<title>Modified Hartmann-Shack wavefront sensing and iterative wavefront reconstruction</title>

Abstract

ABSTRACT Conventional modal compensation using Zernike polynomial expansion by means of Hartmann-Shackwavefront sensors is discussed. Cross-talk problems of Zernike coefficients have been found to beserious, especially for large sub-aperture configurations. A proposal for use of a modified Hartmann-Shack wavefront sensor and iterative wavefront reconstruction is presented and a comparison is madebetween conventional and proposed methods. 1. INTRODUCTION Wavefront sensing and reconstruction is a key procedure in adaptive optics and other fields, such aspost-detection turbulence compensation. In adaptive optics, there are mainly three different kinds ofwavefront sensing methods, namely shearing interferometry, Hartmann-Shack (hear-after H-S) wavefront sensing and curvature sensing. The first two methods measure the local tilt (first derivative) of the unknown wavefront over a sub-aperture, while the last method measures the wavefront curvature (secondderivative). The purpose of wavefront sensing is to obtain necessary information on wavefronts. Whenthe information is obtained, the reconstruction of the wavefront is performed.In general, wavefront reconstruction can be categorised into two approaches, zonal and modal. In thezonal concept, the wavefront in a certain sub-aperture is fitted by means of phase directional derivativemeasurements. In the modal concept, wavefront is decomposed into a series of orthogonal polynomials,and the coefficients of the polynomials are estimated using the phase derivative measurements. Bothmethods use least square estimation.Modal wavefront reconstruction using H-S wavefront sensing is commonly used, since the H-S wave-front sensing method is widely chosen in adaptive optics and modal reconstruction has been shown tobe superior to zonal reconstruction1. In the modal approach, due to the finite summation of the decom-posed polynomials, cross-talk of high order coefficients unavoidably affects those of lower orders2. Thisproblem is severe, especially when the number of sub-apertures is small. In this paper, we propose the