Optimization methods for in-line holography

TL;DR

This paper introduces an advanced reconstruction method for in-line holography that combines topological derivatives, parameter optimization, and electric field approximation to achieve high-resolution imaging of objects.

Contribution

It develops a novel iterative framework integrating topological and parameter optimization techniques for improved hologram-based object reconstruction.

Findings

Achieves nanometer resolution in object prediction.

Effectively estimates object shape, size, and permittivity.

Provides a method to approximate the full electric field from holograms.

Abstract

We present a procedure to reconstruct objects from holograms recorded in in-line holography settings. Working with one beam of polarized light, the topological derivatives and energies of functionals quantifying hologram deviations yield predictions of the number, location, shape and size of objects with nanometer resolution. When the permittivity of the objects is unknown, we approximate it by parameter optimization techniques. Iterative procedures combining topological field based geometry corrections and parameter optimization sharpen the initial predictions. Additionally, we devise a strategy which exploits the measured holograms to produce numerical approximations of the full electric field (amplitude and phase) at the screen where the hologram is recorded. Shape and parameter optimization of functionals employing such approximations of the electric field also yield images of the holographied objects.