Explore the vast range of titles available.

We present approximate analytical solutions, based on anomalous diffraction theory and the modified Rayleigh‐Debye approach for the backscattering/extinction coefficients and apply them to the elastic lidar equation. Figure shows a log polar plot of the angular dependence of the Mie scattering intensityfor a large particle size parameter, which resembles a flatfish facing the backscattering direction and provides a lidar signal.

Quasi-continuous metasurfaces are widely used in various optical systems and their subwavelength structures invalidate traditional design methods based on scalar diffraction theory. Here, a novel vector iterative Fourier transform algorithm (IFTA) is proposed to realize the fast design of quasi-continuous metasurface beam splitters with subwavelength structures. Compared with traditional optimization algorithms that either require extensive numerical simulations or lack accuracy, this method has the advantages of accuracy and low computational cost. As proof-of-concept demonstrations, several beam splitters with custom-tailored diffraction patterns and a 7 × 7 beam splitter are numerically demonstrated, among which the maximal diffraction angle reaches 70° and the best uniformity error reaches 0.0195, showing good consistency with the target energy distribution and these results suggest that the proposed vector IFTA may find wide applications in three-dimensional imaging, lidar techniques, machine vision, and so forth.

A novel anti-cat-eye effect imaging technique based on wavefront coding is proposed as a solution to the problem of previous anti-cat-eye effect imaging techniques where imaging quality was sacrificed to reduce the retroreflection from the photoelectric imaging equipment. With the application of the Fresnel–Kirchhoff diffraction theory, and the definition of generalized pupil function combining both phase modulation and defocus factors, the cat-eye echo formation of the wavefront coded imaging system is theoretically modeled. Based on the physical model, the diffracted spot profile distribution and the light intensity distribution on the observation plane are further simulated with the changes in the defocus parameter and the phase modulation coefficient. A verification test on the cat-eye laser echo power of the wavefront coded imaging system and that of the conventional imaging system at a 20 m distance are conducted, respectively. Simulations and experiment results show that compared with conventional imaging systems, the wavefront coding imaging system can reduce the retroreflection echo by two orders of magnitude while maintaining better imaging quality through defocusing.

Phase contrast is widely used in all fields for visualization of the internal structure of objects using X-ray radiation. The paper proposes a new approach to modeling a phase-contrast X-ray image by the method of free propagation using the Fresnel-Kirchhoff diffraction theory. A simple calculation model was developed, which makes it possible to determine the value of the change in the intensity of X-rays on three-dimensional models of objects of arbitrary shape with macroscopic dimensions. It also allows you to establish the conditions for observing a contrast image with known characteristics of the detector system and the intensity of the radiation source. The possibility of obtaining clear images of objects with small decrements of refraction of matter, determining their geometric dimensions and thickness was shown. A method of calculating the optical properties of metal alloys in the X-ray range has been developed. The approaches presented in the paper can be useful to developers of compact devices for detecting structural inhomogeneities inside the studied objects by a non-destructive method.

We consider topological dynamical systems over Z and, more generally, locally compact, σ -compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of diffraction theory to associate an autocorrelation and a diffraction measure to any L2 -function over such a dynamical system. This diffraction measure is shown to be the spectral measure of the function. If the group has a countable basis of the topology one can also exhibit the underlying autocorrelation by sampling along the orbits. Building on these considerations we then show how the spectral theory of dynamical systems can be reformulated via diffraction theory of function dynamical systems. In particular, we show that the diffraction measures of suitable factors provide a complete spectral invariant.

Complex numbers are basic. An inconsistency would question Wigner’s unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff’s scalar diffraction theory. In the paper, an inconsistency in the real phase angle of a complex number is presented. When this inconsistency is introduced in Kirchoff’s theory, we can study its influence on the experimental success of this theory. There are no a priori reasons to include or exclude real phase angles. Referring to Wigner’s idea of the role of mathematics in empirical science, an experiment can provide more insight. In the experiment, a weak intensity, small wavelength source can be employed. When the contradictory phase angle is excluded, a nonzero diffraction amplitude appears physically possible. If it is included, this amplitude vanishes.

Based on the vector diffraction theory, two kinds of ultra-long transversally polarized optical chains are obtained by tight focusing double-ring azimuthally polarized Laguerre-Gaussian beams with multi-zone fan-shaped filter in a single lens system. One kind of optical chain is consisted by interconnected optical black spots arrays, and we call it as dark optical chain. In the dark optical chain, the axial length extends to 28λ when lateral full-width is 1.8λ at half-maximum, and the volume of black spots is about 3.45λ 3 . The other is consisted by isolated bright spots arrays, and we call it as bright optical chain. In the bright optical chain, the axial length extends to 32λ when lateral full-width is 0.478λ at half-maximum, and the volume of bright spots is about 1.18λ 3 . In addition, the flexible inter-conversion can be realized between the two kinds of optical chains by changing truncation parameters of incident beams. And the length of optical chains can be further extended by increasing the number of fans in multi-zone fan-shaped filter.

The location of the beam focus when monochromatic X‐ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It has little utility for diffraction in Laue geometry. The focusing effect in the Laue symmetrical case is discussed using concepts of dynamical theory and an extension of the lens equation is proposed. The existence of polychromatic focusing is considered and the feasibility of matching the polychromatic and monochromatic focal positions is discussed. A crystal lens equation is deduced to address the location of the focus when monochromatic X‐ray radiation encounters a bent crystal. It is extended using dynamical theory of diffraction for Laue symmetrical diffraction. Combination of polychromatic and monochromatic focusing is also discussed.

The work relates to the study of the internal multi-layered structure of optically inhomogeneous objects by the X-ray phase contrast imaging method, which is an urgent issue of modern science, technology, nuclear physics and medicine. X-ray phase-contrast imaging makes it possible to examine weakly absorbing objects, reduce the radiation dose and increase the spatial resolution. Computer modeling of X-ray diffraction within the Fresnel-Kirchhoff scalar diffraction theory was used as the research method. An algorithm was developed for creating a model of a multilayer object with different values of the refraction decrement, which allows to specify the shape, size, number and thickness of layers, and the refractive index of each layer of the object. X-ray phase-contrast image was obtained for a multilayer object with a proportional decrease in the refraction decrement from the center to the edges by the free propagation approach. A comparative analysis was carried out with an X-ray image of a homogeneous object of the same size and shape. It is shown that the modeling result contains quantitative information about the internal structure of the object and its multi-layered nature.

This article introduces a uniform theory of diffraction–physical optics (UTD–PO) formulation for analyzing radiowave multiple diffraction emanating from trees and buildings in green urban areas, considering illumination from a low transmitter and assuming spherical-wave incidence. Based on Babinet’s principle, this solution models buildings as rectangular sections and accounts for the influence of tree crowns (assuming these rise above the average rooftop height) by incorporating appropriate attenuation factors/phasors into the diffraction phenomena of buildings. The validation of the formulation is achieved through measurements made at the 39 GHz 6G mmWave frequency on a scale model of a green urban environment comprising bonsai trees and bricks. The main advantage of the proposed solution is that the calculations only include single diffractions due to recursion, circumventing the need to use higher-order diffraction terms in the diffraction coefficients, thus reducing the computation time and power. Our results may be beneficial for the design of mobile communication systems, including 6G networks, situated in green urban areas and with transmission source positioned lower than the surrounding infrastructure.