Linear analytical solution to the phase diversity problem for extended objects based on the Born approximation

Raluca M. Andrei; Carlas S. Smith; Rufus Fraanje; Michel Verhaegen; Visa A. Korkiakoski; Christoph U. Keller; Niek Doelman

doi:10.1117/12.926119

13 September 2012 Linear analytical solution to the phase diversity problem for extended objects based on the Born approximation

Raluca M. Andrei, Carlas S. Smith, Rufus Fraanje, Michel Verhaegen, Visa A. Korkiakoski, Christoph U. Keller, Niek Doelman

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Proceedings Volume 8447, Adaptive Optics Systems III; 84476U (2012) https://doi.org/10.1117/12.926119
Event: SPIE Astronomical Telescopes + Instrumentation, 2012, Amsterdam, Netherlands

Abstract

In this paper we give a new wavefront estimation technique that overcomes the main disadvantages of the phase diversity (PD) algorithms, namely the large computational complexity and the fact that the solutions can get stuck in a local minima. Our approach gives a good starting point for an iterative algorithm based on solving a linear system, but it can also be used as a new wavefront estimation method. The method is based on the Born approximation of the wavefront for small phase aberrations which leads to a quadratic point-spread function (PSF), and it requires two diversity images. First we take the differences between the focal plane image and each of the two diversity images, and then we eliminate the constant object, element-wise, from the two equations. The result is an overdetermined set of linear equations for which we give three solutions using linear least squares (LS), truncated total least squares (TTLS) and bounded data uncertainty (BDU). The last two approaches are suited when considering measurements affected by noise. Simulation results show that the estimation is faster than conventional PD algorithms.

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Raluca M. Andrei, Carlas S. Smith, Rufus Fraanje, Michel Verhaegen, Visa A. Korkiakoski, Christoph U. Keller, and Niek Doelman "Linear analytical solution to the phase diversity problem for extended objects based on the Born approximation", Proc. SPIE 8447, Adaptive Optics Systems III, 84476U (13 September 2012); https://doi.org/10.1117/12.926119

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KEYWORDS

Point spread functions

Wavefronts

Data transmission

Turbulence

Computer simulations

Zernike polynomials

Chemical elements

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