Conditions for invariant spectrum of light generated by scattering of partially coherent wave from quasi-homogeneous medium

•The spectrum of light scattered from a QH medium is derived.•Young's pinholes are used to adjust the spectral profile of scattered waves.•A scaling law is obtained to ensure the invariance of the scattered spectrum.•The scaling law has constrains on dimensions of the scattering system.

Within the first-order Born approximation, the spectrum of light generated by the scattering of a partially coherent wave from a quasi-homogeneous (QH) medium is derived. In particular, the partially coherent incident wave is produced by Young's pinholes. It is shown that the spectrum of the scattered field is identical to the spectrum of incident plane waves if the Fourier transform of the normalized correlation coefficient (NCC) of the scattering potential satisfies a certain scaling law. The scaling law is valid when the medium size is sufficiently small compared with the space between Young׳ pinholes. Furthermore, comparisons are made between our conditions with the previous results.