Calibration and performances of the integrated Mach—Zehnder wavefront sensor for extreme adaptive optics

Centre de recherche astrophysique de Lyon (CRAL), Université Claude Bernard Lyon 1, CNRS, ENS, 9 avenue Charles Andre, 69561 Saint Genis Laval, France

^★ Corresponding author: camille.graf@univ-lyon1.fr

Received: 31 January 2025
Accepted: 20 June 2025

Abstract

Context. Direct imaging of circumstellar environments around nearby stars requires eXtreme Adaptive Optics (XAO) systems. These systems must integrate advanced wavefront sensors (WFSs) to reach a high Strehl ratio (SR) in the near-infrared and at visible wavelengths on future giant segmented mirror telescopes (GSMTs). Direct detection of faint exoplanets with these extremely large telescopes will require tens of thousands of correction modes. In addition, highly accurate and sensitive WFSs set key requirements. The precise measurement of the wavefront degradation for both static and dynamic aberrations with a limited number of photons is still an issue for most WFSs, which are often limited either in sensitivity or in dynamical range.

Aims. We present the integrated Mach–Zehnder (iMZ), a self-referenced interferometric WFS developed for XAO and implemented on an XAO test bench at CRAL. The WFS concept consists of creating two opposite sets of interferences between the wavefront phase to be measured and the spatially filtered reference beam. We describe the implementation of this concept, including the scheme we have developed to extend its dynamical range by using phase diversity.

Methods. We present an iMZ physical model that allows the performance of this sensor to be studied in closed loop for different telescopes (the Very Large Telescope (VLT) and the Extremely Large Telescope (ELT)) in different turbulence regimes and including island effects, cophasing residuals, or low wind effects. A calibration method adapted to the iMZ that takes into account the nonlinearities of the signal was developed to use this WFS for diverse types of phase measurements. We analytically computed the photon noise error propagation of the iMZ, setting its ultimate sensitivity, and we compared it with several WFSs used in adaptive optics. Finally, we demonstrated the performances of the iMZ in closed loop by using end-to-end (E2E) simulations and experimental validations.

Results. The proposed iMZ WFS demonstrates a significant gain in sensitivity compared to the Shack–Hartmann WFS traditionally used in AO. The iMZ dynamical range, reduced to a wavelength in closed-loop operations, can be extended to several wavelengths by using phase diversity strategies developed in this paper. We demonstrate, with simulations and experimentally, a new calibration method for the iMZ, which is an essential step for the precise reconstruction of the phase. It is achieved by solving an inverse problem based on the interferometric model of the data. Our E2E numerical simulations confirm the very good performances of this sensor and the possibility of using it without a first stage of correction in good turbulence conditions. Experimental laboratory results demonstrate the efficiency of the iMZ in closed loop under good seeing conditions. The development of the iMZ is also motivated by the arrival of GSMTs leading to challenging new optical aberrations, such as differential pistons between different segments constituting the pupil and the pupil fragmentation (also called petal modes). The iMZ can efficiently measure these type of aberrations as well, to which most WFSs are not sensitive or are only slightly sensitive because their responses are generally proportional to the derivative of the incident wavefront. With its two complementary outputs, the iMZ WFS also offers the possibility of measuring the amplitude of the incident wave jointly with its phase without sensitivity loss, which makes it possible to consider correcting the effects of scintillation due to the atmosphere.

Conclusions. We conclude that the iMZ is an excellent WFS candidate for future XAO systems, in particular on GSMTs.