Uniform theory of the Talbot effect with partially coherent light illumination

Effect of nonuniform pit structure on self-imaging of periodical gratings

Self-imaging possibilities for periodical gratings that have nonuniform pit structure are theoretically investigated. The diffraction of periodic arrays in the deep Fresnel region is analyzed according to the scalar diffraction theory. The expressions of the diffraction intensities of three different gratings that have binary square, binary circle, and Gaussian pit structure are considered. Talbot images of gratings with nonuniform pit structure are predicted to appear at multiple certain distances. The present paper shows that even a structure in short-range disorder may take on the self-imaging effect in a Fresnel field.

Propagation of optical coherence lattices in the turbulent atmosphere

We explore the propagation of recently introduced optical coherence lattices (OCLs) in the turbulent atmosphere. We show that the lattice intensity profile and the spatial degree of coherence will display periodicity reciprocity over long propagation distances even though the lattices are affected by the turbulence. The lattice periodicity reciprocity has been previously conjectured to be advantageous for free-space information transfer and optical communications. We then show how one can increase the distance over which the lattice periodicity reciprocity is preserved in the turbulent atmosphere by engineering input lattice beam parameters. We also show that the OCLs have scintillation indices lower than those of Gaussian beams.

Self-imaging of partially coherent light in graded-index media

We demonstrate that partially coherent light beams of arbitrary intensity and spectral degree of coherence profiles can self-image in linear graded-index media. The results can be applicable to imaging with noisy spatial or temporal light sources.

Free-space propagation of optical coherence lattices and periodicity reciprocity

We examine paraxial propagation of recently introduced optical coherence lattices in free space and demonstrate a novel phenomenon of periodicity reciprocity between their intensity and coherence properties. The periodicity reciprocity arises because an aperiodic source intensity profile of an optical coherence lattice evolves into a lattice-like far-field profile, while the periodic spectral degree of coherence at the source becomes aperiodic on free-space propagation. We discuss how the discovered periodicity reciprocity can make optical coherence lattices attractive for robust free-space optical communications.

Diffraction by metallic planar gratings

In this work, a kind of grating that, to our knowledge, has not yet been analyzed for diffractive purposes is proposed. The mentioned grating consists of metallic intercalated slits of two different metals on a glass substrate. The main characteristic and peculiarity of the proposed grating is that it is totally planar, without any slopes or grooves. We analyze the intensity distribution at the near- and far-field produced by the grating. The method used is rigorous-coupled wave analysis. We show how the metallic layer thickness is a crucial parameter to achieve the highest efficiency of the diffraction orders and, therefore, the highest contrast of the diffracted fringes. To conclude, we investigate how parameters such as the period, duty cycle, wavelength, or the used metals affect the diffracted field. Some nonexpected behaviors have been found. As we demonstrate by comparing with other kinds of gratings, the proposed grating would be useful in applications in which fringes are needed in both the front and back sides of the grating.

Talbot effect of quasi-periodic grating

Theoretic and experimental studies of the Talbot effect of quasi-periodic gratings are performed in this paper. The diffractions of periodic and quasi-periodic square aperture arrays in Fresnel fields are analyzed according to the scalar diffraction theory. The expressions of the diffraction intensities of two types of quasi-periodic gratings are deduced. Talbot images of the quasi-periodic gratings are predicted to appear at multiple certain distances. The quasi-periodic square aperture arrays are produced with the aid of a liquid crystal light modulator, and the self-images of the quasi-periodic gratings are measured successfully in the experiment. This study indicates that even a structure in short-range disorder may take on the self-imaging effect in a Fresnel field.

Relaxation of the Talbot condition in generalized grating imaging

We can form a grating image with two gratings having different pitches with an extended light source. It is called generalized grating imaging or the Talbot-Lau effect. When we want to obtain high contrast image with pure absorption gratings or pure phase gratings, the separation between the two gratings is restricted. This corresponds to the Talbot condition. In this paper, we propose to use a combination of absorption grating and phase grating to relax the separation restriction. The theory of generalized grating imaging is applied to the system with this kind of grating. Simulations are performed for calculating contrast variation and show that the proposed system practically relaxes the Talbot condition. An experiment verifies the result of the simulation.

