The accurate modelling of the Point Spread Function (PSF) is of paramount importance in astronomical observations, as it allows for the correction of distortions and blurring caused by the telescope and atmosphere. PSF modelling is crucial for accurately measuring celestial objects' properties. The last decades brought us a steady increase in the power and complexity of astronomical telescopes and instruments. Upcoming galaxy surveys like Euclid and LSST will observe an unprecedented amount and quality of data. Modelling the PSF for these new facilities and surveys requires novel modelling techniques that can cope with the ever-tightening error requirements. The purpose of this review is three-fold. First, we introduce the optical background required for a more physically-motivated PSF modelling and propose an observational model that can be reused for future developments. Second, we provide an overview of the different physical contributors of the PSF, including the optic- and detector-level contributors and the atmosphere. We expect that the overview will help better understand the modelled effects. Third, we discuss the different methods for PSF modelling from the parametric and non-parametric families for ground- and space-based telescopes, with their advantages and limitations. Validation methods for PSF models are then addressed, with several metrics related to weak lensing studies discussed in detail. Finally, we explore current challenges and future directions in PSF modelling for astronomical telescopes.

翻译：精确建模点扩散函数（PSF）在天文观测中至关重要，因为它能够校正由望远镜和大气引起的畸变与模糊。PSF建模是精确测量天体物理属性的关键。过去几十年，天文望远镜及仪器的性能与复杂性稳步提升。即将开展的星系巡天项目如Euclid和LSST将观测到前所未有的海量高质量数据。为这些新设施和巡天项目建模PSF，需要能够满足日益严苛的误差要求的新型建模技术。本综述旨在实现三个目标：首先，介绍构建更具物理动机的PSF模型所需的光学背景知识，并提出一个可复用于未来开发的观测模型；其次，概述PSF的不同物理贡献源，包括光学器件级、探测器级贡献源及大气因素，预期此概述将有助于更好地理解被建模的效应；第三，探讨地面与空间望远镜中源自参数化及非参数化族系的不同PSF建模方法及其优缺点。随后讨论PSF模型的验证方法，并详细分析与弱引力透镜研究相关的若干度量指标。最后，展望天文望远镜PSF建模当前面临的挑战与未来发展方向。