Fourier optical analysis of gradient-index array imaging

We present theory and experiments in which Fourier optics and the generalized Fresnel-zone integral form are used to characterize the imaging both of a single gradient-index rod and an array of nine rods. For the unity magnification SELFOC imager, we show that it has both internal and external Fourier transform planes. Careful treatment of the aperture function for off-axis points leads to a theoretical point-spread function that is in close agreement with experiments. Experiments are presented to illustrate the Fourier transform patterns as well as the imaging for single rods and for the entire array.