3	−1	$2 \sqrt{2} (3 r^{3} - 2 r) sin (θ)$	Coma
9	3	3	$2 \sqrt{2} r^{3} cos (3 θ)$
10	3	−3	$2 \sqrt{2} r^{3} sin (3 θ)$
11	4	0	$\sqrt{5} (6 r^{4} - 6 r^{2} + 1)$	Spherical (1st)
12	4	2	$\sqrt{10} (4 r^{4} - 3 r^{2}) cos (2 θ)$
13	4	−2	$\sqrt{10} (4 r^{4} - 3 r^{2}) sin (2 θ)$
14	4	4	$\sqrt{10} r^{4} cos (4 θ)$
15	4	−4	$\sqrt{10} r^{4} sin (4 θ)$
16	5	1	$2 \sqrt{3} (10 r^{5} - 12 r^{3} + 3 r) cos (θ)$
17	5	−1	$2 \sqrt{3} (10 r^{5} - 12 r^{3} + 3 r) sin (θ)$
18	5	3	$2 \sqrt{3} (5 r^{5} - 4 r^{3}) cos (3 θ)$
19	5	−3	$2 \sqrt{3} (5 r^{5} - 4 r^{3}) sin (3 θ)$
20	5	5	$2 \sqrt{3} r^{5} cos (5 θ)$
21	5	−5	$2 \sqrt{3} r^{5} sin (5 θ)$
22	6	0	$\sqrt{7} (20 r^{6} - 30 r^{4} + 12 r^{2} - 1)$	Spherical (2nd)

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Applied Optics