Mitigation of truncation effects in elongated Shack–Hartmann laser guide star wavefront sensor images

Richard M. Clare; Stephen J. Weddell; Miska Le Louarn

doi:10.1364/AO.394751

Applied Optics
Vol. 59,
Issue 22,
pp. 6431-6442
(2020)
•https://doi.org/10.1364/AO.394751

Mitigation of truncation effects in elongated Shack–Hartmann laser guide star wavefront sensor images

Richard M. Clare, Stephen J. Weddell, and Miska Le Louarn

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Richard M. Clare, Stephen J. Weddell, and Miska Le Louarn, "Mitigation of truncation effects in elongated Shack–Hartmann laser guide star wavefront sensor images," Appl. Opt. 59, 6431-6442 (2020)

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Abstract

Laser guide star Shack–Hartmann wavefront sensor images on extremely large telescopes (ELT) will be significantly elongated due to the off-axis projection of the laser relative to the subapertures. The finite number of pixels of the wavefront sensor detector means the most elongated images will be truncated, introducing errors in the centroid measurements. In this paper, we propose appending to the truncated wavefront sensor image the most likely missing tails from a high-resolution nontruncated reference image, which can be calculated from all of the low-resolution images. We show, via numerical simulation, that we can improve the centroid estimate for the most elongated subapertures on an ELT in the presence of read and photon noise.

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Parameter	Value
Telescope diameter	40 m
Number of subapertures	$80 \times 80$
Zenith angle ( $ζ$ )	0°
Nonelongated spot FWHM	1.1 arcsec
Pixels per subaperture ( $N_{P}$ )	$10 \times 10$
Pixel scale	1.1 arcsec/pixel
RMS read noise ( $N_{r}$ )	3 electrons/pixel/read
Flux level ( $N_{p h}$ )	1000 photons/subaperture/frame
RMS jitter	0.5 pixels
Laser launch location	(20,0) m (Side launch)
Trials	500
Iterations ( $N_{I t e r}$ )	100

Algorithm	$σ_{x}^{2}$	$σ_{y}^{2}$
Algorithm	$(p i x e l s)^{2}$	$(p i x e l s)^{2}$
COG	0.0859	0.0088
Appended COG	0.0278	0.0077
WCOG	0.0800	0.0016
Appended WCOG	0.0300	0.0015
CORR	0.0451	0.0009
Appended CORR	0.0295	0.0009

Algorithm	$σ_{x}^{2}$	$σ_{y}^{2}$
Algorithm	$(p i x e l s)^{2}$	$(p i x e l s)^{2}$
COG	0.1903	0.0093
Appended COG	0.0384	0.0073
WCOG	0.2019	0.0017
Appended WCOG	0.0434	0.0015
CORR	0.0299	0.0009
Appended CORR	0.0283	0.0009

Parameter	Value
Telescope diameter	40 m
Number of subapertures	$80 \times 80$
Zenith angle ( $ζ$ )	0°
Nonelongated spot FWHM	1.1 arcsec
Pixels per subaperture ( $N_{P}$ )	$10 \times 10$
Pixel scale	1.1 arcsec/pixel
RMS read noise ( $N_{r}$ )	3 electrons/pixel/read
Flux level ( $N_{p h}$ )	1000 photons/subaperture/frame
RMS jitter	0.5 pixels
Laser launch location	(20,0) m (Side launch)
Trials	500
Iterations ( $N_{I t e r}$ )	100

Algorithm	$σ_{x}^{2}$	$σ_{y}^{2}$
Algorithm	$(p i x e l s)^{2}$	$(p i x e l s)^{2}$
COG	0.0859	0.0088
Appended COG	0.0278	0.0077
WCOG	0.0800	0.0016
Appended WCOG	0.0300	0.0015
CORR	0.0451	0.0009
Appended CORR	0.0295	0.0009

Abstract

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Equations (18)

Applied Optics