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Proceedings Paper

Linear analytical solution to the phase diversity problem for extended objects based on the Born approximation
Author(s): Raluca M. Andrei; Carlas S. Smith; Rufus Fraanje; Michel Verhaegen; Visa A. Korkiakoski; Christoph U. Keller; Niek Doelman
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Paper 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.

Paper Details

Date Published: 13 September 2012
PDF: 10 pages
Proc. SPIE 8447, Adaptive Optics Systems III, 84476U (13 September 2012); doi: 10.1117/12.926119
Show Author Affiliations
Raluca M. Andrei, Delft Ctr. for Systems and Control (Netherlands)
Carlas S. Smith, Delft Ctr. for Systems and Control (Netherlands)
Rufus Fraanje, Delft Ctr. for Systems and Control (Netherlands)
Michel Verhaegen, Delft Ctr. for Systems and Control (Netherlands)
Visa A. Korkiakoski, Leiden Observatory (Netherlands)
Christoph U. Keller, Leiden Observatory (Netherlands)
Niek Doelman, TNO Science and Industry (Netherlands)

Published in SPIE Proceedings Vol. 8447:
Adaptive Optics Systems III
Brent L. Ellerbroek; Enrico Marchetti; Jean-Pierre Véran, Editor(s)

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