Space-variant point spread function measurement and interpolation at any depth based on single-pixel imaging

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.