Linearity of the pyramid wavefront sensor

Anna Burvall,Christopher Dainty,Elizabeth Daly,Stéphane R Chamot

doi:10.1364/oe.14.011925

Abstract

The pyramid wavefront sensor is very similar to the Fourier knife-edge test, but employs dynamic modulation to quantify the phase derivative. For circular modulation, we compare approximate geometrical optics calculations, more exact diffraction calculations, and experimental results. We show that both the sinusoidal and the approximate linear relationship between wavefront derivative and wavefront sensor response can be derived rigorously from diffraction theory. We also show that geometrical, diffraction and experimental results are very similar, and conclude that the approximate geometrical predictions can be used in place of the more complex diffraction results.

Highlights

The pyramid wavefront sensor was first introduced by Ragazzoni [1] for astronomical applications
The effects of circular modulation have been investigated by approximate geometrical theory [11, 12], and the effects of linear modulation have been partly clarified from diffraction theory [12, 13]
We show that the same results can be obtained from the simple geometrical prediction of pyramid sensor linearity as from an analytical derivation from diffraction theory

Summary

Introduction

The pyramid wavefront sensor was first introduced by Ragazzoni [1] for astronomical applications. It is a modified version of the Foucault knife-edge test [2, 3], where a refractive element (the pyramid) is used to produce four images of the entrance pupil, and spatial modulation is introduced to control the gain of the phase slope measurements. The effects of circular modulation have been investigated by approximate geometrical theory [11, 12], and the effects of linear modulation have been partly clarified from diffraction theory [12, 13]. In this paper we investigate the response of a circularly modulated wavefront sensor, deriving and comparing results from geometrical theory, diffraction theory, and experiments.

Geometrical theory

Diffraction theory

Numerical evaluation

Experiment

Conclusions