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.

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.

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.

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.

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.