A derivation of the temporal spectrum a the far zone field diffracted by a uniformly translating planar aperture in front of a quasimonochromatic, temporally stationary, spatially homogeneous, incoherent, primary source is performed and numerical examples are provided. It is shown that the diffracted field spectrum can be expressed as the convolution of the spectrum of the source with a "modulating spectrum" determined by the shape and velocity of the aperture, as well as the direction of observation in the far zone.
Ivan J. LaHaie,
"Spectra Of Fields Diffracted By Moving Apertures In Front Of An Incoherent Source", Proc. SPIE 0976, Statistical Optics, (2 December 1988); doi: 10.1117/12.948536; https://doi.org/10.1117/12.948536