Displacement measurement using the Talbot effect with a Ronchi grating

Retrieving the Talbot length of arbitrary 2D gratings

The Talbot effect has been revived in many fields of modern optics. As a key number of self-imaging, the fundamental Talbot length plays a crucial role in many applications. However, the inspection of the Talbot carpet for determining the Talbot length is applicable only if the 2D field distribution behind the grating is represented by a 1D cross section. In this Letter, we show an effective way to overcome this limitation to explore the self-imaging of gratings with complex 2D periodicities. For that purpose, the near-field diffraction is analyzed using the Pearson correlation coefficient of the intensity distribution in Fourier space. We report results on linear, ring, and spiral gratings.

Distance and depth modulation of Talbot imaging via specified design of the grating structure

For positioning Talbot encoder and Talbot lithography, etc., properties manipulation of Talbot imaging is highly expected. In this work, an investigation on the distance and depth modulation of Talbot imaging, which employs a specially designed grating structure, is presented. Compared with the current grating structure, the proposed grating structure is characterized by having the phase layers with uneven thicknesses. Such a specific structural design can cause the offset of Talbot image from its nominal position, which in turn generates the spatial distance modulation of self-imaging and imaging depth expansion. Theoretical analysis is performed to explain its operating principle, and simulations and experiments are carried out to demonstrate its effectiveness.

Life cycle analysis of electrically actuated SMA spring using Talbot interferometry

Electrically actuated shape memory alloys (SMAs) find widespread applications in engineering and science. Such materials are known to retain/remember their state. In the stressed/deformed state, when activated by the application of a suitable excitation mechanism, such as the use of heat or potential, they return to their original unstressed state. To test their reliability, it is a standard procedure to undertake a life cycle analysis. In this paper, the life cycle analysis of a SMA spring using the Talbot interferometric technique is reported. The life cycle of the SMA spring is analyzed in terms of the displacement drift, which sets in because of the functional fatigue generated due to its repeated use. Collimated light from a He-Ne laser transmitted through a beam splitter is converged through a focusing lens onto a plane mirror attached to the spring. Backreflected light from the mirror is incident on a set of two Ronchi gratings separated by the Talbot distance, forming a moiré pattern. The resulting interferograms are analyzed using a fringe rotation mechanism. The angle of orientation is a function of displacement drift. There is deterioration in the SMA property because of repeated cycles, and the spring loses its ability to return to its original unstretched position. The values of the displacement drift generated after 1, 1000, 2000, 3000, 4000, and 5000 such cycles as measured using a Talbot interferometer are 0, 0.875, 1.275, 1.459, 1.720, and 1.859 mm, respectively. It is observed that the SMA effect deteriorates as the number of stretching/contraction cycles increases. The uncertainty analysis is also reported. The expanded uncertainty was determined to be 201.61 μm.

Grating- and checkerboard-based zone plates as an optical array generator with a favorable beam shape

The combination of a grating as a periodic object and a Fresnel zone plate with a quasi-periodic structure leads us to propose some novel array generator elements. It is shown that diffraction performance of the proposed element depends on the grating structure, so that the diffraction performance may efficiently be increased if the grating is replaced with a checkerboard structure. Depending on the kind of zone plate, we have demonstrated that the corresponding array generator is also created. For instance, a focused array of vortices is generated when the zone plate is replaced with a spiral zone plate. We have also clarified that the method allows us to generalize it to the other class of the zone plate-based elements, e.g., a cross zone plate. Namely, when the cross zone plate is used instead of the Fresnel zone plate, a spot array generator is again created whose diffractive performance is improved by modifying its phase structure. Also, it is clearly shown that the focusing feature of the element depends on the grating period. Finally, there is a good agreement between the simulation results and the corresponding experimental works.

Diffraction by gratings with random fill factor

In this work, we analyze the diffraction produced by Ronchi gratings where the fill factor is not constant, but presents random fluctuations around its nominal value. This effect can be produced while developing the grating with etchers since the process can be slightly unpredictable. We obtain the theoretical formalism to describe the intensity produced by the grating at near and far field, showing that smoothing of the self-images is produced at the near field and, consequently, cancellation of higher diffraction orders is obtained at the far field. In addition, different nominal fill factors produce different diffraction behaviors in terms of the randomness. We corroborate the analytical formalism using a direct integration method based on the Rayleigh-Sommerfeld formula and conclude that the numerical results are in high agreement with the theoretical predictions.

Diffraction by random Ronchi gratings

In this work, we obtain analytical expressions for the near-and far-field diffraction of random Ronchi diffraction gratings where the slits of the grating are randomly displaced around their periodical positions. We theoretically show that the effect of randomness in the position of the slits of the grating produces a decrease of the contrast and even disappearance of the self-images for high randomness level at the near field. On the other hand, it cancels high-order harmonics in far field, resulting in only a few central diffraction orders. Numerical simulations by means of the Rayleigh-Sommerfeld diffraction formula are performed in order to corroborate the analytical results. These results are of interest for industrial and technological applications where manufacture errors need to be considered.

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.

Talbot effect in weakly coupled monolayer graphene sheet arrays

We theoretically investigate the plasmonic Talbot effect in monolayer graphene sheet arrays (MGSAs) when surface plasmon polaritons (SPPs) between graphene experience weak coupling. The Talbot effect occurs only when the incident field has a pattern with a few selected periods. The Talbot distance is found to decrease exponentially with the decreasing period of the MGSA and can be as small as 1/20 of the incident wavelength. In addition, the Talbot distance can be further reduced by increasing the chemical potential of graphene or operating at longer wavelengths.

