Gravitational microlensing is a key probe of the nature of dark matter and its distribution on the smallest scales. For many practical purposes, confronting theory to observation requires to model the probability that a light source is highly amplified by many-lens systems. This article reviews four simple analytic models of the amplification probability distribution, based on different approximations: (i) the strongest-lens model; (ii) the multiplicative model, where the total amplification is assumed to be the product of all the lenses’ individual amplifications; (iii) a hybrid version of the previous two; and (iv) an empirical fitting function. In particular, a new derivation of the multiplicative amplification distribution is proposed, thereby correcting errors in the literature. Finally, the accuracy of these models is tested against ray-shooting simulations. They all produce excellent results as long as lenses are light and rare (low optical depth); however, for larger optical depths, none of them succeeds in capturing the relevant features of the amplification distribution. This conclusion emphasizes the crucial role of lens–lens coupling at large optical depths.

引力微透镜是暗物质性质及其在最小尺度上分布的关键探测器。出于许多实际目的，将理论与观察相面对需要对光源被多镜头系统高度放大的概率进行建模。本文基于不同的近似方法，对放大概率分布的四个简单分析模型进行了回顾：（i）最强透镜模型；（ii）乘法模型，其中总放大率假定为所有镜片各自放大率的乘积；（iii）前两个的混合版本；（iv）经验拟合函数。特别地，提出了乘性放大分布的新推导，从而校正了文献中的误差。最后，这些模型的准确性已针对射线拍摄模拟进行了测试。只要镜片轻巧且稀有（低光学深度），它们都能产生出色的效果。但是，对于较大的光学深度，它们都无法成功捕获放大分布的相关特征。该结论强调了大光学深度下透镜-透镜耦合的关键作用。