Adding colour to the Zernike wavefront sensor: Advantages of including multi-wavelength measurements for wavefront reconstruction

¹ SRON – Space Research Organisation Netherlands, Niels Bohrweg 4, 2333 CA Leiden, The Netherlands
² Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
³ Steward Observatory, The University of Arizona, 933 North Cherry Avenue, Tuscon, Arizona, USA
⁴ University of California Santa Cruz, 1156 High St, Santa Cruz, USA

^★ Corresponding author: m.darcis@sron.nl

Received: 9 May 2025
Accepted: 18 July 2025

Abstract

Context. To directly image Earth-like planets, contrast levels of 10⁻⁸−10⁻¹⁰ are required. The next generation of instruments will need wavefront control below the nanometer level to achieve these goals. The Zernike wavefront sensor (ZWFS) is a promising candidate thanks to its sensitivity, which reaches the fundamental quantum information limits. However, its highly non-linear response restricts its practical use case.

Aims. We aim to demonstrate the improvement in robustness of the ZWFS by reconstructing the wavefront based on multi-wavelength measurements facilitated by technologies such as the microwave kinetic inductance detectors (MKIDs).

Methods. We performed numerical simulations using an accelerated multi-wavelength gradient descent reconstruction algorithm. Three aspects are considered: dynamic range, photon noise sensitivity, and phase unwrapping. We examined both the scalar and vector ZWFS.

Results. Firstly, we find that using multiple wavelengths improves the dynamic range of the scalar ZWFS. However, for the vector ZWFS, its already extended range was not further increased. In addition, a multi-wavelength reconstruction allowed us to take advantage of a broader bandpass, which increases the number of available photons, making the reconstruction more robust to photon noise. Finally, multi-wavelength phase unwrapping enabled the measurement of large discontinuities such as petal errors with a trade-off in noise performance.