Chromatic Anisoplanatism in Adaptive Optics: A detailed comparison of theory with numerical simulations

Abstract

Context. Chromatic Anisoplanatism arises in Adaptive Optics because atmospheric refraction makes rays of different wavelengths follow different paths through the atmosphere resulting in different wavefronts at the sensing wavelength and the science wavelength, introducing a correction error that grows rapidly with zenith distance. Aims. Using numerical simulations based purely on geometric optical propagation we aim to validate the theoretical framework describing wavefront errors caused by Chromatic Anisoplanatism. We characterize the resulting phase variance and Strehl ratio loss for telescope apertures up to 39 m, retrieving their second-order statistics. Methods. We compare the analytical expressions for the Chromatic Anisoplanatism wavefront phase variance against independent Monte Carlo simulations. The framework models an 8-layer approximation of the median Cerro Armazones turbulence profile using Kolmogorov and von Karman turbulence models. We simulate pupil diameters from 4.2 to 39 m with lambda_WFS = 589.16 nm for the wavefront sensing and lambda_Sci = 1.25 microns as the science wavelength. A phase-screen recombination strategy increases the number of quasi-independent realizations up to ~ 5 x 10^5, optimizing statistical accuracy. Results. Simulated phase variances match theoretical predictions well across all apertures, though theory slightly overestimates variance in the von Karman case. The Strehl Ratio loss exceeds 30% for zenith angles >= 70 deg. The residual wavefront is dominated by high spatial frequencies; removing tip-tilt reduces phase variance by <= 1% for apertures >= 10 m. The massive dataset reveals highly non-Gaussian probability density functions for the phase variance and Strehl Ratio values, both characterized by non-zero skewness and kurtosis, and long tails toward rare, high wavefront phase variance and/or low Strehl Ratio error events.