Nail Sabitov

Information extraction from digital holograms for particle flow analysis

The goal of our project is to observe the distribution of steady and moving colloidal polystyrene particles within a micro-optofluidic canal system. To this end, we apply a classical in-line holographic setup with a magnifying telescope and a digital camera sensor. The capabilities of numerical hologram reconstruction and the subsequent image processing offer new possibilities concerning the digital hologram analysis. We demonstrate new concepts for a four-dimensional particle flow observation using a captured holographic video as well as the potentials for information extraction.

Two-step phase-shift interferometry with known but arbitrary reference waves: a graphical interpretation

There are many applications in biology and metrology where it is important to be able to measure both the amplitude and phase of an optical wave field. There are several different techniques for making this type of measurement, including digital holography and phase retrieval methods. In this paper we propose an analytical generalization of this two-step phase-shifting algorithm. We investigate how to reconstruct the object signal if both reference waves are different in phase and amplitude. The resulting equations produce two different solutions and hence an ambiguity remains as to the correct solution. Because of the complexity of the generalized analytical expressions we propose a graphical-vectorial method for solution of this ambiguity problem. Combining our graphical method with a constraint on the amplitude of the object field we can unambiguously determine the correct result. The results of the simulation are presented and discussed.

Digital holography and phase retrieval: a theoretical investigation.

Iterative Phase Retrieval (PR) techniques represent an alternative means to Digital Holography (DH) for estimating the complex amplitude of an optical wavefront. To achieve a high-resolution reconstruction from a digital hologram, one must use Phase-Shifting Interferometric (PSI) techniques to remove the DC and twin image terms that are a feature of holographic recordings. Unfortunately this approach is not suitable for imaging dynamic events, since a minimum of 3 sequential captures, are typically required and the scene cannot change during this recording process. PR algorithms may provide a solution to this dynamic imaging problem, however these algorithms provide solutions that are not unique and hence cannot ensure an accurate solution to the problem.

Wavefront sensing by numerical evaluation of diffracted wavefields

A novel wavefront sensor principle based on diffraction theory and Fourier analysis with a modified angular spectrum propagator has been developed. We observe the propagation of a wavefront behind a two-dimensional cross grating and derive a universal method to extract the phase gradient directly from a captured intensity image. To this end the intensity distribution is analyzed in the spectral domain, and the processing is simplified by an appropriate decomposition of the propagator kernel. This method works for arbitrary distances behind the grating. Our new formulation is verified through simulations. The wavefront generated by a freeform surface is measured by the new method and compared with measurements from a commercial Shack–Hartmann wavefront sensor.