Can different media generate scattered field with identical spectral coherence?

The possibility for different media to generate scattered field with identical spectral coherence is discussed. It is shown that two random media, with different characters of correlation function, may generate scattered field with identical spectral coherence property. An example of light waves on scattering from Gaussian-Schell model media is discussed, and a condition for identical spectral coherence of the far-zone scattered field is obtained.