Inverse-scattering of absorptive samples via beam propagation

Inverse-scattering methods enable label-free, quantitative visualization of a sample's three-dimensional (3D) refractive index (RI), providing intrinsic and volumetric morphological contrast without exogenous labels. This is achieved by developing computational frameworks that reconstruct the sample's 3D RI from a series of scattering measurements acquired under different data-capture conditions. Recent advances have demonstrated successful 3D RI reconstructions in multiple-scattering samples using angle-varying illuminations; however, these studies have primarily focused on non-absorptive samples. Here, we extend the multi-slice beam propagation (MSBP) inverse-scattering framework to reconstruct complex-valued RI, encompassing both the sample's conventional RI (real part) and absorptivity (imaginary part). We show that reconstructing complex-valued RI makes the inverse problem ill-posed under angle-varying illumination alone, and that incorporating measurement diversity from both angle-varying illumination and sample defocus is necessary to ensure stable and accurate convergence. Experimental demonstrations were conducted on 1) dyed microsphere samples to characterize accuracy of reconstructed RI and absorptivity; and 2) diverse absorptive scattering samples to demonstrate biological utility. These results represent an important step for label-free volumetric imaging in biological tissue, which typically exhibits both scattering and absorption.