Initial Antinoise Performance Analysis of Pupil Phase Diversity Based on Genetic Algorithm

Pupil phase diversity (PPD) wavefront sensor is a new kind of phase-visualization methods, and the output signal of PPD represents the input pupil phase and shows a 1-1 mapping between the position of the wavefront error in the pupil and its position in the output signal. High-precisely wavefront measuring can be obtained under no noise by using appropriate phase restoration algorithm while performance of PPD under noise is unknown. We analyzed antinoise performance of PPD based on genetic algorithm (GA) through measuring the distorted wavefront under different noise level. Simulation results show that wavefront measuring is almost not affected by the existence of noise, which indicates that PPD based on GA can be used in applications with noise. 1. Introduction Phase diversity (PD) refers to a method of image-based wavefront sensing where multiple images of an unknown extended object or scene are used to estimate both the unknown phase parameters and the unknown object [1, 2]. A quadratically distorted diffraction grating can be used to simultaneously image multiple object planes onto a single detector [3]. The diffraction grating provides a different level of defocus in each diffraction order, and the intensity images formed on a CCD detector provide data for the PD algorithm, which is called as defocus PD (DPD). Campbell et al. put forward the generalized phase diversity (GPD) method in 2004 [4]. The GPD, like the DPD sensor, uses two intensity images to perform wavefront sensing and has more extensive applications. However, DPD’s use of two images that are symmetrically defocused with respect to the unknown wavefront is replaced in GPD by a pair of images of the wavefront plane, each convolved with arbitrary but related aberration functions. These functions may include, but not be limited to, defocus. GPD has two different kinds of optics constructions, one is based on image plane and the other based on pupil plane [5]. In this paper, we use the optics constructions of pupil plane and call them pupil phase diversity (PPD). High-precisely wavefront measuring can be obtained under no noise by using appropriate phase restoration algorithm while performance of PPD wavefront sensor under noise is unknown. In this paper, we analyze the performance of PPD sensor in confronting noise through measuring the distorted wavefront under different noise level. The most widely used algorithms for phase retrieval of PD wavefront sensor are Gerchberg-Saxton approach [6] or its modified editions and iteration algorithms [7]. Previous approaches can not take full