Light field image sensors based on the Talbot effect

We present a pixel-scale sensor that uses the Talbot effect to detect the local intensity and incident angle of light. The sensor comprises two local diffraction gratings stacked above a photodiode. When illuminated by a plane wave, the upper grating generates a self-image at the half Talbot depth. The second grating, placed at this depth, blocks or passes light depending upon incident angle. Several such structures, tuned to different incident angles, are sufficient to extract local incident angle and intensity. Furthermore, arrays of such structures are sufficient to localize light sources in three dimensions without any additional optics.

Fringe projection with a sinusoidal phase grating

Phase-shifting profilometry requires projection of sinusoidal fringes on a 3D object. We analyze the visibility and frequency content of fringes created by a sinusoidal phase grating at coherent illumination. We derive an expression for the intensity of fringes in the Fresnel zone and measure their visibility and frequency content for a grating that has been interferometrically recorded on a holographic plate. Both evaluation of the systematic errors due to the presence of higher harmonics by simulation of a profilometric measurement and measurement of 3D coordinates of test objects confirm the good performance of the sinusoidal phase grating as a projective element. In addition, we prove theoretically that in comparison with a sinusoidal amplitude grating this grating produces better quality of fringes in the near-infrared region. Sinusoidal phase gratings are fabricated easily, and their implementation in fringe projection profilometry facilitates construction of portable, small size, and low-cost devices.

Invariant grating pseudoimaging using polychromatic light and a finite extension source

The Talbot effect is a well studied phenomenon by which grating pseudoimages appear at certain periodic distances when monochromatic light is used. Recently, numerical simulations have shown a new phenomenon; when a polychromatic light beam is used in a double grating system, the intensity of the pseudoimages presents a transverse-profile that remains unaffected over a wide range of propagation distances. This effect can be used to increase the tolerances of gratings based optical devices, such as displacement measurement systems, interferometers, and spectrometers. The pseudoimages formation with a polychromatic and finite extension light source is analytically and experimentally demonstrated. Relatively simple analytical expressions for the intensity and the contrast allow us to predict when pseudoimages present a constant contrast and when they disappear. Furthermore, we experimentally obtain the pseudoimages using the proposed configuration, corroborating the theoretical predictions.

Comparison of simulated quenching algorithms for design of diffractive optical elements

We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity.

Talbot effect with rough reflection gratings

The Talbot effect is analyzed when steel tape gratings are used. These gratings are made on a steel substrate, and, because of the manufacture process, both levels of the grating are rough with different roughness parameters. A theoretical analysis based on Fresnel regime, which considers the statistical properties of roughness, is developed. Analytical formulas that show a decreasing exponential dependence on the intensity in terms of the distance between the grating and the observation plane are obtained, and an experimental verification is also performed.

Quasi-Talbot effect of a grating in the deep Fresnel diffraction region

Based on the theory of scalar diffraction, the diffraction of gratings in the deep Fresnel diffraction region is developed, and the general formula of the diffraction intensity of the one-dimensional grating is presented by using the Hankel function. Through numerical calculations, some interesting diffraction phenomena are found. In the deep Fresnel diffraction region, the dominant effects, with increasing propagation distance from the grating, are, in order, the geometrical effect, the quasi-geometrical effect, and the interference and diffraction effects. Furthermore, the diffraction intensities vary periodically in the diffraction effect region with increasing propagation distance. Quasi-Talbot imaging of the grating exists in the interference and diffraction regions, and the intensity distributions most similar to the structure of the grating are not at the exact Talbot distances. These phenomena in the deep Fresnel diffraction region are distinct from those in the Fresnel diffraction region. The formation origin of quasi-Talbot imaging of the grating is also discussed, and the numerical calculations powerfully verify the theoretical results.