Incident power-dependent spectral density analysis for multi-Gaussian Schell-model beams scattered by particle collections

Light scattering, a fundamental phenomenon in optical physics, underpins critical applications ranging from biomedical imaging to atmospheric studies. Despite advancements in potential scattering theory, a significant limitation persists: current analyses of scattered field spectral densities rely on normalized quantities, ignoring the input power of the incident field. This limitation hinders the ability to effectively resolve inverse scattering problems. In this study, by introducing the incident light wave input power, we investigate the spectral density variations for multi-Gaussian Schell-model beams scattered by two distinct types of particle collections: one consists of deterministic particles with random density distributions, and the other consists of random particles with deterministic density distributions. Through comparative analysis, we identify how both source parameters and scatterer structural parameters govern spectral density magnitude and profile. Key findings show that, under the influence of the structural parameters of both the source and scatterer, the spectral density profile and central point spectral density magnitude exhibit distinct parameter-dependent variations and various linear relationships, respectively. Crucially, the spectral density profile parameter-dependent variations and the central point spectral density magnitude linear relationships provide two degrees of freedom for distinguishing and identifying structures of distinct scatterers (or light sources). Our work establishes a novel framework for quantitative scattering analysis by incorporating incident power considerations, advancing potential applications in solving the inverse scattering problem.