Wave-front sensing with a sampling field sensor

Remy Tumbar; Ronald A. Stack; David J. Brady

doi:10.1364/AO.39.000072

Applied Optics
Vol. 39,
Issue 1,
pp. 72-84
(2000)
•https://doi.org/10.1364/AO.39.000072

Wave-front sensing with a sampling field sensor

Remy Tumbar, Ronald A. Stack, and David J. Brady

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Remy Tumbar, Ronald A. Stack, and David J. Brady, "Wave-front sensing with a sampling field sensor," Appl. Opt. 39, 72-84 (2000)

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Abstract

We present a new type of optical wave-front sensor: the sampling field sensor (SFS). The SFS attempts to solve the problem of real-time optical phase detection. It has a high space-bandwidth product and can be made compact and vibration insensitive. We describe a particular implementation of this sensor and compare it, through numerical simulations, with a more mature technique based on the Shack–Hartmann wave-front sensor. We also present experimental results for SFS phase estimation. Finally, we discuss the advantages and drawbacks of this SFS implementation and suggest alternative implementations.

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Field Bandwidth (µm^-1)	Calibration Error
	Phase Pixel 1		Phase Pixel 2
	Percentile Error (%)	Residual Errorb (a.u.)	Percentile Error (%)	Residual Errorb (a.u.)
1/2200	0.26 ± 0.49	7.52 × 10^-6	0.19 ± 0.41	9.96 × 10^-6
1/1980	0.26 ± 0.46	8.26 × 10^-6	0.16 ± 0.6	8.40 × 10^-6
1/1760	0.19 ± 0.4	4.39 × 10^-6	0.14 ± 0.4	1.20 × 10^-5
1/1540	0.2 ± 0.35	4.77 × 10^-6	0.16 ± 0.29	2.29 × 10^-5
1/1320	0.3 ± 0.95	8.22 × 10^-6	0.29 ± 0.74	2.42 × 10^-5
1/1100	0.36 ± 0.95	1.33 × 10^-5	0.35 ± 0.88	1.41 × 10^-5
1/880	0.4 ± 1.15	1.52 × 10^-5	0.56 ± 1.35	3.60 × 10^-5
1/660	0.85 ± 1.65	3.85 × 10^-5	0.83 ± 1.35	5.03 × 10^-5
1/440	1.21 ± 2.28	6.34 × 10^-5	1.89 ± 2.95	1.05 × 10^-4
1/220	2.64 ± 3.28	2.18 × 10^-4	5.6 ± 6.1	3.17 × 10^-4

Field Bandwidth	Absolute Error (rad)		Relative Error
Field Bandwidth	SFSa	SHSa	SFS (%)	SHS (%)
1/2200	0.002 ± 0.004	0.02 ± 0.16	1.5 ± 3	3 ± 10
1/1980	0.002 ± 0.004	0.01 ± 0.1	1.5 ± 2	2 ± 8
1/1760	0.002 ± 0.004	0.02 ± 0.15	2 ± 5	4 ± 10
1/1540	0.003 ± 0.005	0.04 ± 0.24	3 ± 7	6 ± 14
1/1320	0.004 ± 0.0075	0.01 ± 0.08	3 ± 20	3 ± 6
1/1100	0.007 ± 0.05	0.05 ± 0.3	3 ± 8	10 ± 20
1/880b	0.02 ± 0.27	0.1 ± 0.3	5 ± 16	12 ± 20
1/660	0.01 ± 0.05	0.1 ± 0.4	6 ± 23	15 ± 30
1/440b	0.04 ± 0.2	0.3 ± 0.6	9 ± 23	30 ± 50
1/220b	0.12 ± 0.5	0.95 ± 1.0	20 ± 110	80 ± 120

Field Bandwidth (µm^-1)	Calibration Error
	Phase Pixel 1		Phase Pixel 2
	Percentile Error (%)	Residual Errorb (a.u.)	Percentile Error (%)	Residual Errorb (a.u.)
1/2200	0.26 ± 0.49	7.52 × 10^-6	0.19 ± 0.41	9.96 × 10^-6
1/1980	0.26 ± 0.46	8.26 × 10^-6	0.16 ± 0.6	8.40 × 10^-6
1/1760	0.19 ± 0.4	4.39 × 10^-6	0.14 ± 0.4	1.20 × 10^-5
1/1540	0.2 ± 0.35	4.77 × 10^-6	0.16 ± 0.29	2.29 × 10^-5
1/1320	0.3 ± 0.95	8.22 × 10^-6	0.29 ± 0.74	2.42 × 10^-5
1/1100	0.36 ± 0.95	1.33 × 10^-5	0.35 ± 0.88	1.41 × 10^-5
1/880	0.4 ± 1.15	1.52 × 10^-5	0.56 ± 1.35	3.60 × 10^-5
1/660	0.85 ± 1.65	3.85 × 10^-5	0.83 ± 1.35	5.03 × 10^-5
1/440	1.21 ± 2.28	6.34 × 10^-5	1.89 ± 2.95	1.05 × 10^-4
1/220	2.64 ± 3.28	2.18 × 10^-4	5.6 ± 6.1	3.17 × 10^-4

Field Bandwidth	Absolute Error (rad)		Relative Error
Field Bandwidth	SFSa	SHSa	SFS (%)	SHS (%)
1/2200	0.002 ± 0.004	0.02 ± 0.16	1.5 ± 3	3 ± 10
1/1980	0.002 ± 0.004	0.01 ± 0.1	1.5 ± 2	2 ± 8
1/1760	0.002 ± 0.004	0.02 ± 0.15	2 ± 5	4 ± 10
1/1540	0.003 ± 0.005	0.04 ± 0.24	3 ± 7	6 ± 14
1/1320	0.004 ± 0.0075	0.01 ± 0.08	3 ± 20	3 ± 6
1/1100	0.007 ± 0.05	0.05 ± 0.3	3 ± 8	10 ± 20
1/880b	0.02 ± 0.27	0.1 ± 0.3	5 ± 16	12 ± 20
1/660	0.01 ± 0.05	0.1 ± 0.4	6 ± 23	15 ± 30
1/440b	0.04 ± 0.2	0.3 ± 0.6	9 ± 23	30 ± 50
1/220b	0.12 ± 0.5	0.95 ± 1.0	20 ± 110	80 ± 120

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Applied Optics