3D-PSF Modeling of High-Magnification Optical Microscopes for Image Deblurring and System Calibration

Intensity-distribution calculation in a microscope imaging system is extremely significant for imaging resolution estimation. However, existing estimation methods are either overly complicated or have lower accuracy due to challenges associated with light-wave diffraction. This study proposes a simplified 3-D point spread function (PSF) model for high-magnification optical microscopes. First, the property of the calculated intensity distribution obtained from the existing model simplified with orthogonal polynomials is analyzed, which involves assessing the limitations and errors introduced by the simplification modeling. Second, according to the propagation characteristics of the incident light, the analyzable mathematical expression of a light-intensity-distribution deceleration factor is established to compensate for calculation errors in the light-intensity distribution. Third, the parameters in the deceleration factor are identified using the multivariate nonlinear regression method; thus, a high-precision 3D-PSF model is proposed to precisely describe the light-intensity-diffusion property in a high-magnification microscope. Finally, the accuracy of the proposed model is verified with our assembled microscope and extended to fluorescence-calibrated microbeads and multiple fluorescent biological samples, including actual nuclei and protein molecules, and the average mean-square error between our model and the ground truth is only 0.003.