Optimization methods for in-line holography

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.