Optics and Photonics Journal, 2013, 3, 86-89

doi:10.4236/opj.2013.32B022 Published Online June 2013 (http://www.scirp.org/journal/opj)

Comparison of Iterative Wavefront Estimation Methods*

Y. Pankratova, A. Larichev, N. Iroshnikov

Faculty of Physics, Lomonosov MSU, Moscow, Russian Federation

Email: pankratovajv@gmail.com, larichev@optics.ru

Received 2013

ABSTRACT

The iterative reconstruction methods of the wavefront phase estimation from a set of discrete phase slope measurements

have been considered. The values of the root-mean-square difference between the reconstructed and original wavefront

have been received for Jacobi, Gauss-Seidel, Successive over-relaxation and Successive over-relaxation with Simpson

Reconstructor methods. The method with the highest accuracy has been defined.

Keywords: Wavefront Estimation; Phase; Reconstruction; Iterative Methods

1. Introduction

Now methods of adaptive optics become more and more

widespread in optics. That appears to be particularly im-

portant for ultra-high intensity lasers as the number of

optical elements that this lasers include is rather high so

the appearance of static and thermo-induced aberrations

of the wavefront are possible [1], for diagnostic medical

systems for correction of the crystalline lens and corneal

aberrations[2] and for ground-based telescopes to correct

for the atmospheric aberrations. In this paper we consider

the comparison research of the iterative methods of esti-

mating wavefront phase from a set of discrete phase

slope measurements that was obtained from a Hartmann

sensor.

2. Shack-Hartmann Wavefront Sensor

2.1. Operation Principle

The Shack-Hartmann wavefront sensor contains a lenslet

array that consists of a two-dimensional array of a few

hundred lenslets all with the same diameter and the same

focal length. The light ray spatially sampled into many

individual beams by the lenslet array and forms multiple

spots in the focal plane of the lenslets. A CCD camera

placed in the focal plane of the lanslet array records the

spot array pattern for wavefront calculation. For a wave

with plane wavefront the Shack-Hartmann spots are

formed along the optical axis of each lenslet, resulting in

a regularly spaced grid of spots in the focal plane of the

lenslet array. In contrast, individual spots formed by

wavefront with aberrations are displaced from the optical

axis of each lenslet. The displacement of each spot is

proportional to the wavefront slope.[2]

2.2. Specific Features

Modern Shack-Hartmann sensors consist of a large

number of lenslets, this number can exceed 10000. While

using such sensors it's possible to face the problem of

crosstalk, limited aperture and the loss of some points.

Not all methods of wavefront estimation are suitable un-

der these conditions.

3. Wavefront Reconstruction Methods

As an example of reconstruction methods can be taken

modal and zonal wavefront reconstruction methods.

• In the modal approach the wavefront is expanded

into a set of orthogonal basis functions, and the coeffi-

cients of the set of basis functions are estimated from the

discrete phase-slope measurements. The appearance of

the large reconstruction error is possible.

• In the zonal approach, the wavefront is estimated

directly from a set of discrete phase-slope measurements.

Estimated with this method wavefront has less recon-

struction error then that in modal approach. For the zonal

reconstruction method the iterative algorithms may be

used.

4. Iterative Methods

4.1. Jacobi and Gauss-Seidel Methods

One of the first iterative methods are Jacobi and Gauss-

Seidel methods. These methods were proposed by South-

well for wavefront reconstruction. The idea behind this

method is to take into account the wavefront deformation

for some vertical and horizontal adjacent spots in the

calculation of the wavefront deformation for all spots.

Southwell proposed an iterative solution where for any

point (n,m) the wavefront is calculated with (1), (2) and

*Russian Foundation for Basic Research №11-02-01353-a.

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