  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.
