Phase space measurements by a finite-width slit

Two dimensional phase space density distribution ρ(x,x' in x - x' space is usually employed to describe most practical beams for which two planes of symmetry exist. In order to unfold the transverse beam velocity distribution, a thin slit is commonly used. The slit samples the beam at a given slit location, and the beamlet is allowed to disperse after passing through the slit. The density profile of the dispersed beamlet is then measured at the detector plane. Ideally, an infinitely thin slit should be used which would produce a density profile that is equivalent to that of the velocity distribution of the beam. In actual experiments, however, use of a finite-width slit is inevitable: narrower slit reduces the beam intensity resulting in a poor signal-to-noise ratio of data, a minimum slit size is limited by a fabrication technique employed, and narrower width with a finite thickness of slit plate reduces the maximum acceptance angle. The authors describe a general method of correcting the width and the height of beamlet's density profile, which are in general wider and higher than those of the original distribution function due to the finite slit