Generation of phase edge singularities by coplanar three-beam interference and their detection.

In recent years singular optics has gained considerable attention in science and technology. Up to now optical vortices (phase point dislocations) have been of main interest. This paper presents the first general analysis of formation of phase edge singularities by coplanar three-beam interference.

Diffraction grating three-beam interferometry without self-imaging regime contrast modulations.

Achromatic grating shearing interferometry method for wave front sensing is developed. Two Fresnel diffraction patterns formed by grating three lowest diffraction orders are recorded. The beam-splitter grating is displaced laterally by half its period between exposures.

Circular-linear grating Talbot interferometry with moiré Fresnel imaging for beam collimation.

The Talbot interferometer using different self-imaging structures is studied and applied for laser beam collimation. A circular-linear grating pair enables visual dynamic detection and computer moirégram analysis. Automatic single-frame processing is performed using a 2D continuous wavelet transform.

Hilbert-Huang processing for single-exposure two-dimensional grating interferometry.

Single-shot crossed-type fringe pattern processing and analysis method called Hilbert-Huang grating interferometry (HHGI) is proposed. It consist of three main procedures: (1) crossed pattern is resolved into two fringe families using novel orthogonal empirical mode decomposition approach, (2) separated fringe sets are filtered using modified automatic selective reconstruction aided by enhanced fast empirical mode decomposition and mutual information detrending, and (3) Hilbert spiral transform is employed for fringe phase demodulation. Numerical and experimental studies corroborate the validity, versatility and robustness of the proposed HHGI technique.

Processing and phase analysis of fringe patterns with contrast reversals.

A method for demodulating fringe patterns containing contrast reversals is proposed. It consists of two steps. First, the absolute value of the fringe intensity distribution with its background removed is calculated.

Separation of complex fringe patterns using two-dimensional continuous wavelet transform.

A method for processing fringe patterns containing additively superimposed multiple fringe sets is presented. It enables to analyze different fringe families present in a single image separately. The proposed method is based on a two-dimensional continuous wavelet transform.

Fourier domain interpretation of real and pseudo-moiré phenomena.

Unified interpretation for the real and pseudo moiré phenomena using the concept of biased and unbiased frequency pairs in the Fourier spectrum is given. Intensity modulations are responsible for pseudo moiré appearance in the image plane rather than average intensity variations dominating real moiré. Detection of pseudo moiré necessitates resolving superimposed structures in the image plane.

Examination of singular scalar light fields using wavelet processing of fork fringes.

A single frame fork fringe pattern automatic processing method for detecting optical vortices in coherent light fields using two-dimensional continuous wavelet transformation is proposed. When a vortex sign is of no importance, it is sufficient to calculate the fork interferogram modulation distribution and its normalized gradient map to establish vortex locations without resorting to complicated phase calculations. Normalization of modulation gradient maps enables unambiguous vortex discrimination from local modulation minima without phase singularity.

Visualization of additive-type moiré and time-average fringe patterns using the continuous wavelet transform.

An application of the continuous wavelet transform to modulation extraction of additive moiré fringes and time-average patterns is proposed. We present numerical studies of the influence of various parameters of the wavelet transformation itself and a fringe pattern under study on the demodulation results. To facilitate the task of demodulating a signal with zero crossing values, a two-frame approach for wavelet ridge extraction is proposed.