RISTRETTO: a comparative performance analysis of the unmodulated Pyramid wavefront sensor and the Zernike wavefront sensor

The RISTRETTO instrument, a proposed visible high-contrast, high-resolution spectrograph for the VLT, has the primary science goal of detecting reflected light from nearby exoplanets and characterizing their atmospheres. Specifically, it aims to atmospherically characterize Proxima b, our closest temperate rocky exoplanet, located $37 mas$ from its host star, corresponding to $2\lambda/D$ at $\lambda=750 nm$. To achieve this goal, a raw contrast of less than $10^{-4}$ at $2\lambda/D$ and a Strehl ratio greater than 70% are required, necessitating an extreme adaptive optics system (XAO) for the spectrograph. To meet the performance requirements for RISTRETTO, high sensitivity to low-order wavefront aberrations and petal modes is essential. Therefore, unmodulated Pyramid wavefront sensors (PWFS) and Zernike wavefront sensors (ZWFS) are under consideration. However, these sensors exhibit non-linearities and have a limited dynamic range, requiring different strategies to optimize their performance. The dynamic range of the sensors increases at longer wavelengths. Thus, in this study, we compare the performance of the 3-sided unmodulated PWFS, the 4-sided unmodulated PWFS, and the Zerniike WFS at different wavelengths in the visible and near-infrared regime.