Computational method for deriving the geometric point spread function of an optical system

The distribution of the ray density of the spot diagram formed in the image plane is called the geometric point spread function (PSF). It plays an important role in the image formation theory, since it describes the impulse response of an optical system to a source point. However, the literature contains very few techniques for deriving the PSFof optical systems. Accordingly, this study presents a method based on an irradiance model for computing the geometric PSF of an optical system by considering the energy conservation along a single light ray. It is shown that the proposed method obtains a reliable and accurate estimate of the PSFand enables the computation of the centroid and root-mean-square radius of the focus spot on the image plane. In addition, compared to existing ray-counting methods presented in the literature, in which the quality of the PSF solution depends on the number of rays traced and the grid size used to mesh the image plane, the proposed irradiance-based method requires just one tracing operation. Overall, the results presented in this study confirm that the proposed method provides an ideal solution for calculating the merit function and modulation transfer function of an optical system.