Reciprocal relations for light from Young’s pinholes scattering upon a quasi-homogeneous medium

Abstract

Within the validity of the first-order Born approximation, a group of reciprocal relations are derived for light from Young’s pinholes scattering upon a spatially quasi-homogeneous (QH) medium. It is shown that the spectral degree of coherence (SDOC) of the scattered field is proportional to the Fourier transform of the strength of the scattering potential, and the spectral density of the scattered field is proportional to the Fourier transform of the normalized correlation coefficient of the scattering potential. By considering a particular case where the correlation function of the QH medium obeys the Gaussian distribution, we obtain the far-zone spectral density and SDOC of the scattered field which satisfy the derived reciprocal relations. Compared with previous reciprocal relations for scattering, our relations additionally introduce Young’s pinhole parameter that characterizes the geometry of Young’s pinholes.