This Point spread function (PSF) plays a crucial role in many computational imaging applications, such as shape from focus/defocus, depth estimation, and fluorescence microscopy. However, the mathematical model of the defocus process is still unclear. In this work, we develop an alternative method to estimate the precise mathematical model of the point spread function to describe the defocus process. We first derive the mathematical algorithm for the PSF which is used to generate the simulated focused images for different focus depth. Then we compute the loss function of the similarity between the simulated focused images and real focused images where we design a novel and efficient metric based on the defocus histogram to evaluate the difference between the focused images. After we solve the minimum value of the loss function, it means we find the optimal parameters for the PSF. We also construct a hardware system consisting of a focusing system and a structured light system to acquire the all-in-focus image, the focused image with corresponding focus depth, and the depth map in the same view. The three types of images, as a dataset, are used to obtain the precise PSF. Our experiments on standard planes and actual objects show that the proposed algorithm can accurately describe the defocus process. The accuracy of our algorithm is further proved by evaluating the difference among the actual focused images, the focused image generated by our algorithm, the focused image generated by others. The results show that the loss of our algorithm is 40% less than others on average.
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