Electro-optical processor for measuring displacement employing the Talbot and the nonsteady-state photo-electromotive force effects

We present a device for measuring displacement based on the Talbot and the nonsteady photo-electromotive force effects. The proposed device does not require any numerical signal processing since its output signal is, in appropriate regions, linearly related to the measured displacement. The proposed system requires an illuminating field with a sinusoidal amplitude distribution and low fringe visibility. The dynamic range can be adjusted according to the illuminating field spatial period or wavelength. Displacements with an estimated resolution better than 10 μm in a dynamic range of 1.5 mm were detected using a sinusoidal amplitude grating with a period d=100 μm.

Phase anomalies in Talbot light carpets of self-images

An interesting feature of light fields is a phase anomaly, which occurs on the optical axis when light is converging as in a focal spot. Since in Talbot images the light is periodically confined in both transverse and axial directions, it remains an open question whether at all and to which extent the phase in the Talbot images sustains an analogous phase anomaly. Here, we investigate experimentally and theoretically the anomalous phase behavior of Talbot images that emerge from a 1D amplitude grating with a period only slightly larger than the illumination wavelength. Talbot light carpets are observed close to the grating. We concisely show that the phase in each of the Talbot images possesses an anomalous axial shift. We show that this phase shift is analogous to a Gouy phase of a converging wave and occurs due to the periodic light confinement caused by the interference of various diffraction orders. Longitudinal-differential interferometry is used to directly demonstrate the axial phase shifts by comparing Talbot images phase maps to a plane wave. Supporting simulations based on rigorous diffraction theory are used to explore the effect numerically. Numerical and experimental results are in excellent agreement. We discover that the phase anomaly, i.e., the difference of the phase of the field behind the grating to the phase of a referential plane wave, is an increasing function with respect to the propagation distance. We also observe within one Talbot length an irregular wavefront spacing that causes a deviation from the linear slope of the phase anomaly. We complement our work by providing an analytical model that explains these features of the axial phase shift.

Axial resonance of periodic patterns by using a Fresnel biprism

This paper proposes a method for the generation of high-contrast localized sinusoidal fringes with spatially noncoherent illumination and relatively high light throughput. The method, somehow similar to the classical Lau effect, is based on the use of a Fresnel biprism. It has some advantages over previous methods for the noncoherent production of interference fringes. One is the flexibility of the method, which allows the control of the fringe period by means of a simple axial shift of the biprism. Second is the rapid axial fall-off in visibility around the high-contrast fringe planes. And third is the possibility of creating fringes with increasing or with constant period as the light beam propagates. Experimental verifications of the theoretical statements are also provided.

Talbot images of wavelength-scale amplitude gratings

By means of experiment and simulation, we achieve unprecedented insights into the formation of Talbot images to be observed in transmission for light diffracted at wavelength-scale amplitude gratings. Emphasis is put on disclosing the impact and the interplay of various diffraction orders to the formation of Talbot images. They can be manipulated by selective filtering in the Fourier plane. Experiments are performed with a high-resolution interference microscope that measures the amplitude and phase of fields in real-space. Simulations have been performed using rigorous diffraction theory. Specific phase features, such as singularities found in the Talbot images, are discussed. This detailed analysis helps to understand the response of fine gratings. It provides moreover new insights into the fundamental properties of gratings that often find use in applications such as, e.g., lithography, sensing, and imaging.

Realization of optical carpets in the Talbot and Talbot-Lau configurations

Talbot and Talbot-Lau effects are frequently used in lensless imaging applications with light, ultrasound, x-rays, atoms and molecules--generally in situations where refractive optical elements are non-existent or not suitable. We here show an experimental visualization of the intriguing wave patterns that are associated with near-field interferometry behind a single periodic diffraction grating under plane wave illumination and which are often referred to as Talbot carpets or quantum carpets. We also show the patterns behind two separated diffraction gratings under nearly-monochromatic but spatially incoherent illumination that illustrate the nature of Talbot-Lau carpets.

Continuous self-imaging regime with a double-grating mask

We analyze the Talbot effect produced by a mask composed of two diffraction gratings. Combinations with phase and amplitude gratings have been studied in the near-field regime. For a two-phase-gratings configuration, the Talbot effect is canceled, even when using monochromatic light; that is, the intensity distribution is nearly independent of the distance from the mask to the observation plane. Therefore, the mechanical tolerances of devices that use the Talbot effect may be improved. In addition, the spatial frequency of the fringes is quadrupled, which improves the accuracy of devices that employ this mask. An experimental verification for the best case two phase gratings, has also been performed, validating the theoretical results.

High resolution Talbot self-imaging applied to structural characterization of self-assembled monolayers of microspheres

We report the observation of the Talbot self-imaging effect in high resolution digital in-line holographic microscopy (DIHM) and its application to structural characterization of periodic samples. Holograms of self-assembled monolayers of micron-sized polystyrene spheres are reconstructed at different image planes. The point-source method of DIHM and the consequent high lateral resolution allows the true image (object) plane to be identified. The Talbot effect is then exploited to improve the evaluation of the pitch of the assembly and to examine defects in its periodicity.

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.

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.

Two-wavelength Talbot effect and its application for three-dimensional step-height measurement

The phenomenon of Talbot self-image shift by changing the wavelength of the illuminating light is described and demonstrated experimentally. A periodic grating is illuminated by light with wavelengths lambda1 and lambda2 generated by two lasers, and the Talbot self-images are recorded along the longitudinal direction at individual wavelengths. The Talbot self-image shift due to the change in the wavelength of light is implemented for the measurement of the three-dimensional step height of a large discontinuous object without any phase ambiguity problem. Fourier-transform fringe analysis was used to determine the maximum contrast of the high-visibility bands for the measurement of the step height of the object. The main advantages of the proposed system are nonmechanical scanning, high stability because of its common path geometry, compactness, and a wide range of measurement as compared to interferometric three- dimensional profilers.