Self-imaging of gratings with rough strips

We analyze the self-imaging process produced by a transmission grating whose strips present two different roughness levels. This kind of grating periodically modulates the transmitted light owing only to the different microtopographic properties of the strips. In spite of the fact that the grating is not purely periodic, it produces a kind of self-image at Talbot distances. These self-images gradually appear as light propagates, but they are not present just after the grating, as occurs in amplitude or phase gratings. There exists a distance from the grating, which depends on the stochastic properties of roughness, from which the contrast of the self-images becomes stable. Important cases are analyzed in detail, such as low- and high-roughness limits. We assume for the calculations that the grating can be used in a mobile system. Simulations using the Rayleigh-Sommerfeld regime have been performed, which confirm the validity of the theoretical approach proposed in this work.     

Gaussian-Schell-model beams propagating through rough gratings

In this work we analyze the near-field intensity distribution produced by a rough grating illuminated with a Gaussian-Schell-model beam. This kind of grating is formed by rough and smooth slits. Statistical techniques are used to describe the grating, and the Fresnel approach is used to perform the propagation of light. Two kinds of coherence affect the light propagation. One of them comes from the light beam, since it is not totally coherent. The other one comes from the rough topography of the grating surface. We have found that the Talbot effect is not present just after the grating, but it gradually increases. In addition, the contrast of the self-images decreases from a certain distance due to the coherence properties of the illumination beam. Then, the self-imaging process is only present between two specific distances from the grating. To corroborate the analytical results, we have performed numerical simulations for the mean intensity distribution based on the Sommerfeld-Rayleigh approach, showing their validity.     

SAW diffraction using the thin-element decomposition method

We adapt the angular spectrum of plane waves (ASPW) decomposition to numerical simulations of the diffraction of surface-acoustic waves (SAWs) on anisotropic model substrate, such as YZ lithium niobate. We utilize the thin-element decomposition (TED) method, appropriately modified for an anisotropic substrate; we also introduce a novel "average-wavenumber" variation of this scheme; these are numerically found to be mutually consistent. We apply the TED method to simulate wave propagation both in infinite periodic structures of metallized gratings and also in finite gratings. We demonstrate that the ASPW provides a convenient and numerically fast tool for precise diffraction calculations in practical SAW devices which also display structural variations in the lateral direction, perpendicular to the principal direction of wave propagation. Additionally, we compare the present TED method to waveguide theory in an analysis of the role of SAW reflections from the electrodes.     

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.     

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.     

Analytic phase-factor equations for Talbot array illuminations

Under specific circumstances the fractional Talbot effect can be described by simplified equations. We have obtained simplified analytic phase-factor equations to describe the relation between the pure-phase factors and their fractional Talbot distances behind a binary amplitude grating with an opening ratio of (1/M). We explain how these simple equations are obtained from the regularly rearranged neighboring phase differences. We point out that any intensity distribution with an irreducible opening ratio (M(N)/M) (M(N) < M, where M(N) and M are positive integers) generated by such an amplitude grating can be described by similar phase-factor equations. It is interesting to note that an amplitude grating with additional arbitrary phase modulation can also generate pure-phase distributions at the fractional Talbot distance. We have applied these analytic phase-factor equations to neighboring (0, pi) phase-modulated amplitude gratings and have analytically derived a new set of simple phase-factor equations for Talbot array illumination in this case. Experimental verification of our theoretical results is given.     

White-light-modified Talbot array illuminator with a variable density of light spots

A flexible array illuminator, comprising only two conventional optical elements, with a variable density of bright white-light spots is presented. The key to our method is to obtain with a single diffractive lens an achromatic version of different fractional Talbot images, produced by free-space propagation, of the amplitude distribution at the back focal plane of a periodic refractive microlens array under a broadband point-source illumination. Some experimental results of our optical procedure are also shown.     

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.     

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.     

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.     

Lau array illuminator

Spatial coherence can be created by appropriate spatial arrangements of incoherent point sources. Lau used a source of extended light and two amplitude gratings of identical periods, separated by the quarter Talbot distance, to provide coherent light. Because of the two successive amplitude gratings, most of the power is lost. By modifying the geometry of the second grating, I designed an array illuminator, providing several compression ratios and various topologies of the output plane, with significantly reduced losses. To further improve the power efficiency of the system, I used a longitudinal mirror system to collect the light rays that are lost in the initial Lau setup. Both one- and two-dimensional geometries are considered.     

Single-shot color digital holography based on the fractional Talbot effect

We present a method for recording on-axis color digital holograms in a single shot. Our system performs parallel phase-shifting interferometry by using the fractional Talbot effect for every chromatic channel simultaneously. A two-dimensional binary amplitude grating is used to generate Talbot periodic phase distributions in the reference beam. The interference patterns corresponding to the three chromatic channels are captured at once at different axial distances. In this scheme, one-shot recording and digital reconstruction allow for real-time measurement. Computer simulations and experimental results confirm the validity of our method.     

