Inverse problem approach for the reconstruction of lateral shearing digital holograms

Unstained biological samples (e.g. cells or bacteria) are mostly transparent objects, optically described by their optical thickness and refractive index changes. The knowledge of this information could help to better identify or at least classify cells according to their types or state. Holographic microscopy techniques are effective methods to obtain quantitative phase profiles of biological samples. These techniques, however, may require high temporal stability to measure cell thickness fluctuations. A simple and low-cost way to ensure temporal stability consists in using a “common path” configuration. In this configuration the reference and signal beams follow the same optical path, leading to high temporal stability. The beam paths are split by a glass plate whose thickness introduces a lateral shift between the beams, reflected by the front and back surfaces. This configuration is an off-axis holographic microscopy setup since the glass plate introduces an angle between the two reflected spherical wavefronts. The inverse problem approach proposes to reconstruct the objects directly from the holograms without any filtering of the signal and with prior information on the objects. In this framework, a good knowledge of the image formation model is important. We propose a reconstruction algorithm based on a parametric inverse problem approach to reconstruct phase objects holograms acquired by the lateral shearing digital holographic system. Assuming the noise in the data to be white and Gaussian, it mainly consists in fitting a model to the data. The algorithm is applied to silica micro-beads on out-of-focus off-axis holograms recorded with the lateral shearing configuration.