Bargman Transforms and Phase Space Filters Summary

Abstract

The Bargman transform is an outgrowth of the phase space representations of Electromagnetic Fields in Quantum Optics. It transforms fields from the time domain to the phase plane where they are functions of the phase variables p and q . The transform is another form of the windowed Fourier transform. The space in which the transform resides is called the Bargman space and has the important property that it contains analytic entire functions of the variable z = q ip. The analytic properties of the transform are utilized to construct phase space filters which are used to selectively access portions of the phase plane. The phase space filtering is used to analyze target returns from canonical targets such as dielectric slabs and perfectly conducting spheres.