Title
Linear analytical solution to the phase diversity problem for extended objects based on the Born approximation
Author
Andrei, R.M.
Smith, C.S.
Fraanje, P.R.
Verhaegen, M.
Korkiakoski, V.A.
Keller, C.U.
Doelman, N.J.
Publication year
2012
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. © 2012 SPIE.
Subject
Born approximation
Least squares
Point-spread function
Wavefront estimation
High Tech Systems & Materials
Industrial Innovation
Mechatronics, Mechanics & Materials
OM - Opto-Mechatronics
TS - Technical Sciences
To reference this document use:
http://resolver.tudelft.nl/uuid:427ab594-3831-487a-b66a-2881b0614866
TNO identifier
469144
ISBN
9780819491480
ISSN
0277-786X
Source
Adaptive Optics Systems III, 1 July 2012 through 6 July 2012, Amsterdam, 8447 (8447)
Series
Proceedings of SPIE - The International Society for Optical Engineering
Document type
conference paper