New modal wave-front sensor: a theoretical analysis

Mark A. A. Neil; Martin J. Booth; Tony Wilson

doi:10.1364/JOSAA.17.001098

Journal of the Optical Society of America A
Vol. 17,
Issue 6,
pp. 1098-1107
(2000)
•https://doi.org/10.1364/JOSAA.17.001098

New modal wave-front sensor: a theoretical analysis

Mark A. A. Neil, Martin J. Booth, and Tony Wilson

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Mark A. A. Neil, Martin J. Booth, and Tony Wilson, "New modal wave-front sensor: a theoretical analysis," J. Opt. Soc. Am. A 17, 1098-1107 (2000)

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Abstract

We present a new design of a modal wave-front sensor capable of measuring directly the Zernike components of an aberrated wave front. The sensor shows good linearity for small aberration amplitudes and is particularly suitable for integration in a closed-loop adaptive system. We introduce a sensitivity matrix and show that it is sparse, and we derive conditions specifying which elements are necessarily zero. The sensor may be temporally or spatially multiplexed, the former using a reconfigurable optical element, the latter using a numerically optimized binary optical element. Different optimization schemes are discussed, and their performance is compared.

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Input Mode	Sensor Designed for Mode
Input Mode	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
4	-0.664	0	0	0	0	0	0	0.227	0	0	0	0	0	0	0	0
5	0	-0.492	0	0	0	0	0	0	0.157	0	0	0	0	0	0	0
6	0	0	-0.492	0	0	0	0	0	0	0.157	0	0	0	0	0	0
7	0	0	0	-0.685	0	0.035	0	0	0	0	0	0	0.243	0	0.052	0
8	0	0	0	0	-0.685	0	-0.035	0	0	0	0	0	0	0.243	0	-0.052
9	0	0	0	0	0	-0.506	0	0	0	0	0	0	0	0	0.188	0
10	0	0	0	0	0	0	-0.506	0	0	0	0	0	0	0	0	0.188
11	0.178	0	0	0	0	0	0	-0.754	0	0	0	0	0	0	0	0
12	0	0.147	0	0	0	0	0	0	-0.687	0	0	0	0	0	0	0
13	0	0	0.147	0	0	0	0	0	0	-0.687	0	0	0	0	0	0
14	0	0	0	0	0	0	0	0	0	0	-0.469	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	-0.469	0	0	0	0
16	0	0	0	0.206	0	0.008	0	0	0	0	0	0	-0.712	0	0.030	0
17	0	0	0	0	0.206	0	-0.008	0	0	0	0	0	0	-0.712	0	-0.030
18	0	0	0	0	0	0.148	0	0	0	0	0	0	0	0	-0.652	0
19	0	0	0	0	0	0	0.148	0	0	0	0	0	0	0	0	-0.652

Input Mode	Sensor Designed for Mode
Input Mode	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
4	-1.637	0	0	0	0	0	0	-0.493	0	0	0	0	0	0	0	0
5	0	-2.180	0	0	0	0	0	0	-0.499	0	0	0	0	0	0	0
6	0	0	-2.180	0	0	0	0	0	0	-0.499	0	0	0	0	0	0
7	0	0	0	-1.627	0	-0.183	0	0	0	0	0	0	-0.556	0	-0.207	0
8	0	0	0	0	-1.627	0	0.183	0	0	0	0	0	0	-0.556	0	0.207
9	0	0	0	0	0	-2.157	0	0	0	0	0	0	0	0	-0.622	0
10	0	0	0	0	0	0	-2.157	0	0	0	0	0	0	0	0	-0.622
11	-0.386	0	0	0	0	0	0	-1.442	0	0	0	0	0	0	0	0
12	0	-0.465	0	0	0	0	0	0	-1.563	0	0	0	0	0	0	0
13	0	0	-0.465	0	0	0	0	0	0	-1.563	0	0	0	0	0	0
14	0	0	0	0	0	0	0	0	0	0	-2.133	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	-2.133	0	0	0	0
16	0	0	0	-0.470	0	-0.099	0	0	0	0	0	0	-1.565	0	-0.137	0
17	0	0	0	0	-0.470	0	0.099	0	0	0	0	0	0	-1.565	0	0.137
18	0	0	0	0	0	-0.491	0	0	0	0	0	0	0	0	-1.676	0
19	0	0	0	0	0	0	-0.491	0	0	0	0	0	0	0	0	-1.676

