Scattering of light waves from a collection of particles of L types

A new, to the best of our knowledge, pathway is paved within the first-order Born approximation to access light scattering from a collection of particles of L types. Two L×L matrices called a pair-potential matrix (PPM) and a pair-structure matrix (PSM) are introduced to jointly characterize the scattered field. We show that the cross-spectral density function of the scattered field equals the trace of the product of the PSM and the transpose of the PPM, and thus these two matrices allow us to determine all the second-order statistical properties of the scattered field. Based on this, the spectral degree of coherence (SDOC) of the scattered field is further analyzed. In a special case where the spatial distributions of the scattering potentials of particles of different types are similar and the same is true of their density distributions, it is found that the PPM and the PSM will reduce to two new matrices whose elements separately quantify the degree of angular correlation of the scattering potentials of particles and their density distributions, and the number of species of particles in this special case will appear as a scaled factor to ensure the normalization of the SDOC. The importance of our new approach is illustrated by an example.