Estimation of the adaptive optics long-exposure point-spread function using control loop data

Jean-Pierre Véran; François Rigaut; Henri Maı̂tre; Daniel Rouan

doi:10.1364/JOSAA.14.003057

Journal of the Optical Society of America A
Vol. 14,
Issue 11,
pp. 3057-3069
(1997)
•https://doi.org/10.1364/JOSAA.14.003057

Estimation of the adaptive optics long-exposure point-spread function using control loop data

Jean-Pierre Véran, François Rigaut, Henri Maı̂tre, and Daniel Rouan

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Jean-Pierre Véran, François Rigaut, Henri Maı̂tre, and Daniel Rouan, "Estimation of the adaptive optics long-exposure point-spread function using control loop data," J. Opt. Soc. Am. A 14, 3057-3069 (1997)

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Abstract

Astronomical images obtained with adaptive optics systems can be enhanced by using image restoration techniques. However, this usually requires an accurate knowledge of the system point-spread function (PSF) which is variable in time. We present a method to estimate the PSF related to each image, using data from the adaptive optics control computer, namely, the wave-front sensor measurements and the commands to the deformable mirror, accumulated in synchronization with the acquisition. This method requires no extra observing time and has been successfully tested on PUEO, the Canada–France–Hawaii Telescope adaptive optics system. With this system, accurate PSF estimations could be achieved for guide stars of magnitude 13 or brighter.

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Atmospheric and AO Loop Quantities	Example 1	Example 2	Example 3
Guide star magnitude	10.4	12.7	15.4
$r_{0}$ (cm)	18.7	19.8	18.5

Mirror component $({rad}^{2}) :$
Estimated uncorrected phase $\sum σ_{a_{i}}^{2}$	109.8	83.0	79.9
RTC estimated residual phase $\sum σ_{{\bar{∊}}_{i}}^{2}$	3.4	30.0	110.3
Estimated WFS measurement error $\sum σ_{n_{i}}^{2}$	3.0	27.8	97.5
Estimated remaining error $\sum σ_{r_{i}}^{2}$	2.9	2.6	2.9
Estimated residual phase $\sum σ_{∊_{i}}^{2}$	3.3	4.7	15.8

Estimated high-order component $σ_{ϕ_{⊥}}^{2} ({rad}^{2})$	2.6	2.3	2.6

PSF	Example 1		Example 2		Example 3
PSF	Strehl Ratio (%)	FWHM (arc sec)	Strehl Ratio (%)	FWHM (arc sec)	Strehl Ratio (%)	FWHM (arc sec)
Real	62.2	0.121	45.2	0.100	16.3	0.160
Estimated	63.6	0.121	41.8	0.107	21.6	0.154

Atmospheric and AO Loop Quantities	Example 1	Example 2	Example 3
Guide star magnitude	10.4	12.7	15.4
$r_{0}$ (cm)	18.7	19.8	18.5

Mirror component $({rad}^{2}) :$
Estimated uncorrected phase $\sum σ_{a_{i}}^{2}$	109.8	83.0	79.9
RTC estimated residual phase $\sum σ_{{\bar{∊}}_{i}}^{2}$	3.4	30.0	110.3
Estimated WFS measurement error $\sum σ_{n_{i}}^{2}$	3.0	27.8	97.5
Estimated remaining error $\sum σ_{r_{i}}^{2}$	2.9	2.6	2.9
Estimated residual phase $\sum σ_{∊_{i}}^{2}$	3.3	4.7	15.8

Estimated high-order component $σ_{ϕ_{⊥}}^{2} ({rad}^{2})$	2.6	2.3	2.6

PSF	Example 1		Example 2		Example 3
PSF	Strehl Ratio (%)	FWHM (arc sec)	Strehl Ratio (%)	FWHM (arc sec)	Strehl Ratio (%)	FWHM (arc sec)
Real	62.2	0.121	45.2	0.100	16.3	0.160
Estimated	63.6	0.121	41.8	0.107	21.6	0.154

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Journal of the Optical Society of America A