Quasi-periodic Gratings Research Articles

Spatial frequency shift super-resolution imaging based on quasiperiodic grating and deep learning.

In this study, we propose a pioneering spatially frequency-shifted super-resolution microscopy technique that utilizes the synergy of quasiperiodic gratings and deep learning. First, a quasiperiodic grating capable of converting evanescent waves into propagating waves is designed. The grating is positioned between the object under investigation and the objective lens, and the high-frequency information carried by the evanescent waves in the near-field region of the object is shifted into the detection window and becomes accessible in the far field for imaging. Subsequently, we provide two deep learning models for image and video reconstructions to achieve the reconstruction of static and dynamic samples respectively. Simulation results demonstrate the high feasibility of the proposed method, and both static and dynamic objects with sub-wavelength features can be resolved. The developed method paves the way to the realization of super-resolution imaging by using a traditional bright-field microscope without the need for an extensive optical system design.

Controlling multiple diffraction with quasiperiodic gratings

Complex diffraction patterns are formed by sophisticated diffraction gratings. However, the methods of synthesizing of such gratings are complicated and resource intensive. We propose a simple analytical approach to forming one- and two-dimensional quasiperiodic gratings supporting multiple diffraction consisting of a set of diffraction maxima with the specified spatial frequency of certain diffraction order. The structure of a quasiperiodic grating is a superposition of harmonic functions, which provide a discrete spatial spectrum. The number of diffraction maxima, their angular positions, and intensity distribution between them can be controlled by choosing appropriate reciprocal lattice vectors and their amplitudes. This effect confirmed by the experiment opens new possibilities for light shaping, imaging, and radiation coupling.

Effects of structure parameters on high-order diffraction suppression of quasi-periodic gratings

We introduce the design and implementation of quasi-periodic gratings for high-order diffraction suppression. The effects of hole shape (circle, rectangle, diamond, and hexagon) and location distribution on the diffraction properties are investigated. We theoretically and experimentally demonstrate that the quasi-triangle array with hexagonal holes is highly advantageous for suppressing high-order diffractions. Additionally, the quasi-periodic location distribution also helps to suppress high-order diffraction. Remarkably, the analytical results show that the 1st, 2nd, 3rd, 4th, 5th, and 6th order diffractions can be completely suppressed for the special structure parameters of the quasi-periodic gratings, and the 7th order diffraction intensity is as low as 2.2×10−5 of the 1st order. The experimental results show there exist only 0th and ±1st order diffraction peaks along the ξ axis, which qualitatively agree with the theoretical and numerical predictions. Compared with the traditional 1∶1 grating, the quasi-triangle array with hexagonal holes can effectively suppress high-order diffractions. We except the quasi-periodic gratings may find significant applications in high-accuracy wide spectral measurement ranging from the far infrared to the x-ray regions.

Talbot interferometry with curved quasi-periodic gratings: towards large field of view X-ray phase-contrast imaging.

X-ray phase-contrast imaging based on grating interferometry has become a common method due to its superior contrast in biological soft tissue imaging. The high sensitivity relies on the high-aspect ratio structures of the planar gratings, which prohibit the large field of view applications with a diverging X-ray source. Curved gratings allow a high X-ray flux for a wider angular range, but the interference fringes are only visible within ~10° range due to the geometrical mismatch with the commonly used flat array detectors. In this paper, we propose a design using a curved quasi-periodic grating for large field of view imaging with a flat detector array. Our scheme is numerically verified in the X-ray regime and experimentally verified in the visible optical regime. The interference fringe pattern is observed over 25°, with less than 10% of decrease in visibility in our experiments.

Efecto Talbot Unidimensional y Bidimensional

En este trabajo se muestran los resultados de los experimentos realizados en el verano del 2014 en el IPICYT, para corroborar la existencia del efecto Talbot el cual consiste en la reaparición de una imagen nítida de un objeto periódico iluminado por una fuente de luz cada cierta distancia después del objeto. Esta distancia se le conoce como distancia de Talbot y da la escala espacial de este fenómeno. Se utilizaron rejillas unidimensionales periódicas, aperiódicas y bidimensionales con estructura hexagonal, todas fueron creadas previamente con el programa grafico Adobe Illustrator con las frecuencias espaciales que se calcularon que darían una distancia de Talbot que permite la observación del efecto en el laboratorio. Las rejillas se iluminaron con un láser de He-Ne de longitud de onda de 633 nm (rojo) y posteriormente se localizó a que distancia se volvía a formar la auto-imagen de la rejilla.

Quasi-periodic gratings: diffraction orders accelerate along curves

Light diffracting to different diffraction orders of a periodic grating generally propagates along a set of straight trajectories. Here we show that certain quasi-periodic gratings can produce curved diffraction orders. These curved lobes are created by the caustic interference of the originally straight diffraction orders and manifest themselves as accelerating beams. Both numerical simulations and experimental results demonstrate the validity of multiple accelerating beam generation with a single binary grating. Our work makes a quantitative link between the quasi-periodicity of a grating and the resulting caustic diffraction orders. Furthermore, the use of binary devices has important applications in acoustics, x-ray optics, and electron beam engineering and is also useful when high optical power is needed.

