Numerical calculation of three-dimensional point spread function оf optical systems

The paper presents the mathematical apparatus for precise calculation of the three-dimensional point spread function (3D PSF) of optical systems. The method is based on the Huygens-Fresnel principle: a spherical wave on the threedimensional surface of the exit pupil is considered as result of the superposition of elementary secondary point radiation sources. These point sources emit coherent electromagnetic waves with a spherical wave front. They form a certain distribution of generalized complex amplitudes in three-dimensional space near the focus point. This distribution is used to calculate the intensity distribution in the focus area of the optical system, which is the PSF. The advantage of the proposed technique is direct calculation of the 3D PSF with taking into account wave aberrations and without usage of Fresnel or Fraunhofer approximations. In case of small aperture optical systems the proposed technique coincides with classical theory that specifies the link between a pupil function and PSF via Fourier transform. The differences between precise and approximated techniques for 3D PSF calculation are also discussed.