Gram–Charlier matched filter for Shack–Hartmann sensing at low light levels

J.-M. Ruggiu; C. J. Solomon; G. Loos

doi:10.1364/OL.23.000235

Optics Letters
Vol. 23,
Issue 4,
pp. 235-237
(1998)
•https://doi.org/10.1364/OL.23.000235

Gram–Charlier matched filter for Shack–Hartmann sensing at low light levels

J.-M. Ruggiu, C. J. Solomon, and G. Loos

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J.-M. Ruggiu, C. J. Solomon, and G. Loos, "Gram–Charlier matched filter for Shack–Hartmann sensing at low light levels," Opt. Lett. 23, 235-237 (1998)

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Abstract

A study has been made of a Gram–Charlier matched filter for Shack–Hartmann sensing of wavefront slopes. The method is based on modeling the point-spread function by an expansion in terms of Gauss–Hermite polynomials. We present results for several subaperture/coherence area sizes both with and without CCD read noise. A more accurate estimation of the local slopes can be achieved at low light levels in this way than with the standard first-moment estimator.

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$l / r_{0}$	$r_{0} (m)$	$D (m)$	Number of Subapertures	Fluxb	Corresponding Visual Magnitude	A priori Phase Variance $[1.015 {(D / r_{0})}^{5 / 6} rad]$	rms Error (rad)
$l / r_{0}$	$r_{0} (m)$	$D (m)$	Number of Subapertures	Fluxb	Corresponding Visual Magnitude		First-Moment Estimator	Gram–Charlier Estimator
1	0.1	0.7	32	30	10.73	5.14	zrms, 1.29190;	zrms, 1.1189;
1	0.1	0.7	32	30	10.73	5.14	maprms, 1.0356	maprms, 0.973
2	0.1	1.3	32	7.5	12.24	8.61	zrms, 4.1890;	zrms, 3.8648;
2	0.1	1.3	32	7.5	12.24	8.61	maprms, 2.8663	maprms, 2.7052
3	0.08	1.6	32	3.33	12.63	12.32	zrms, 7.3787;	zrms, 6.8812;
3	0.08	1.6	32	3.33	12.63	12.32	maprms, 4.8561	maprms, 4.6128
1	0.1	1.3	124	30	10.73	8.61	zrms, 1.0612;	zrms, 0.9191;
1	0.1	1.3	124	30	10.73	8.61	maprms, 1.0265	maprms, 0.8967
2	0.08	2.1	124	7.5	11.75	15.46	zrms, 3.2369;	zrms, 2.9914;
2	0.08	2.1	124	7.5	11.75	15.46	maprms, 2.9700	maprms, 2.7733
3	0.08	3.2	124	3.33	12.63	21.95	zrms, 6.572;	zrms, 6.0866;
3	0.08	3.2	124	3.33	12.63	21.95	maprms, 5.6489	maprms, 5.3383

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