Co-design of an in-line holographic microscope with enhanced axial resolution: selective filtering digital holography.

Common-path digital in-line holography is considered as a valuable 3D diagnostic technique for a wide range of applications. This configuration is cost effective and relatively immune to variation in the experimental environment. Nevertheless, due to its common-path geometry, the signal-to-noise ratio of the acquired hologram is weak as most of the detector (i.e., CCD/CMOS sensor) dynamics are occupied by the reference field signal, whose energy is orders of magnitude higher than the field scattered by the imaged object. As it is intrinsically impossible to modify the ratio of energy of reference to the object field, we propose a co-design approach (optics/data processing) to tackle this issue. The reference to the object field ratio is adjusted by adding a 4-f device to a conventional in-line holographic setup, making it possible to reduce the weight of the reference field while keeping the object field almost constant. Theoretical analysis of the Crámer-Rao lower bounds of the corresponding imaging model illustrates the advantages of this approach. These lower bounds can be asymptotically reached using a parametric inverse problem reconstruction. This implementation results in a 60% gain in axial localization accuracy (for 100 μm diameter spherical objects) compared to a classical in-line holography setup.