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

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

Andrei, R.M.

Smith, C.S.

Fraanje, P.R.

Verhaegen, M.

Korkiakoski, V.A.

Keller, C.U.

Doelman, N.J.

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.

SubjectBorn approximation

Least squares

Point-spread function

Wavefront estimation

High Tech Systems & Materials

Industrial Innovation

Mechatronics, Mechanics & Materials

OM - Opto-Mechatronics

TS - Technical Sciences

http://resolver.tudelft.nl/uuid:427ab594-3831-487a-b66a-2881b0614866

TNO identifier469144

9780819491480

0277-786X

Adaptive Optics Systems III, 1 July 2012 through 6 July 2012, Amsterdam, 8447 (8447)

SeriesProceedings of SPIE - The International Society for Optical Engineering

Document typeconference paper

andrei-2012-linear.pdf |