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

摘要

We propose a new approach for the joint estimation of aberration parameters and unknown object from diversityimages with applications in imaging systems with extended objects as astronomical ground-based observationsor solar telescopes. The motivation behind our idea is to decrease the computational complexity of the conventionalphase diversity (PD) algorithm and avoid the convergence to local minima due to the use of nonlinearestimation algorithms. Our approach is able to give a good starting point for an iterative algorithm or it canbe used as a new wavefront estimation method. When the wavefront aberrations are small, the wavefront can be approximated with a linear term which leads to a quadratic point-spread function (PSF) in the aberration parameters. The presented approach involves recording two or more diversity images and, based on the before mentioned approximation estimates the aberration parameters and the object by solving a system of bilinear equations, which is obtained by subtracting from each diversity image the focal plane image. Moreover, using the quadratic PSFs gives improved performance to the conventional PD algorithm through the fact that the gradients of the PSFs have simple analytical formulas.© (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.