Jiang Hongzhi, Wang Yu, Li Xudong, Zhao Huijie, Li Yuxi
Opt Express. 2020 Mar 30;28(7):9244-9258. doi: 10.1364/OE.386366.
Point spread function (PSF) is important for evaluating an optical system and image deblurring. In this paper, we proposed a method to measure space-variant PSF at any depth based on single-pixel imaging (SPI), and we initiated a depth-variant PSF interpolation model. In our method, we regarded space-variant PSF as light transport coefficients from object points to image pixels. By applying SPI to each image pixel to obtain these light transport coefficients at different depths, the PSF of each object point can be extracted. The depth calculation of PSF is based on multi-frequency heterodyne phase-shifting principles and perspective-n-point (PnP) algorithm. In our PSF interpolation model, we interpolated the light transport coefficients from different object points to an image pixel first. We then obtained the interpolated PSF indirectly from the interpolated coefficients. With simple experimental facilities containing a digital camera and a liquid crystal display (LCD) screen to display and capture specific patterns, which relative distance is changed, the proposed method accurately obtained the space-variant PSF at any depth. Without complicated calculation, PSF at a certain depth can be interpolated from the PSF measured data at another depth with our PSF interpolation method. Significant similarities exist between the interpolated PSF and directly measured PSF. Our work is a successful attempt in using SPI to solve traditional optical problems.
点扩散函数（PSF）对于评估光学系统和图像去模糊很重要。在本文中，我们提出了一种基于单像素成像（SPI）在任意深度测量空间变化PSF的方法，并建立了深度变化PSF插值模型。在我们的方法中，我们将空间变化PSF视为从物点到图像像素的光传输系数。通过将SPI应用于每个图像像素以获得不同深度处的这些光传输系数，可以提取每个物点的PSF。PSF的深度计算基于多频外差相移原理和透视n点（PnP）算法。在我们的PSF插值模型中，我们首先将来自不同物点的光传输系数插值到一个图像像素。然后我们从插值系数间接获得插值后的PSF。利用包含数码相机和液晶显示器（LCD）屏幕以显示和捕获特定图案且相对距离可变的简单实验设备，所提出的方法准确地获得了任意深度处的空间变化PSF。通过我们的PSF插值方法，无需复杂计算，就可以从在另一个深度测量的PSF数据插值得到某一深度处的PSF。插值后的PSF与直接测量的PSF之间存在显著相似性。我们的工作是利用SPI解决传统光学问题的一次成功尝试。
