Huang Jianhui, Bao Yijun, Gaylord Thomas K
J Opt Soc Am A Opt Image Sci Vis. 2020 Dec 1;37(12):1857-1872. doi: 10.1364/JOSAA.403861.
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.
三维定量相位成像（3D QPI）被广泛认为是一种具有潜在高影响力的微观成像方式。决定3D QPI分辨率能力的核心是相位光学传递函数（POTF）。POTF在其空间频率覆盖范围（SFC）上的幅度指定了每个允许空间频率的响应强度。本文对轴对称光学配置的POTF进行了详细分析。首先，给出了SFC的一种有用的几何解释，这使得它能够被可视化。其次，在一般非傍轴情况下，推导出了POTF的一维封闭形式积分表达式，这使得能够快速计算POTF。第三，将该公式应用于圆盘、环形、多环形和高斯照明以及环形物镜。综上所述，这些贡献使得三维轴对称POTF能够被可视化并简化计算，并为在广泛应用中优化QPI提供了基础。
