JEOS RP ISSN01 | Page 6

J. Eur. Opt. Society-Rapid Publ. 2025, 21, 1 Ó The Author( s), published by EDP Sciences, 2025 https:// doi. org / 10.1051 / jeos / 2024045 Available online at: https:// jeos. edpsciences. org

Journal of the European Optical Society-Rapid Publications

Using wavefronts: detection and processing Guest editors: José Benito Vázquez Dorrío and Jorge García Marquez

RESEARCH ARTICLE

Design considerations for wavefront sensing with self-referencing interferometers in adaptive optics systems

1 School of Engineering, The University of British Columbia, 1137 Alumni Avenue, Kelowna, BC, V1V 1V7, Canada 2 German Aerospace Center( Deutsches Zentrum für Luft- und Raumfahrt, DLR), Münchnerstrasse 20, 82234 Wessling, Germany

Received 9 September 2024 / Accepted 12 November 2024

Abstract. In this work, we show the design and implementation of wavefront sensing with a self-referencing interferometer( SRI). The SRI is developed to aid adaptive optics( AO) control, via deformable mirrors, in correcting wavefront error from atmospheric turbulence in( laser-based) free-space optical communication links. The SRI is used here given its potential to outperform more common wavefront sensors in functioning over weak through strong turbulence conditions. In this study, we identify and analyse the key parameters in the SRI’ s optical design and show guiding principles for its subsequent image processing.

Keywords: Wavefront sensing, Self-referencing interferometer, Adaptive optics, Free-space optics.

1 Introduction

Adaptive optics( AO) technology has spurred many advancements by its enabling of real-time correction of optical distortion. This has led to remarkable achievements by ground-based astronomical imaging systems [ 1, 2 ] and growing interest on ground-to-satellite( laser-based) freespace optical communication( FSOC) links [ 3, 4 ]. At the core of such links is their ability to measure wavefront( phase) distortion across transverse profiles of received laser beams, with wavefront sensors [ 5 – 8 ], and then compensate for this distortion with deformable mirrors [ 4 ].

The recent works on AO-augmented FSOC links often relate to their wavefront sensors, as it is a critical AO element. Such wavefront sensors must provide fast and accurate characterizations of the received laser wavefronts over a wide range of elevation angles in the sky, at all times of day, and various wavefront sensors have been developed in this effort. In the earlier literature, the curvature wavefront sensor was introduced. It measured the local wavefront curvature, the Laplacian of the wavefront surface, and the radial tilt at the aperture edge to carry out its wavefront characterization [ 9 ]. Following this, a phase-shifting phasedifference interferometer was developed. It measured four p / 2 phase-stepped interferograms on a camera and used a local reconstructor to return the phase [ 10 ]. In more recent years, the Fresnel sensor was introduced. It employed near-field diffraction methods to improve the wavefront

* Corresponding author: jonathan. holzman @ ubc. ca detection under moderate to high turbulence conditions [ 11 ]. More recently, developments have been seen on holographic wavefront sensors, which apply holography to reconstruct the amplitude and phase [ 12 – 15 ]. Nonetheless, through these developments, the Shack-Hartmann wavefront sensor [ 16 ] has remained the most common sensor in use. This is because its simple operation, with the deflections of focal spots measured under a lenslet array, offers wellestablished processing and robust packaging. However, FSOC links developed by ourselves [ 17 ] and others [ 18, 19 ] have shown such wavefront sensing to be challenging when the atmospheric turbulence transitions from weak to strong conditions.

In this work, we consider the self-referencing interferometer( SRI) as a viable technology for wavefront sensing in weak through strong turbulence conditions [ 10 ]. The SRI wavefront sensor takes the form of a Mach-Zehnder interferometer, which splits the input beam( having distorted wavefronts) into a signal beam( with tilt applied across its wavefronts) and a reference beam( with flat wavefronts). The signal and reference beams are then overlapped as an output beam, whose interference pattern characterizes wavefrontdistortionacrosstheinputbeam. Thelevelsof tilt and flattening applied to the signal and reference beams dictate the performance of the SRI wavefront sensor, to a large extent, and we focus on these characteristics in the optical design. We then put forward guiding principles for the subsequent image processing. This is done to help realize an SRI wavefront sensor with functionality that enables future FSOC links.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License( https:// creativecommons. org / licenses / by / 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.