Hybrid single shot algorithm for accurate phase demodulation of complex fringe patterns is proposed. It employs empirical mode decomposition based adaptive fringe pattern enhancement (i.e., denoising, background removal and amplitude normalization) and subsequent boosted phase demodulation using 2D Hilbert spiral transform aided by the Principal Component Analysis method for novel, correct and accurate local fringe direction map calculation. Robustness to fringe pattern significant noise, uneven background and amplitude modulation as well as local fringe period and shape variations is corroborated by numerical simulations and experiments. Proposed automatic, adaptive, fast and comprehensive fringe analysis solution compares favorably with other previously reported techniques.

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Crossed grating 3×3 beam lateral shear interferometry for extended range wave front sensing is presented. A Fresnel diffraction pattern of two multiplicatively superimposed linear diffraction gratings each generating three diffraction orders is recorded. A simple solution employs a common crossed binary amplitude Ronchi grating with spatial filtering. Digital processing of a single-shot pattern includes separating multidirectional pairs of orthogonal lateral shear interferograms, retrieving second harmonics of their intensity distribution, and calculating shearing phases. Single-frame automatic fringe pattern processing based on the Hilbert-Huang transform is used for this purpose. Using second harmonics extends the aberration measurement range since they encode self-imaging free two-beam interferograms without contrast modulations. Experimental works corroborate the principle and capabilities of the proposed approach.

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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.