Reciprocity relations for light wave scattered by a particulate collection

Two Fourier relations of light waves scattered by a random-distributed particulate medium have been investigated. We find that the scattered field and the particulate collection satisfy two Fourier relations, i.e. the spectral density is directly proportional to a Fourier transform of a convolution of correlation coefficient of each particle and correlation coefficient of distribution function of the whole collection, and the spectral degree of coherence is directly proportional to a Fourier transform of a convolution of strength of the scattering potential of each particle and strength of the distribution function of the whole collection. To illustrate these relations, behaviors of the far-field generated by Gaussian-correlated particles with Gaussian-correlated distributions have been discussed.