Numerical estimation of wavefront error breakdown in adaptive optics

Aims. Adaptive optics (AO) system performance is improved using post-processing techniques, such as point spread function (PSF) deconvolution. The PSF estimation involves characterization of the different wavefront (WF) error sources in the AO system. We propose a numerical error breakdown estimation tool that allows studying AO error source behavior such as their correlations. We also propose a new analytical model for anisoplanatism and bandwidth errors that were validated with the error breakdown estimation tool. This model is the first step for a complete AO residual error model that is expressed in deformable mirror space, leading to practical usage such as PSF reconstruction or turbulent parameters identification. Methods. We have developed in the computing platform for adaptive optics systems (COMPASS) code, which is an end-to-end simulation code using graphics processing units (GPU) acceleration, an estimation tool that provides a comprehensive error breakdown by the outputs of a single simulation run. We derive the various contributors from the end-to-end simulator at each iteration step: this method provides temporal buffers of each contributor. Then, we use this tool to validate a new model of anisoplanatism and bandwidth errors including their correlation. This model is based on a statistical approach that computes the error covariance matrices using structure functions. Results. On a SPHERE-like system, the comparison between a PSF computed from the error breakdown with a PSF obtained from classical end-to-end simulation shows that the statistics convergence limits converge very well, with a sub-percent difference in terms of Strehl ratio and ensquared energy at 5λ/D$5\frac{\lambda}{D}$5λD separation. A correlation analysis shows significant correlations between some contributors, especially WF measurement deviation error and bandwidth error due to centroid gain, and the well-known correlation between bandwidth and anisoplanatism errors is also retrieved. The model we propose for the two latter errors shows an SR and EE difference of about one percent compared to the end-to-end simulation, even if some approximations exist.