Extracting particle size distribution from laser speckle with a physics-enhanced autocorrelation-based estimator (PEACE)

Extracting quantitative information about highly scattering surfaces from an imaging system is challenging because the phase of the scattered light undergoes multiple folds upon propagation, resulting in complex speckle patterns. One specific application is the drying of wet powders in the pharmaceutical industry, where quantifying the particle size distribution (PSD) is of particular interest. A non-invasive and real-time monitoring probe in the drying process is required, but there is no suitable candidate for this purpose. In this report, we develop a theoretical relationship from the PSD to the speckle image and describe a physics-enhanced autocorrelation-based estimator (PEACE) machine learning algorithm for speckle analysis to measure the PSD of a powder surface. This method solves both the forward and inverse problems together and enjoys increased interpretability, since the machine learning approximator is regularized by the physical law. The authors demonstrate a real-time, non-invasive, far-field optical probe to monitor particle size distribution in pharmaceutical manufacturing. It characterizes the speckle scattered from the surface using machine learning weaved into optical physics.