Talbot effect by a photorefractive volume phase grating

In our proposal a light intensity distribution generated by an incoherently illuminated planar amplitude grating is projected into a photorefractive crystal. This 3D distribution is mapped as an index refractive perturbation via the photorefractive effect thereby generating a volume phase grating. The self-imaging phenomenon in the Fresnel field of this volume phase grating coherently illuminated is theoretically and experimentally analyzed. A model to simulate this volume grating that considers the 3D light intensity distribution formed in the crystal combined with the photorefractive grating formation theory is proposed. A path-integral approach to calculate the self-image patterns which account for the inhomogeneous propagation through the photorefractive grating is employed. The experimental and theoretical results show that the self-images location coincides with that of the self-images generated by planar phase grating of the same period. Moreover, the self-images visibility depends on three parameters: the exit pupil diameter of the incoherent recording optical system, the external electric field applied on the crystal, and the crystal thickness. To study the visibility behavior, a phase parameter which includes the three mentioned parameters is proposed. The self-images visibility shows the typical sinusoidal dependence found in planar phase grating. A good agreement between theoretical and experimental results is observed.     

Wavefront sensor based on the Talbot effect with the precorrected holographic grating

A holographic wavefront sensor based on the Talbot effect is proposed. Optical wavefronts are measured by sampling the light amplitude distribution with a two-dimensional (2D) precorrected holographic grating. The factors that allow changing an angular measurement range and a spatial resolution of the sensor are discussed. A comparative analysis with the Shack-Hartmann sensor is illustrated with some experimental results.     

Compact sensor for measuring two-dimensional tilt using a two-dimensional transmission grating and the Talbot effect

This paper proposes a tilt sensor that measures the small two-dimensional tilt of a plane reflective object using the Talbot effect. It is an extension of a previously proposed one-dimensional tilt sensor. The light beam reflected from the object impinges on a hexagonal grating, and the intensity of the diffracted wave is detected on an image sensor located at a Talbot distance from the grating. The diffraction intensity displaces due to the tilt of the object. The displacement is calculated by the Fourier transform method to obtain the two-dimensional tilt. This sensor is very simple and compact. The principle of the sensor is explained for a grating with a general pattern. An experiment using a hexagonal grating shows its validity. Discussions are given for making it more practical.     

Effects of unparallel grating planes in Talbot interferometry

The properties of moiré fringes in Talbot interferometry are analyzed when the angle between the two grating planes is small. The results indicate that the tilt angle of the moiré fringes, observed just behind the test grating, is sensitive to the small angle. Based on this sensitivity, several features of parallelism of the two grating planes are presented, and the influence of the small angle when checking the beam collimation of a lens is also discussed. The validity of the theoretical analysis is illustrated by experiment.     

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.     

Polarization-dependent Talbot effect

The term "polarization-dependent Talbot effect" means that the Talbot self-imaging intensity of a high-density grating is different for TE and TM polarization modes. Numerical simulations with the finite-difference time-domain method show that the polarization dependence of the Talbot images is obvious for gratings with period d between 2 lambda and 3 lambda. Such a polarization-dependent difference for TE and TM polarization of a high-density grating of 630 lines/mm (corresponding to d/lambda=2.5) is verified through experiments with the scanning near-field optical microscopy technique, in which a He-Ne laser is used as its polarization is changed from the TE mode to the TM mode. The polarization-dependent Talbot effect should help us to understand more clearly the diffraction behavior of a high-density grating in nano-optics and contribute to wide application of the Talbot effect.     

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.     

Talbot effect and Cornu's spiral

Cornu's spiral is used in the testing and extension of a recent explanation of the Talbot effect, which occurs in the Fresnel domain. The results confirm all parts tested. They also indicate that each band of a Talbot plane is controlled primarily by light from only a few slits of the grating, contrary to earlier assumptions. Increases in slit width are found to limit the number of Talbot planes that can be observed.     

