Physics-based inversion of digital in-line holograms for accurate refractive-index and size measurements of drops and bubbles

The near-periodic structures of highly symmetric, non-absorbing particle holograms significantly limit the robustness and efficiency of conventional inverse methods. A physically grounded iterative inverse approach is introduced to address the abundance of secondary minima of cost functions and the resulting parameter dependencies. Accelerated scattering computations based on hybrid and asymptotic models are used rather than the full Lorenz–Mie theory. Particular emphasis is placed on determining the refractive index (linked to the particle composition), a parameter often neglected despite its central importance. The ranges of particle–photosensor distances, particle diameters, and refractive indices over which reliable parameter recovery can be achieved are delineated. Finally, a numerical analysis of synthetic holograms is used to quantify the expected root-mean-square error (RMSE) on the retrieved parameters, revealing a marked increase in precision with both decreasing photosensor–particle distance and particle-to-medium refractive index contrast.