Subsampled digital holographic image reconstruction by a compressive sensing approach.

We show an in-line digital holographic image reconstruction from subsampled holograms with resolution improvement and lensless magnification with high noise immunity by a compressive sensing approach. Our method treats the sensed field as subsampled, low-pass filtered and projected on a Fresnel-Bluestein base in an inverse problem approach to image reconstruction with controlled lensless magnification. So, we have demonstrated by simulation and experimental results that the approach can reconstruct images with quality even when used in holograms obtained from unusual subsampling schemes.

Estimation of statistical properties of rough surface profiles from the Hurst exponent of speckle patterns.

We applied the Hurst exponent technique to an experimental study of rough metallic surface profiles and the speckle patterns generated by them. Characterization of important statistical properties of the surface profile and speckle patterns were performed. We observed a clear correlation between the Hurst exponent of a surface profile and the one calculated from the associated speckle patterns. Therefore, in principle, information of the Hurst exponent of the profile can be obtained from the Hurst exponent of speckle patterns. Range and sampling analyses were performed in the Hurst exponent calculations showing the robustness of the method. As an additional application, we performed a basic simulation to show that the Hurst exponent is sensitive to surface waviness.

Photorefractive moiré-like patterns for the multifringe projection method in Fourier transform profilometry.

In the present paper, the method of simultaneous moiré-like fringe pattern projection for Fourier transform profilometry is described. The photorefractive holographic interferometric process produces controlled moiré-like patterns with two or more different variation directions. Each low spatial frequency fringe pattern is experimentally obtained as a result of the superposition of two high spatial frequency sinusoidal gratings, with slightly different pitches, for each fringe variation direction. These dynamic moiré-like patterns are induced due to an optical holographic beating of the sinusoidal induced gratings in the volume of the photorefractive Bi12TiO20 (BTO) crystal sample used as dynamic holographic medium. Two or more moiré-like fringe patterns, with at least two different variation directions, simultaneously (or not), are projected onto the object surface. Thus, this is the 2D fringe projection stage of our proposed Fourier transform procedure to determine the profile of a simple object.

Branch-cut algorithm for optical phase unwrapping.

In this Letter, a proposal addressing the problem of two-dimensional phase unwrapping based on the theory of residues is presented. Here, wrapped phase maps with shifted phase jumps are used to balance residue charges. With this approach, we seek to minimize processing time and residue connection, which is essential in the development of branch-cut algorithms. Finally, a phase-unwrapping algorithm is applied to these wrapped maps, generated by Fourier transform profilometry to obtain three-dimensional profiles of objects illuminated by photorefractive moiré-like patterns generated in an experiment of real-time dynamic holography, and by fringe patterns generated with a Michelson interferometer.

Photorefractive holographic moiré-like patterns for secure numerical code generation.

In this Letter, low-frequency photorefractive holographic moiré fringe patterns are proposed as secure numerical code generators that could be useful for storage or data transmission. These dynamic moiré patterns are holographically obtained by the superposition of two or more sinusoidal gratings with slightly different pitches. The Bi(12)TiO(20) photorefractive crystal sample is used as holographic medium. An optical numerical base was defined with patterns representing the 0, 1 and -1 digits as bits. Then, the complete set of these optical bits is combined to form bytes, where a numerical sequence is represented. The results show that the proposed numerical code is simple, robust and extremely secure, then could be used efficiently as standard numerical identification in robotic vision or eventually in storage or transmission of secure numerical data.

Topological defects in moiré fringes with spiral zone plates.

We present a study of spatial structures created by superposition of spiral zone plates used for generating optical beams with phase singularities. Moiré fringes are observed that show topological defects similar to those appearing in interference patterns of optical vortices. A brief theoretical discussion is included that supports the similarities between the two phenomena. Our results may lead to interesting applications to digital information processing by optical means.