The Rayleigh range of partially coherent beams

The concept of the Rayleigh range, well known in the theory of coherent beams, is extended to partially coherent beams. A simple formula is derived, which expresses it in terms of the rms widths of the source intensity and of the intensity of the field far from the source. In the special cases when the beam is completely coherent or is of the Gaussian Schell-model type, our formula reduces to known expressions. It is also shown that a partially coherent beam will always have a Rayleigh range that is shorter than that of a fully coherent beam with the same intensity distribution in the beam waist. (C) 2001 Published by Elsevier Science B.V.