Reciprocal vector theory for diffractive self-imaging

A reciprocal vector theory for analysis of the Talbot effect of periodic objects is proposed. Using this method we deduce a general condition for determining the Talbot distance. Talbot distances of some typical arrays (a rectangular array, a centered-square array, and a hexagonal array) are derived from this condition. Further, the fractional Talbot effect of a one-dimensional grating, a square array, a centered-square array, and a hexagonal array is analyzed and some simple analytical expressions for calculation of the complex amplitude distribution at any fractional Talbot plane are deduced. Based on these formulas, we design some Talbot array illuminators with a high compression ratio. Finally, some computer-simulated results consistent with the theoretical analysis are given.     

Sharpness limitations in the projection of thin lines by use of the Talbot experiment

Studying the limitations of sharpness in self-images of the Talbot effect leads us to abandon the use of the paraxial assumption. In this respect, we will clarify the self-image concept and show experimentally and theoretically the influence of "nonparaxial effects" on the self-image. The boundary between paraxial and nonparaxial scalar theory is also clarified in this context. The Rayleigh criterion in aberration diffraction theory is adapted for explicit estimations of this boundary and the maximum sharpness of lines projected by use of the Talbot effect.     

Mirror-based double diffraction grating system for coherence generation: additional study of periodicity error

The Lau effect consists of generating spatial coherence by using an extended light source that illuminates a double diffraction grating system. The price of this coherence generation is a huge energy loss caused by the successive amplitude gratings, which are blocking elements. To significantly reduce the energy loss, our approach consists in using a longitudinal mirror system to collect the light rays initially blocked by the gratings of the Lau set-up. This technique offers high power efficiency and can be straightforwardly extended to provide Talbot array illuminators. The impact of periodicity error is studied and illustrations are given at the end.     

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.     

Dynamic Control of Light Direction Enabled by Stimuli‐Responsive Liquid Crystal Gratings

The ability to control light direction with tailored precision via facile means is long‐desired in science and industry. With the advances in optics, a periodic structure called diffraction grating gains prominence and renders a more flexible control over light propagation when compared to prisms. Today, diffraction gratings are common components in wavelength division multiplexing devices, monochromators, lasers, spectrometers, media storage, beam steering, and many other applications. Next‐generation optical devices, however, demand nonmechanical, full and remote control, besides generating higher than 1D diffraction patterns with as few optical elements as possible. Liquid crystals (LCs) are great candidates for light control since they can form various patterns under different stimuli, including periodic structures capable of behaving as diffraction gratings. The characteristics of such gratings depend on several physical properties of the LCs such as film thickness, periodicity, and molecular orientation, all resulting from the internal constraints of the sample, and all of these are easily controllable. In this review, the authors summarize the research and development on stimuli‐controllable diffraction gratings and beam steering using LCs as the active optical materials. Dynamic gratings fabricated by applying external field forces or surface treatments and made of chiral and nonchiral LCs with and without polymer networks are described. LC gratings capable of switching under external stimuli such as light, electric and magnetic fields, heat, and chemical composition are discussed. The focus is on the materials, designs, applications, and future prospects of diffraction gratings using LC materials as active layers.     

Diffractive simultaneous bidirectional shearing interferometry using tailored spatially coherent light

Measurements of wavefront deformations can be carried out with the help of lateral shearing interferometers. Here the focus is on a setup providing two shears along orthogonal directions simultaneously to generate the data needed for a reconstruction. We describe a diffractive solution using Ronchi phase gratings with a suppressed zeroth order for both the doubling of the wavefront under test and the bidirectional shearing unit. A series arrangement of the gratings offers an on-axis geometry, which minimizes the systematic errors of the test. For illumination, an extended incoherent monochromatic light source is used. High-contrast fringes can be obtained by tailoring the degree of coherence via a periodic intensity distribution.     

Cross-type optical particle separation in a microchannel

A continuous, real-time optical particle separation, which was previously delineated theoretically, is successfully implemented experimentally for the first time. In this method, particles suspended in a flowing fluid are irradiated with a laser beam propagating in a direction perpendicular to direction of fluid flow. Upstream of the laser beam, the particles move parallel to the direction of fluid flow. When the particles pass through the laser beam, the scattering force pushes them in the direction of laser beam propagation, causing the particles to be displaced perpendicular to the fluid flow direction. This displacement, known as the retention distance, depends on the particle size and the laser beam parameters. Finally, the particles escape from the laser beam and maintain their retention distances as they move downstream. In the present work, the trajectories and retention distances of polystyrene latex microspheres with three distinct diameters were monitored and measured using cross-type optical particle separation. The measured retention distances for different-sized particles were in good agreement with theoretical predictions.     

近代天津地毯图案设计

目的研究天津近代地毯业成功的原因。方法分析天津近代地毯图案设计的类型、纹样、布局、颜色等要素,分析地毯图案的设计方法和制作特点。结果天津近代地毯图案设计是将"宫廷式地毯"商业化;将"美术式地毯"本土化;将伊斯法罕地毯纹样和喀山地毯纹样融合后创造出"津锦式地毯";借鉴天津小洋楼建筑装饰纹样创造出"建筑式地毯";在制作上体现了工匠精神,在质量上具有精品特征,在形象上塑造世界名牌。结论近代天津地毯业的成功,得益于京津地区和三北地区的共同合作;得益于中国与中亚各国的交流和海上贸易的发展,其成功经验必将对京津冀一体化战略的发展、对一带一路建设的不断完善起到有益的作用。