The fact that a Fourier transform relationship exists between the front and back focal planes of a thin spherical lens can be used to obtain the power spectral distribution of two-dimensional holographic data. In particular, this form of optical data processing is considered for obtaining the spectral variation as a function of the recording distance of the holographic intensity distribution caused by illuminating an opaque sphere with plane waves. An approximate, closed form solution for the two-dimensional Fourier transform of this problem is derived.
F. M. Shofner, T. G. Russell, and R. Menzel, "Two-Dimensional Spatial Frequency Analysis of the Fraunhofer Hologram of a Small Opaque Sphere," Appl. Opt. 8, 2043-2046 (1969)