Statistical properties of scattering fields and intensity fluctuation correlation function from rarefied randomly distributed particles

Discrete particles randomly distributed in the ground-space link significantly impact laser signal transmission. Studying their scattering fields is crucial for laser speckle imaging and weak signal detection. This paper uses Mie theory to derive the statistical characteristics of scattering fields from laser-particle interactions, providing expressions for second and fourth-order statistical properties and the intensity fluctuation correlation function. Numerical calculations were performed on the mean function, correlation function, and intensity fluctuation cross-correlation function for a Gaussian-distributed rarefied particle group, considering particle radius changes. Results show that particle scattering fields have inherent correlation, which increases with particle size and shows periodicity. This correlation is largely independent of the particle's distance from the observation point, while particles at different locations exhibit high correlation for larger sizes. When the particle radius is near 0.2 mm, the speckle intensity cross-correlation function approaches 1. This research enhances our understanding of laser speckle imaging and weak laser scattering signals, aiding the development of more efficient optical communication systems and laying a foundation for future studies on laser speckle characteristics.