Rotational frequency shifts in partially coherent optical fields

We study the frequency shifts taking place when a random, stationary optical field rotates with respect to an observer. The field is expanded in terms of fully coherent Laguerre–Gaussian basis modes, for which the rotational frequency shifts have been studied previously. We demonstrate the formalism by considering the spectrum of a Gaussian Schell-model field, and show that for a spatially highly incoherent field, significant spectral changes can be expected.