Three-level transmittance 2D grating with reduced spectrum and its self-imaging.

A simple method for generating 2D binary amplitude structure with additive superimposition of mutually orthogonal 1D amplitude gratings is proposed. Its implementation requires software generated three binary amplitude gratings, i.e., the crossed Ronchi, checker board and 1D Ronchi gratings with aspect ratio equal to 0.5. Their computer processing involves only two steps. First the checker grating is multiplied by a high frequency 1D grating. Next the product is added to the crossed grating. In result 3-level transmittance (0, 0.5, 1) hybrid diffraction structure is obtained. The intermediate level results from the use of a dense 1D grating. The zero diffraction order, well separated from the rest of the spectrum, consists of crossed spectra of additively superimposed 1D Ronchi gratings. Detailed heuristic explanation of the process aided by spectrum domain analyses is presented. Additionally, simulations and experiments conducted in the Fresnel diffraction field exemplify the invented structure properties in comparison with the multiplicative superimposition crossed Ronchi grating. Up to authors' best knowledge the Fresnel field (self-imaging phenomenon or Talbot effect) properties of 2D periodic structure with additive superimposition of component 1D gratings have not been published in the literature.

5-beam grating interferometry for extended phase gradient sensing.

A novel, single-shot, low-cost, multidirectional lateral shear interferometer for extended range wave front phase gradient sensing has been developed. It exploits the Fresnel diffraction field, which is formed by the five lowest diffraction orders of a simple binary amplitude checker grating. The Fresnel intensity pattern encodes information on four directional partial derivatives of the wave front under test. It has been theoretically, numerically, and experimentally shown that for larger gradient phase objects or shear amounts only the diagonal derivative information is easily accessible. The horizontal and vertical direction gradient maps are strongly amplitude modulated. Therefore, their demodulation becomes a challenging task. The same feature has been found in widely used quadriwave interferometer, which was developed at ONERA, France. The results of analytical and numerical studies and experimental works, including fringe pattern processing and phase demodulation, are presented.

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.

Single-shot 3 × 3 beam grating interferometry for self-imaging free extended range wave front sensing.

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.

Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis.

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.