Quantitative Decomposition of Speckle Decorrelation for Inverse Problems in Complex Wave Scattering

Abstract

Optical scattering remains one of the richest phenomena to study in classical optics. Wavefronts that are severely distorted due to scattering still carry significant information about the optical path upstream. Decoding typically starts with the autocorrelation function; yet the precise relationship between it and scatterer statistics still remains unexplored, hindering the model-based method for inverse problems. Here, we reveal that decorrelation due to backward scattering may be quantified as two distinct terms: the first expresses scattering from the surface, whereas the second is due to the volume beneath. The two terms encode higher-order statistics of their respective regimes within the specimen; Experimental studies on representative custom-made scatterers match theoretical predictions with an overall L1-error of less than 0.2%, providing an advanced forward model for various model-based inverse approaches. As a proof-of-concept, we present two examples, scatterer particle size estimation and reconstruction of the incident beam profile, to validate this improvement.