Spreading properties of beams radiated by partially coherent Schell-model sources

We derive a general law for the M-2 factor of any beam generated by a partially coherent Schell-model source. The fourth power of M differs from its minimum value, attained in the coherent limit, by a term proportional to the second derivative of the modulus of the spectral degree of coherence evaluated for zero argument. Examples are given for cases of practical interest. (C) 1999 Optical Society of America [S0740-3232(99)01501-X]