<title>Measurement of the Wigner distribution function based on the inverse Radon transformation</title>

Abstract

The Wigner Distribution Function (WDF) has been well known in quantum mechanics since the thirties. Applied to paraxial optics it can be considered as a phase-space representation of quasi-monochromatic, partially coherent beams. For a two-dimensional beam (one transverse dimension) it depends on one spatial and one angular coordinate. Due to some properties of the WDF, it may be considered as an intensity distribution of geometrical rays, depending on position and direction, although this analogy is limited. Once the WDF of a laser beam in one transverse plane is known, the intensity distribution behind any optical system can be derived from it. The measurement of the WDF cannot be connected with a single intensity measurement as can be shown easily. Several suggestions for measurement procedures involving different kinds of apertures have been made. But all of them suffer from the influences of those apertures. Here we present a method which uses only a single focusing lens and several intensity measurements. It is based on a known mathematical procedure called the inverse radon transformation. An experimental result of applying this method to a laser beam emerged by an unstable resonator is presented, too.