Alignment of the active secondary mirror of a space telescope using model-based wavefront sensorless adaptive optics

Hongxi Ren; Bing Dong; Yan Li

doi:10.1364/AO.415435

Applied Optics
Vol. 60,
Issue 8,
pp. 2228-2234
(2021)
•https://doi.org/10.1364/AO.415435

Alignment of the active secondary mirror of a space telescope using model-based wavefront sensorless adaptive optics

Hongxi Ren, Bing Dong, and Yan Li

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Hongxi Ren, Bing Dong, and Yan Li, "Alignment of the active secondary mirror of a space telescope using model-based wavefront sensorless adaptive optics," Appl. Opt. 60, 2228-2234 (2021)

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Abstract

The precise alignment of the space telescope with an active secondary mirror (ASM) is essential to high-quality imaging. The traditional alignment methods either require a dedicated wavefront sensor or a lot of iterations to optimize a metric function, which is not suitable for on-orbit instant alignment. A model-based wavefront sensorless adaptive optics method is proposed for the alignment of the ASM of a wide field-of-view space telescope. In our method, the aberration is estimated by introducing a series of modal biases successively into the system using the ASM. Unlike the traditional wavefront sensing methods that intend to measure all aberration modes, only five aberration modes that can be compensated by the ASM are estimated. Two alignment schemes either using single-field or multi-field images are proposed to calculate the control signals of the ASM, depending on if the aberration is mainly caused by the ASM. Simulations are made to evaluate the performance of our method under different scenarios. The influence of image sampling frequency, image size, and image noise on alignment are also investigated.

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Equations (18)

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			$d$			$d_{m} - (d - d_{0})$
	$d_{m}$	$d_{0}$	SPGD	$2 N + 1$	$3 N$	SPGD	$2 N + 1$	$3 N$
$d z / µ m$	12.589	−0.942	11.451	11.579	11.643	0.196	0.398	0.082
$d x / µ m$	162.317	1.192	162.559	163.213	163.464	0.095	2.594	1.007
$d y / µ m$	−149.205	35.973	−105.358	−113.548	−113.200	−7.874	−0.964	−0.730
$t x / a r c s e c$	23.810	−2.873	19.599	20.952	20.932	1.338	0.147	0.116
$t y / a r c s e c$	7.624	0.017	7.781	7.617	7.634	−0.140	0.290	0.143

		Image Sampling Frequency		Image Size		Image Noise
	$λ F # / p = 2$ $δ = 1 / 128$ $S N R = \infty$	$λ F # / p = 1$ $δ = 1 / 128$ $S N R = \infty$	$λ F # / p = 0.5$ $δ = 1 / 128$ $S N R = \infty$	$λ F # / p = 2$ $δ = 1 / 64$ $S N R = \infty$	$λ F # / p = 2$ $δ = 1 / 32$ $S N R = \infty$	$λ F # / p = 2$ $δ = 1 / 128$ $S N R = 60 d B$	$λ F # / p = 2$ $δ = 1 / 128$ $S N R = 40 d B$
$d z / µ m$	0.082	0.082	0.066	0.366	−0.043	0.095	−0.366
$d x / µ m$	1.007	1.012	0.996	5.417	−5.963	0.712	−2.197
$d y / µ m$	−0.730	−0.735	−0.445	−0.839	3.358	−0.914	1.620
$t x / a r c s e c$	0.116	0.117	0.086	0.279	−0.247	0.154	−0.144
$t y / a r c s e c$	0.143	0.144	0.113	1.333	−0.202	0.097	−0.559
$R M S / λ$	0.0445	0.0445	0.0448	0.0485	0.0507	0.0446	0.0507

			$d$			$d_{m} - (d - d_{0})$
	$d_{m}$	$d_{0}$	SPGD	$2 N + 1$	$3 N$	SPGD	$2 N + 1$	$3 N$
$d z / µ m$	12.589	−0.942	11.451	11.579	11.643	0.196	0.398	0.082
$d x / µ m$	162.317	1.192	162.559	163.213	163.464	0.095	2.594	1.007
$d y / µ m$	−149.205	35.973	−105.358	−113.548	−113.200	−7.874	−0.964	−0.730
$t x / a r c s e c$	23.810	−2.873	19.599	20.952	20.932	1.338	0.147	0.116
$t y / a r c s e c$	7.624	0.017	7.781	7.617	7.634	−0.140	0.290	0.143

		Image Sampling Frequency		Image Size		Image Noise
	$λ F # / p = 2$ $δ = 1 / 128$ $S N R = \infty$	$λ F # / p = 1$ $δ = 1 / 128$ $S N R = \infty$	$λ F # / p = 0.5$ $δ = 1 / 128$ $S N R = \infty$	$λ F # / p = 2$ $δ = 1 / 64$ $S N R = \infty$	$λ F # / p = 2$ $δ = 1 / 32$ $S N R = \infty$	$λ F # / p = 2$ $δ = 1 / 128$ $S N R = 60 d B$	$λ F # / p = 2$ $δ = 1 / 128$ $S N R = 40 d B$
$d z / µ m$	0.082	0.082	0.066	0.366	−0.043	0.095	−0.366
$d x / µ m$	1.007	1.012	0.996	5.417	−5.963	0.712	−2.197
$d y / µ m$	−0.730	−0.735	−0.445	−0.839	3.358	−0.914	1.620
$t x / a r c s e c$	0.116	0.117	0.086	0.279	−0.247	0.154	−0.144
$t y / a r c s e c$	0.143	0.144	0.113	1.333	−0.202	0.097	−0.559
$R M S / λ$	0.0445	0.0445	0.0448	0.0485	0.0507	0.0446	0.0507

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Applied Optics