# Physics-based model of the adaptive-optics corrected point-spread-function

## TL;DR

This paper presents a physics-based model for the adaptive-optics corrected PSF that accurately captures core and halo features, correlates well with external turbulence measurements, and adapts to various seeing conditions.

## Contribution

It introduces a parsimonious, physically motivated PSF model with parameters directly linked to turbulence strength, enabling accurate fitting and turbulence parameter retrieval from AO data.

## Key findings

- Model matches simulated and real PSFs with <1% error.
- Retrieves Fried parameter r0 with subcentimeter accuracy.
- Shows strong correlation (97%) between estimated and measured r0.

## Abstract

Context. Adaptive optics (AO) systems greatly increase the resolution of large telescopes, but produce complex point spread function (PSF) shapes, varying in time and across the field of view. This PSF must be accurately known since it provides crucial information about optical systems for design, characterisation, diagnostics and image post processing. Aims. We develop here a model of the AO long exposure PSF, adapted to various seeing conditions and any AO system. This model is made to match accurately both the core of the PSF and its turbulent halo. Methods. The PSF model we develop is based on a parsimonious parameterization of the phase power spectral density with only five parameters to describe circularly symmetric PSFs and seven parameters for asymmetrical ones. Moreover, one of the parameters is directly the Fried parameter r0 of the turbulence s strength. This physical parameter is an asset in the PSF model since it can be correlated with external measurements of the r0, such as phase slopes from the AO real time computer (RTC) or site seeing monitoring. Results. We fit our model against endtoend simulated PSFs using OOMAO tool, and against on sky PSFs from the SPHERE ZIMPOL imager and the MUSE integral field spectrometer working in AO narrowfield mode. Our model matches the shape of the AO PSF both in the core and the halo, with a sub 1 percent relative error for simulated and experimental data. We also show that we retrieve the r0 parameter with subcentimeter precision on simulated data. For ZIMPOL data, we show a correlation of 97 percent between our r0 estimation and the RTC estimation. Finally, MUSE allows us to test the spectral dependency of the fitted r0 parameter. It follows the theoretical $\lambda^{6/5}$ evolution with a standard deviation of 0.3 cm. Evolution of other PSF parameters, such as residual phase variance or aliasing, is also discussed.