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

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.