Estimating stochastic noise using in situ measurements from a linear wavefront slope sensor

Nazim Ali Bharmal; Andrew P. Reeves

doi:10.1364/OL.41.000428

Optics Letters
Vol. 41,
Issue 2,
pp. 428-431
(2016)
•https://doi.org/10.1364/OL.41.000428

Estimating stochastic noise using in situ measurements from a linear wavefront slope sensor

Nazim Ali Bharmal and Andrew P. Reeves

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Nazim Ali Bharmal and Andrew P. Reeves, "Estimating stochastic noise using in situ measurements from a linear wavefront slope sensor," Opt. Lett. 41, 428-431 (2016)

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Abstract

It is shown how the solenoidal component of noise from the measurements of a wavefront slope sensor can be utilized to estimate the total noise: specifically, the ensemble noise variance. It is well known that solenoidal noise is orthogonal to the reconstruction of the wavefront under conditions of low scintillation (absence of wavefront vortices). Therefore, it can be retrieved even with a nonzero slope signal present. By explicitly estimating the solenoidal noise from an ensemble of slopes, it can be retrieved for any wavefront sensor configuration. Furthermore, the ensemble variance is demonstrated to be related to the total noise variance via a straightforward relationship. This relationship is revealed via the method of the explicit estimation: it consists of a small, heuristic set of four constants that do not depend on the underlying statistics of the incoming wavefront. These constants seem to apply to all situations—data from a laboratory experiment as well as many configurations of numerical simulation—so the method is concluded to be generic.

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Pupil shape	circular
$N$ (sub-aperture resolution scale)	16
pixels/sub-aperture focus	4
Focal length	$4 \times Δ_{sa} / λ$
Sub-ap. fractional illumination	$\geq 50 %$
Illumination total/sub-aperture	100 counts
RON-equivalent/sub-aperture	5
SVD singular value elimination	$10^{- 8} \times$ max

No. of References in $L$ to Sub-aperture	$〈 η_{s}^{2} 〉 \to 〈 η^{2} 〉$
1	14/2
2	14/4
3	14/5
4	14/6

Input	Estimated:Measured $〈 η^{2} 〉$
Input	Explicit	Loop Sums
(a) Simulation $s = 0$	$1.1 \pm 0.2$	$1.02 \pm 0.03$
(b) Data $s = 0$	$1.1 \pm 0.3$	$1.1 \pm 0.2$
(c) Simulation $s \neq 0$	$1.1 \pm 0.2$	$1.02 \pm 0.07$
(d) Data $s \neq 0$	$1.8 \pm 0.4$	$1.7 \pm 0.3$

Situation	Regularization?	Normalized Residual/%
Full $H$		$17 \pm 7$
-” $- L$	$N$	$2.4 \pm 4.7$
-” $- L$	$Y$	$3.3 \pm 2.8$
Partial $H$		$- 1 \pm 34$
-” $- L$	$N$	$3.3 \pm 13$
-” $- L$	$Y$	$- 9 \pm 15$

Pupil shape	circular
$N$ (sub-aperture resolution scale)	16
pixels/sub-aperture focus	4
Focal length	$4 \times Δ_{sa} / λ$
Sub-ap. fractional illumination	$\geq 50 %$
Illumination total/sub-aperture	100 counts
RON-equivalent/sub-aperture	5
SVD singular value elimination	$10^{- 8} \times$ max

Abstract

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Tables (4)

Equations (7)

Optics Letters