The point spread function (PSF) describes the response of an imaging system to a point source. The degree of blurring is a measure of the quality of an imaging system. When a large object is analyzed as a composition of point sources, the global response is given by the field of PSFs (one PSF for each point source).

The dot scattering function field (PSF), that is, the PSF as a function of the point source location, characterizes the geometric and diffractive properties of most imaging optical systems. Consequently, tools to accurately calculate the PSF field are invaluable, especially for optical design, and also for image restoration and simulation applications. In particular, within design one field that would greatly benefit from an accurate estimation of PSF is the optimization of joint digital-optical systems. Furthermore, the simulation of realistic images, formed by optical systems, is an important requirement in the new field of computational imaging. There is an extensive literature on this problem, which covers various radiometric considerations, sensor sampling and noise, optical distortion, glare effects, etc. However, surprisingly even in the most ambitious proposals that claim to offer a complete simulation procedure of the image chain, the specific problem of the precise estimation of the PSF field is entirely dependent on computation through commercial optical design software packages. (such as Zemax or CODE V) offered and whose procedures are not available in the scientific literature. Our work also tries to make up for this omission in the estimation of the PSF field.
The conventional method of calculating the PSF field is carried out in two steps: first, the geometric calculation of the wave aberration function, and then the evaluation of the diffraction. This method usually applies two approximations: (1) the intersection coordinates of the exit and entrance pupil rays are equal; and (2) the optical field width distribution does not change between the exit and entrance pupil planes. We propose a variation of the conventional method that allows avoiding these two approaches in axially symmetric optical systems.

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