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