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.

Multiple coupling of surface plasmons in quasiperiodic gratings

Whereas periodic gratings enable us to couple light into a surface plasmon polariton only at a specific angle and wavelength, we show here that quasiperiodic gratings enable the coupling of light at multiple wavelengths and angles. The quasiperiodic grating can be designed in a systematic manner using the dual-grid method, thereby enabling us to control the coupling strength and grating dimensions. We verified the method experimentally by efficiently coupling light into a surface plasmon from several different illumination angles using a single quasiperiodic grating.

Near-threshold femtosecond laser fabrication of one-dimensional subwavelength nanogratings on a graphite surface

Superimposed one-dimensional quasiperiodic gratings with multiple periods \ensuremath{\Lambda} \ensuremath{\approx} 110--800 nm well below or comparable to the pump laser wavelength of 744 nm, and ridge orientations perpendicular to the linear polarization of infrared femtosecond laser pulses, were fabricated after multiple near-threshold laser shots on a planar surface of quasimonocrystalline graphite in ambient air. The broad range of the grating periods corresponds to the large number of spatial Fourier harmonics of the final nanorelief (up to $m=7$th order, ${\ensuremath{\Lambda}}_{m}\ensuremath{\approx}800$ nm/$m=110--800$ nm), qualitatively representing the nonsinusoidal profile of the laser-induced intermediate surface relief (the set of periodic, broadly spaced narrow nanotrenches), which provides the corresponding multiangle diffraction of the incident femtosecond laser pulses. Experimental measurements and modeling of the transient optical constants of the photoexcited graphite justify the excitation, at the first stage, of the first-order (${\ensuremath{\Lambda}}_{1}\ensuremath{\approx}800$ nm) surface plasmon-polaritonic (SPP) wave on the photo-excited initial planar graphite surface becoming metallic via photo-generation of dense electron hole plasma ($\ensuremath{\sim}{10}^{21}$ cm${}^{\ensuremath{-}3}$). Such an SPP wave provides intermediate nanorelief in the form of the nonsinusoidal surface grating via its interference with the incident laser wave, resulting under near-threshold laser irradiation conditions in the highly localized surface ablation of the material in the interference maxima. During the next stage, the multiperiod subwavelength nanogratings develop through the multiangle diffraction of the multiple incident laser pulses on the intermediate nonsinusoidal surface grating.

Characterization of Chromatic Banding Artifact for Secondary Colors in a Polychrome Electrophotographic Process

Several passive and active banding compensation strategies have been proposed in recent literatures for monochrome EP processes. In these studies, quasi-periodic contrast variations can be effectively reduced. For polychrome EP process, in which multiple color layers are superimposed on top of one another, Klassen and Goodman have shown the dependence of contrast sensitivity on variation in chromatic channels such as a* and b*. Chromatic bandings are quasi-periodic gratings with variation in chromatic channels. Chromatic banding may still be perceivable when the achromatic banding on individual color layers has been reduced to under the threshold. The perceptibility of chromatic banding is dependent on the primary colors of the platform. Before a softcopy psychophysics experiment was conducted, a set of tone curves and a model of the mixing of two primary colors, excluding the black, were constructed according to a 4-color EP printer. The psychophysics study confirmed that even if the sinusoidal gratings (in L*) on each individual primary color layer is under the human visual system (HVS) threshold, superimposing one on top of another can increase the perceptibility of the composite gratings. These results will be much valuable to ongoing efforts to reduce chromatic banding.

Spectrum of Light Reflection From a Quasiperiodic Structure of a Dielectric

In the present work, we show that for quasiperiodic gratings that are described by definite functions it is possible to substantially decrease the amplitude of side peaks in the spectral dependence of the reflection factor. The results of numerical integration of a system of differential equations that describe the propagation of waves in a quasiperiodic medium indicate that with an increase in the number of first derivatives of the functions that have zero values on the grating edges the attenuation of the side peaks increases. Analysis of the spectral dependence of the reflection factor for certain functions is carried out.

Diffraction of Light by Quasi-Periodic Gratings

Diffraction of light by quasi-periodic gratings constructed as Fibonacci series or three other similar series are reported. The observed diffraction patterns show rich structures which are self-similar, and the diffraction angles are related to irrational numbers.

Moiré: Formation and interpretation

The superposition of several periodic or quasiperiodic patterns produces moire effects. In particular, the combination of three grid structures adds great flexibility to the use of moire phenomena. Information about the fringe structure, given by vector addition in Fourier space, allows investigation of formations, interpretation, and expectation problems concerning moire-pattern parameters. Any frequency and orientation of the pattern is possible, using three-line gratings. On the other hand, three quasiperiodic gratings with variations of frequency and/or orientation result in a zone-plate shape of the moire pattern regardless of grating distortions. Both elliptical and hyperbolic zone plates occur. Several illustrations demonstrate these phenomena and indicate some potential applications.