i	n	m	$Z_{i} (r, θ)$	Aberration Term
1	0	0	1	Piston
2	1	1	$2 r cos (θ)$	Tip
3	1	-1	$2 r sin (θ)$	Tilt
4	2	0	$\sqrt 3 (2 r^{2} - 1)$	Defocus
5	2	2	$2 \sqrt 3 r^{2} cos (2 θ)$	Astigmatism
6	2	-2	$2 \sqrt 3 r^{2} sin (2 θ)$	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)

Input Mode	Sensor Designed for Mode
Input Mode	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
4	-0.664	0	0	0	0	0	0	0.227	0	0	0	0	0	0	0	0
5	0	-0.492	0	0	0	0	0	0	0.157	0	0	0	0	0	0	0
6	0	0	-0.492	0	0	0	0	0	0	0.157	0	0	0	0	0	0
7	0	0	0	-0.685	0	0.035	0	0	0	0	0	0	0.243	0	0.052	0
8	0	0	0	0	-0.685	0	-0.035	0	0	0	0	0	0	0.243	0	-0.052
9	0	0	0	0	0	-0.506	0	0	0	0	0	0	0	0	0.188	0
10	0	0	0	0	0	0	-0.506	0	0	0	0	0	0	0	0	0.188
11	0.178	0	0	0	0	0	0	-0.754	0	0	0	0	0	0	0	0
12	0	0.147	0	0	0	0	0	0	-0.687	0	0	0	0	0	0	0
13	0	0	0.147	0	0	0	0	0	0	-0.687	0	0	0	0	0	0
14	0	0	0	0	0	0	0	0	0	0	-0.469	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	-0.469	0	0	0	0
16	0	0	0	0.206	0	0.008	0	0	0	0	0	0	-0.712	0	0.030	0
17	0	0	0	0	0.206	0	-0.008	0	0	0	0	0	0	-0.712	0	-0.030
18	0	0	0	0	0	0.148	0	0	0	0	0	0	0	0	-0.652	0
19	0	0	0	0	0	0	0.148	0	0	0	0	0	0	0	0	-0.652

Input Mode	Sensor Designed for Mode
Input Mode	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
4	-1.637	0	0	0	0	0	0	-0.493	0	0	0	0	0	0	0	0
5	0	-2.180	0	0	0	0	0	0	-0.499	0	0	0	0	0	0	0
6	0	0	-2.180	0	0	0	0	0	0	-0.499	0	0	0	0	0	0
7	0	0	0	-1.627	0	-0.183	0	0	0	0	0	0	-0.556	0	-0.207	0
8	0	0	0	0	-1.627	0	0.183	0	0	0	0	0	0	-0.556	0	0.207
9	0	0	0	0	0	-2.157	0	0	0	0	0	0	0	0	-0.622	0
10	0	0	0	0	0	0	-2.157	0	0	0	0	0	0	0	0	-0.622
11	-0.386	0	0	0	0	0	0	-1.442	0	0	0	0	0	0	0	0
12	0	-0.465	0	0	0	0	0	0	-1.563	0	0	0	0	0	0	0
13	0	0	-0.465	0	0	0	0	0	0	-1.563	0	0	0	0	0	0
14	0	0	0	0	0	0	0	0	0	0	-2.133	0	0	0	0	0
15	0	0	0	0	0	0	0	0	0	0	0	-2.133	0	0	0	0
16	0	0	0	-0.470	0	-0.099	0	0	0	0	0	0	-1.565	0	-0.137	0
17	0	0	0	0	-0.470	0	0.099	0	0	0	0	0	0	-1.565	0	0.137
18	0	0	0	0	0	-0.491	0	0	0	0	0	0	0	0	-1.676	0
19	0	0	0	0	0	0	-0.491	0	0	0	0	0	0	0	0	-1.676

Abstract

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Figures (5)

Tables (3)

Equations (47)

Journal of the Optical Society of America A