Variation on a Zernike wavefront sensor theme: optimal use of photons

TL;DR

This paper enhances the Zernike wavefront sensor by optimizing the phase shifting dot diameter, significantly improving sensitivity while maintaining dynamic range, through theoretical analysis and simulations.

Contribution

It introduces a novel variation of the Zernike wavefront sensor with optimized dot diameter, achieving higher sensitivity without sacrificing dynamic range.

Findings

Z2WFS sensitivity is twice that of classical ZWFS for most phase components.

Optimized dot diameter reaches the theoretical sensitivity limit.

Dynamic range remains similar to classical ZWFS despite increased sensitivity.

Abstract

The Zernike wavefront sensor (ZWFS) is a concept belonging to the wide class Fourier-filtering wavefront sensor (FFWFS). The ZWFS is known for its extremely high sensitivity while having a low dynamic range, which makes it a unique sensor for second stage adaptive optics (AO) systems or quasi-static aberrations calibration sensor. This sensor is composed of a focal plane mask made of a phase shifting dot fully described by two parameters: its diameter and depth. In this letter, we aim to improve the performance of this sensor by changing the diameter of its phase shifting dot. We begin with a general theoretical framework providing an analytical description of the FFWFS properties, then we predict the expected ZWFS sensitivity for different configurations of dot diameters and depths. The analytical predictions are then validated with end-to-end simulations. From this, we propose a variation of the classical ZWFS shape which exhibits extremely appealing properties. We show that the ZWFS sensitivity can be optimized by modifying the dot diameter and even reach the optimal theoretical limit, with a trade-off for low spatial frequencies sensitivity. As an example, we show that a ZWFS with a 2{\lambda}/D dot diameter (where {\lambda} is the sensing wavelength and D the telescope diameter), hereafter called Z2WFS, exhibits a sensitivity twice higher than the classical 1.06{\lambda}/D ZWFS for all the phase spatial components except for tip-tilt modes. Furthermore, this gain in sensitivity does not impact the dynamic range of the sensor, and the Z2WFS exhibits a similar dynamical range as the classical 1.06{\lambda}/D ZWFS. This study opens the path to the conception of diameter-optimized ZWFS.