Single-element diffractive optical system for real-time processing of synthetic aperture radar data

I present an optical system for the polar formatting of data in a spotlight-mode synthetic aperture radar. This system is implemented with only one diffractive optical element (DOE). Previously such a DOE could not be produced because the phase of the required transmission function of the DOE does not obey the continuity condition, which is a prerequisite for the conventional implementation of such optical transforms. Here I show how a DOE can be produced to perform the complete polar-formatting transform by incorporating branch-point phase singularities in the transmission function of the DOE. The computation of the transmission function is shown, and numerically computed diffraction patterns obtained from this DOE are also shown.