The imaging performance of tomographic deconvolution phase microscopy can be described in terms of the phase optical transfer function (POTF) which, in turn, depends on the illumination profile. To facilitate the optimization of the illumination profile, an analytical calculation method based on polynomial fitting is developed to describe the POTF for general nonuniform axially symmetric illumination. This is then applied to Gaussian and related profiles. Compared to numerical integration methods that integrate over a series of annuli, the present analytical method is much faster and is equally accurate. Further, a “balanced distribution” criterion for the POTF and a least-squares minimization are presented to optimize the uniformity of the POTF. An optimum general profile is found analytically by relaxed optimal search, and an optimum Gaussian profile is found through a tree search. Numerical simulations confirm the performance of these optimum profiles and support the balanced distribution criterion introduced.

中文翻译：

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高斯照明的解析相位光学传递函数和优化的照明曲线

层析反卷积相位显微镜的成像性能可以用相位光学传递函数（POTF）来描述，而POTF则取决于照明轮廓。为了促进照明轮廓的优化，开发了一种基于多项式拟合的分析计算方法来描述一般非均匀轴对称照明的POTF。然后将其应用于高斯和相关轮廓。与在一系列环上进行积分的数值积分方法相比，本分析方法要快得多并且同样准确。此外，提出了用于POTF的“平衡分布”标准和最小二乘最小化，以优化POTF的均匀性。通过轻松的最佳搜索，可以找到最佳的一般概况，通过树搜索找到最佳的高斯分布。数值模拟证实了这些最佳轮廓的性能，并支持引入的平衡分配标准。