The conditions under which convolution of two degrees of coherence represents a novel legitimate degree of coherence are established for wide-sense statistically stationary Schell-model beam-like optical fields. Several examples are given to illustrate how convolution can be used for generation of a far field being a modulated version of another one. Practically, the convolutions of the degrees of coherence can be achieved by programming the liquid crystal spatial light modulators. (C) 2015 Optical Society of America