Digital Hologram Processing in On-Axis Holography

In the context of fast and 3D quantitative microscopy, on-axis digital holography has a significant potential. This chapter focuses on the numerical reconstruction of digital holograms. After a presentation of classical back-propagation methods, we introduce the general framework of inverse problems that includes recent compressive sensing methods. Inverse problems approaches solve two essential issues in digital holography: the improvement of reconstruction accuracy and the extension of the studied field beyond the physical limit of the sensor size. In addition, the achievable resolution can be derived from the hologram formation model using Cramer-Rao lower bounds. As a drawback of reconstruction methods based on inverse problems is their computational complexity, we suggest two ways to significantly reduce the processing time of holograms.