Multi-Layer Born multiple-scattering model for intensity-based 3D phase microscopy

We propose an accurate and computationally efficient 3D scattering model, Multi-Layer Born (MLB), and use it to recover 3D refractive index (RI) of thick biological samples. For inverse problems recovering the complex-field of thick samples, weak scattering models (e.g. first Born) may fail or underestimate the RI, especially with large index contrast. Multi-Slice (MS) beam propagation methods model multiple scattering between slices of the sample to provide more realistic reconstructions; however, MS does not optimally accommodate for highly oblique scattering. Furthermore, MS does not model backward scattering. Our proposed MLB model uses a first Born model for each slice, accurately capturing the oblique scattering effects and estimating the backward scattering process. This leads to more accurate RI reconstructions from oblique illumination measurements, which are necessary for high-resolution phase tomography. Importantly, MLB retains a reasonable computation time that is critical for practical imaging applications with iterative inverse algorithms.