Modification of the Modified Born Series for strongly-scattering regime

Published online: 22 September 2025

Abstract

For the purpose of Automatic Differentiation 3D imaging, a method which is simultaneously reliable and computationally performant is highly desired. Most methods to solve Maxwell’s equations are either poorly performant, or numerically unstable. One method which has broken this dichotomy is the modified Born series (MBS) by Vellekoop et al.. This method formulates a simple iteration which stably converges without sacrificing per-iteration performance. However, in the case of highly-scattering materials, the iteration must be altered to ensure convergence, generally degrading the convergence rate. After studying the modified Born series, we derived a new variant iteration, making use of a Cayley transform to guarantee stability regardless of scattering strength. Beside this improved stability being desireable in and of itself, this property can be leveraged to potentially outperform the modified Born series, in cases of scattering from strongly-scattering media.