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A new approach is developed within the first-order Born approximation tolight scattering from a collection of particles with $\mathcal{L}$ types. Two$\mathcal{L}\times\mathcal{L}$ matrices called pair-potential matrix (PPM) andpair-structure matrix (PSM) are introduced to jointly formulate the coherenceproperties of the scattered field. We derive a closed-form relation thatassociates the cross-spectral density function of the scattered field with thePPM and the PSM, showing that the the cross-spectral density function equalsthe trace of the product of the PSM and the transpose of the PPM. Based onthis, the spectral degree of coherence (SDOC) of the scattered field is furtheranalysed. We show that for a special case where the spatial distributions ofscattering potentials of different types of particles are similar and the sameis true of their density distributions, the PPM and the PSM will reduce to twonew matrices whose elements separately quantify degree of angular correlationof the scattering potentials of particles and their density distributions, andthe number of species of particles in this special case as a scaled factorensures the normalization of the SDOC. Two special hybrid particulate systemsas examples are given to illustrate the importance of our new approach.

Scattering of light waves from a collection with particles of $\mathcal{L}$ types