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. They can be generated, for example, by three-slit interference or self-imaging in the Fresnel diffraction field of a sinusoidal grating. We derive a general condition for the ratio of amplitudes of interfering beams resulting in phase edge dislocations, lateral separation of dislocations depends on this ratio as well. Analytically derived properties are corroborated by numerical and experimental studies. We develop a simple, robust, common path optical self-imaging configuration aided by a coherent tilted reference wave and spatial filtering. Finally, we propose an automatic fringe pattern analysis technique for detecting phase edge dislocations, based on the continuous wavelet transform. Presented studies open new possibilities for developing grating based sensing techniques for precision metrology of very small phase differences.

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. Calculating the sum of two patterns results in a two-beam interferogram free of inherent light propagation direction and observation plane contrast modulations imposed by the self-imaging phenomenon (Talbot effect). Single-frame automatic fringe pattern processing provides the interferogram phase distribution. The technique enables continuous shear variations suitable for dynamic range sensing. Experimental works corroborate enhanced capabilities of the proposed approach.

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. Conducting moirégram imaging in the Fresnel field of a double-diffraction system is brought up to avoid using distortion-free objectives and simplify the experimental setup. Simulation and experimental results document the method properties and provide beautiful exemplification of the double-grating Fresnel diffraction theory developed earlier.

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. Then, two dimensional continuous wavelet transform with enhanced ridge extraction algorithm is applied to extract the fringe phase map. Proposed approach allows to dispose of phase jumps along the contrast reversal bands. The method requires only one image and has no special demands concerning the fringe pattern design. Method validity and robustness is confirmed using experimentally acquired time-averaged interferograms of vibrating silicon micromembranes.

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. It can be successfully applied to multiplicative and additive type crossed patterns with sinusoidal and binary orthogonal component structures. Efficient adaptive filtering enables successful fast processing and analysis of complex and defected patterns.

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. A robust ridge extraction algorithm for a single fringe set extraction is presented. The method is fully automatic and requires no user interference. Spectral separation of fringe families is not required. Simulations are presented to verify performance and advantage of the proposed method over the Fourier transform based technique. Method validity has been confirmed using experimental images.

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. The issue of vortex detection resolution versus carrier fringe frequency and orientation is discussed. Corroboration of simulation and experimental studies of integer and noninteger singular light beams as well as speckle fields reported in the literature and analyzed using different approaches is presented.

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. In the case of the product type superimposition generating both real and pseudo moiré, our interpretation utilizes the Fourier domain information only. The moiré pattern characteristics such as an effective carrier, modulation and bias intensity distributions can be readily predicted. We corroborate them using two-dimensional continuous wavelet transform and fast adaptive bidimensional empirical mode decomposition methods as complementary image processing tools.

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. Experimental studies of vibration mode patterns by time-average interferometry provide excellent verification of numerical findings. They compare very well with the results of our previous investigations using the temporal phase-shifting method widely considered as the most accurate one. No need of performing phase shifting represents significant simplification of the experimental procedure.