Adaptive optics correction of segment aberration

Natalia Yaitskova

doi:10.1364/JOSAA.26.000059

Journal of the Optical Society of America A
Vol. 26,
Issue 1,
pp. 59-71
(2009)
•https://doi.org/10.1364/JOSAA.26.000059

Adaptive optics correction of segment aberration

Natalia Yaitskova

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Natalia Yaitskova, "Adaptive optics correction of segment aberration," J. Opt. Soc. Am. A 26, 59-71 (2009)

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Abstract

The objective of the present study is to estimate the ability of conventional adaptive optics (AO) to correct for a wavefront created by static errors randomly distributed over the population of a multisegmented primary mirror for an extremely large telescope (ELT). The criterion for the performance of AO is a correction factor: a ratio between two root-mean-square (RMS) values of the phase before and after the AO correction. We define a best value for the correction factor as the one obtained in an AO model described as a hard-edge high-pass filter applied to phase aberrations of the telescope pupil. We compare the results of other AO models with this best value. The relation between RMS and the power spectral density helps us evaluate the initial requirements of segment aberration for optimistic and pessimistic cases without need of specifying the type of AO. This work develops a tool that can be used for segment manufacturing specifications, for defining the requirements on an active optics system controlling segment shape, and for designing a high-contrast imaging instrument for an ELT.

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Equations (44)

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Aberration Name	Expression
Piston	1
Tip	$2 ρ \cos (θ)$
Tilt	$2 ρ \sin (θ)$
Defocus	$\sqrt{3} (2 ρ^{2} - 1)$
Astigmatism X	$\sqrt{6} ρ^{2} \cos (2 θ)$
Astigmatism Y	$\sqrt{6} ρ^{2} \sin (2 θ)$
Coma X	$\sqrt{8} (3 ρ^{3} - 2 ρ^{2}) \cos (θ)$
Coma Y	$\sqrt{8} (3 ρ^{3} - 2 ρ^{2}) \sin (θ)$
Spherical	$\sqrt{5} (6 ρ^{4} - 6 ρ^{2} + 1)$
Trefoil X	$\sqrt{8} ρ^{3} \cos (3 θ)$
Trefoil Y	$\sqrt{8} ρ^{3} \sin (3 θ)$
Second astigmatism X	$\sqrt{10} (4 ρ^{4} - 3 ρ^{2}) \cos (2 θ)$
Second astigmatism Y	$\sqrt{10} (4 ρ^{4} - 3 ρ^{2}) \sin (2 θ)$
Second coma X	$\sqrt{12} (10 ρ^{5} - 12 ρ^{3} + 3 ρ) \cos (θ)$
Second coma Y	$\sqrt{12} (10 ρ^{5} - 12 ρ^{3} + 3 ρ) \sin (θ)$
Second spherical	$\sqrt{7} (20 ρ^{6} - 30 ρ^{4} + 12 ρ^{2} - 1)$

Aberration	Form Factor
Piston	1
Tip	$5 ∕ 6$
Tilt	$5 ∕ 6$
Defocus	$4 ∕ 5$
Astigmatism X	$7 ∕ 10$
Astigmatism Y	$7 ∕ 10$
Coma X	$337 ∕ 420$
Coma Y	$337 ∕ 420$
Sphere	$61 ∕ 70$
Trefoil X	$103 ∕ 140$
Trefoil Y	$9 ∕ 20$
Second astigmatism X	$257 ∕ 315$
Second astigmatism Y	$257 ∕ 315$
Second coma X	$208 ∕ 231$
Second coma Y	$208 ∕ 231$
Second sphere	$27,299 ∕ 30,030$

Aberration Name	Expression
Piston	1
Tip	$2 ρ \cos (θ)$
Tilt	$2 ρ \sin (θ)$
Defocus	$\sqrt{3} (2 ρ^{2} - 1)$
Astigmatism X	$\sqrt{6} ρ^{2} \cos (2 θ)$
Astigmatism Y	$\sqrt{6} ρ^{2} \sin (2 θ)$
Coma X	$\sqrt{8} (3 ρ^{3} - 2 ρ^{2}) \cos (θ)$
Coma Y	$\sqrt{8} (3 ρ^{3} - 2 ρ^{2}) \sin (θ)$
Spherical	$\sqrt{5} (6 ρ^{4} - 6 ρ^{2} + 1)$
Trefoil X	$\sqrt{8} ρ^{3} \cos (3 θ)$
Trefoil Y	$\sqrt{8} ρ^{3} \sin (3 θ)$
Second astigmatism X	$\sqrt{10} (4 ρ^{4} - 3 ρ^{2}) \cos (2 θ)$
Second astigmatism Y	$\sqrt{10} (4 ρ^{4} - 3 ρ^{2}) \sin (2 θ)$
Second coma X	$\sqrt{12} (10 ρ^{5} - 12 ρ^{3} + 3 ρ) \cos (θ)$
Second coma Y	$\sqrt{12} (10 ρ^{5} - 12 ρ^{3} + 3 ρ) \sin (θ)$
Second spherical	$\sqrt{7} (20 ρ^{6} - 30 ρ^{4} + 12 ρ^{2} - 1)$

Aberration	Form Factor
Piston	1
Tip	$5 ∕ 6$
Tilt	$5 ∕ 6$
Defocus	$4 ∕ 5$
Astigmatism X	$7 ∕ 10$
Astigmatism Y	$7 ∕ 10$
Coma X	$337 ∕ 420$
Coma Y	$337 ∕ 420$
Sphere	$61 ∕ 70$
Trefoil X	$103 ∕ 140$
Trefoil Y	$9 ∕ 20$
Second astigmatism X	$257 ∕ 315$
Second astigmatism Y	$257 ∕ 315$
Second coma X	$208 ∕ 231$
Second coma Y	$208 ∕ 231$
Second sphere	$27,299 ∕ 30,030$

Abstract

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Equations (44)

Journal of the Optical Society of America A