Talbot effect of selective reflection from a homogeneous atomic vapour

In the present work, the Talbot effect of selective reflection (SR) modified by the coupling fields is examined. It is shown that SR Talbot (SRT) patterns can be dramatically modified by the detuning, the strength and the incident angles of the coupling fields. SRT patterns at the integer and the half integer planes are similar to conventional Talbot images. However, the manifest change in fractional SRT patterns can be observed at several planes, e.g. at the quarter and the three quarters planes, the spatial frequency of those patterns is doubled comparing to that of the original output plane, and the carpets become blurring with an increasing asymmetry as the coupling fields are detuned away from the resonant transition of atoms, or as its strength increases. These peculiar Talbot patterns are mainly from a combined contribution of real and imaginary parts of source SR field modified by the coupling light. The SRT images may have potential applications in the detection of atom–surface interactionsand the processing of optical information.     

Adaptive photodetector for assisted Talbot effect

We use an adaptive photodetector for measuring the visibility of the Fresnel diffraction patterns generated by a grating. Visibility is measured in real time, with high spatial resolution, and without any signal processing. This method is well suited for analyzing the Talbot effect and its many applications.     

Uniform theory of the Talbot effect with partially coherent light illumination

A uniform formulation for the self-imaging of gratings with any kind of partially coherent illumination is developed in terms of the cross mutual spectral density of the partial coherence theory. The formulation includes the time diffractive intensity distribution and the averaged diffractive intensity distribution at self-imaging distances and can be applied to both continuous and temporal illuminations with any kind of spectra. It is found that the averaged intensity distribution is related only to the intensity spectrum of illumination. The continuous polychromatic illumination and the ultrashort laser pulses with or without frequency chirp are then studied by a numerical stimulation. It is shown that the ultrashort laser pulse and the continuous polychromatic illuminations have similar averaged self-image distributions. Thus the Talbot effect may help in the study of the temporal and spectral characteristics of ultrashort laser pulses. An experiment with an LED is given, as well.     

Lifetime-predictions of a glass-ceramic with machined flaws

A dynamic fatigue study was performed on a Li₂O-Al₂O₃-SiO₂ glass ceramic to assess its susceptibility to delayed failure and to compare the results with those from a previous study. Fracture mechanics techniques were used to analyse the results for the purpose of making lifetime predictions. The material strength and lifetime was seen to increase due to the removal of residual stress through grinding and polishing. Influence on time-to-failure is addressed for the case with and without residual stress present.     

Talbot effect interpreted by number theory.

An interpretation of the Talbot effect in a tapered gradient-index medium by number theory as the output/input relationship between the integer and the noninteger difference of position and the slope of rays is presented. Unit cell and transverse magnification for Talbot images are evaluated, and two criteria for angular magnification are defined. The study is particularized to a finite set of diffracted rays.     

Fractional Talbot effect in a tapered gradient-index medium: unit cell

A generalization of the fractional Talbot effect to the case of a tapered gradient-index medium for uniform illumination is considered. A unit cell of the fractional Talbot image contains the superposition of unit cell images of the periodic object.     

Theory of image formation using the Talbot effect

The information inside each subcell of a two-dimensional periodic object is replicated throughout all the subcells of the unit cell at certain planes. An explicit expression describing the relative phase relationship among the replicated information is derived. From this expression, the wave amplitude at all the subcells caused by the interaction among the information coming from different subcells in the original object is obtained. A computer simulation of gray-level image synthesis using binary substructures and image differentiation is also given.     

Analysis of wavefront propagation using the Talbot effect

Talbot imaging is a well-known effect that causes sinusoidal patterns to be reimaged by diffraction with characteristic period that varies inversely with both wavelength and the square of the spatial frequency. This effect is treated using the Fresnel diffraction integral for fields with sinusoidal ripples in amplitude or phase. The periodic nature is demonstrated and explained, and a sinusoidal approximation is made for the case where the phase or amplitude ripples are small, which allows direct determination of the field for arbitrary propagation distance. Coupled with a straightforward method for calculating the effect in a diverging or converging beam, the Talbot method provides a useful approximation for a class of diffraction problems.     

Temporal Talbot effect in fiber gratings and its applications

We show that a temporal effect equivalent to the spatial Talbot effect (self-imaging) applies to the reflection of periodic pulse trains from linearly chirped fiber gratings (LCFG's). For specific input repetition periods the reflected signal is an exact replica of the input signal. Input repetition period values that give rise to this effect depend on the dispersion coefficient of the grating. We propose to use this effect as an alternative for dispersion measurement in LCFG's. Furthermore, by using the properties of the temporal Talbot effect, we can design linear passive devices (LCFG's) for use as frequency multipliers, able to multiply the repetition rate of a given pulse train.