Image reconstruction with analytical point spread functions

¹ Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife, Spain e-mail: aasensio@iac.es
² Departamento de Astrofísica, Universidad de La Laguna, 38205 La Laguna, Tenerife, Spain
³ THEMIS, CNRS UPS 853, c/vía Láctea s/n, 38200 La Laguna, Tenerife, Spain e-mail: arturo@themis.iac.es

Received: 24 February 2010
Accepted: 19 April 2010

Abstract

Context. The image degradation produced by atmospheric turbulence and optical aberrations is usually alleviated using post-facto image reconstruction techniques, even when observing with adaptive optics systems.

Aims. These techniques rely on the development of the wavefront using Zernike functions and the non-linear optimization of a certain metric. The resulting optimization procedure is computationally heavy. Our aim is to alleviate this computational burden.

Methods. We generalize the extended Zernike-Nijboer theory to carry out the analytical integration of the Fresnel integral and present a natural basis set for the development of the point spread function when the wavefront is described using Zernike functions.

Results. We present a linear expansion of the point spread function in terms of analytic functions, which, in addition, takes defocusing into account in a natural way. This expansion is used to develop a very fast phase-diversity reconstruction technique, which is demonstrated in terms of some applications.

Conclusions. We propose that the linear expansion of the point spread function can be applied to accelerate other reconstruction techniques in use that are based on blind deconvolution.