Three-dimensional quantitative phase imaging (3D QPI) is widely recognized as a potentially high-impact microscopic modality. Central to determining the resolution capability of 3D QPI is the phase optical transfer function (POTF). The magnitude of the POTF over its spatial frequency coverage (SFC) specifies the intensity of the response for each allowed spatial frequency. In this paper, a detailed analysis of the POTF for an axially symmetric optical configuration is presented. First, a useful geometric interpretation of the SFC, which enables its visualization, is presented. Second, a closed-form 1D integral expression is derived for the POTF in the general nonparaxial case, which enables rapid calculation of the POTF. Third, this formulation is applied to disk, annular, multi-annuli, and Gaussian illuminations as well as to an annular objective. Taken together, these contributions enable the visualization and simplified calculation of the 3D axially symmetric POTF and provide a basis for optimizing QPI in a wide range of applications.

中文翻译：

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轴对称显微定量相位成像中的三维相位光学传递函数

三维定量相位成像（3D QPI）被广泛认为是一种潜在的高影响力微观形态。确定3D QPI分辨率的关键是相位光学传递函数（POTF）。POTF在其空间频率覆盖范围（SFC）上的大小指定了每个允许的空间频率的响应强度。在本文中，对轴向对称光学配置的POTF进行了详细分析。首先，对证监会进行了有用的几何解释，以使其可视化。其次，在一般非傍轴情况下，为POTF导出了封闭形式的1D积分表达式，从而可以快速计算POTF。第三，该公式适用于圆盘，环形，多环和高斯照明以及环形物镜。