It is highly desirable to have a compact laser interferometer for detecting gravitational waves. Here, a small-sized tabletop laser interferometer with Fabry–Perot resonators consisting of two spatially distributed “mirrors” for detecting gravitational waves is proposed. It is shown that the spectral resolution of 10−23 cm−1 can be achieved at a distance between mirrors of only 1–3 m. The influence of light absorption in crystals on the limiting resolution of such resonators is also studied. A higher sensitivity of the interferometer to shorter-wave laser radiation is shown. A method for detecting gravitational waves is proposed based on the measurement of the correlation function of the radiation intensities of non-zero-order resonant modes from the two arms of the Mach–Zehnder interferometer.

Signal structures based on OFDM signals and error-correcting codes resistant to the influence of spectrum-concentrated noise are described. An algorithm for receiving such signal structures with the use of weight functions is presented. It is shown by theoretic analysis and simulations that the class of Kravchenko weight functions based on atomic functions represents nearly optimal windows in terms of the minimum error reception probability.

A new method is proposed to increase the spectral resolving power of collinear acousto-optical filters by using optical feedback when the light leaving the region of its interaction with a periodic structure formed in the crystal by an acoustic wave returns to the input of the crystal, in which the diffraction process repeats itself many times. The light beam returned to the interaction region changes the boundary conditions of the parametric diffraction problem, because of which the amplitudes of the diffracted and passed light beams turn out to be strongly dependent on the feedback properties (similar to the processes occurring in a Fabry – Perot optical resonator). It is shown that such a combined acousto-optical Fabry – Perot filter with feedback is able to electronically tune the optical transmission wavelength and simultaneously has a higher spectral resolution than a conventional acousto-optical filter without feedback. It is also shown that the multiple radiation diffraction due to the feedback increases the diffraction efficiency with a comparatively small spatial change in the refractive index of the medium. Explicit analytical expressions for the instrumental functions of a combined acousto-optical Fabry – Perot filter are found and their properties are analysed. It is noted that a change in the feedback by any mechanism, i.e., by changing the returned wave phase or amplitude, leads to modulation of the measured signal, which makes it possible to create more precise methods of spectral measurements.

The diffraction of a pulse in a resonator formed by two spatially distributed “mirrors” created by an acoustic wave is considered. A significant increase in the pulse delay in acousto-optic crystals near the Bragg resonance is shown.

The possibility of efficiently using metamaterials in acousto-optics has been demonstrated. Diffraction of light in heterogeneous medium with non-uniform spatial distribution of dielectric nanoparticles taking into account absorption of light is investigated. It is shown that by changing the concentration of dielectric nanoparticles in the medium, complete elimination of side oscillations and suppression of the "tails" of the diffraction reflection curve can be achieved. The possibility of controlling the hardware function of acousto-optic devices by changing the material, concentration, size, shape and spatial orientation of the inclusions, as well as the polarization of the incident radiation is shown. It is shown, that extremely large electric field enhancement can be observed in an anisotropic crystal in the presence of spatial apodization of the amplitude or abrupt change in the phase of acoustic wave.

A new biorthogonal system of wavelet bases has been constructed, which is oriented toward reconstructing the useful signal of a measuring system if the measurement process is represented as a convolution model. New biorthogonal wavelet bases are obtained by using a instrumental function to modify a Kravchenko orthogonal wavelet system with a finite spectrum. The properties of new biorthogonal frequency-modified wavelets are studied, and digital filters that realize fast computational algorithms are constructed. Schemes for multiresolution analysis are proposed, which, during discrete wavelet transform, immediately solve the problem of reconstructing the useful signal, as well as effective noise suppression, which can significantly speed up computations.

Theoretical analysis of light diffraction on a periodic structure by using exact analytical solutions of the equations and numerical computer calculations has been conducted. The influence of different apodization functions on diffraction curves of reflection and transmission is studied and their comparative analysis is performed. Complete elimination of oscillating sidelobes and a significant suppression of the "tails" of a diffraction reflection curve are achieved for the specific functions of spatial apodization. The maximum values of the reflectivity of the medium with periodic dielectric permittivity are determined. The effects of light absorption in the crystal and moving gratings on the spectral resolution are evaluated. The Fabry-Perot resonator formed by two spatially-distributed "mirrors" is also studied. A significant increase in spectral resolution of filter due to the spatial variation of the refractive index of the medium is shown. It is shown that the high purity crystals are needed to observe the considered effects. Current technologies allow to obtain the glasses with the absorption coefficient alpha=10 (7) cm(1), at which the spectral resolution Delta lambda approximate to 10(-2) pm could be reached. This is three orders of magnitude narrower than the resolution of existing acoustooptic AO filters with the same crystal thickness. The considered system (a Fabry-Perot spectral filter combining a Bragg grating mirrors with apodization) can significantly increase the resolution of optical diffraction filters. Complete elimination of sidelobes and a significant suppression of the "tails" of a diffraction reflection curve are demonstrated. These results open perspectives to significantly enhance the resolution of the spectrometers, improve the parameters of mobile devices and communication channels. The results are of practical interest and can be used in the development of new diffraction acousto-optic modulators, AO filters and spectrometers.

In this paper, we describe some algorithms for generating and receiving structures based on orthogonal frequency division multiplexing (OFDM) signals that are robust to spectrum-concentrated interference. The algorithm for receiving these signal structures in the presence of spectrum-concentrated interference is based on weight functions. We also present the results of investigating Kravchenko weight functions based on atomic functions to improve the noise tolerance of signal structures in the presence of spectrum-concentrated interference, as well as the results of simulating a developed reception algorithm.

Впервые предложен и обоснован подход, позволяющий восстанавливать глубинные карты по стереопарам цветных изображений при визуализации трёхмерных (3D) объектов. Он использует новый локальный дескриптор изображений, основанный на примитивах и отношениях между ними, характеризуя различия в цветах, положении плоскостей, дистанциях и углах между примитивами. Новый подход сравнивается с общеизвестными системами дескрипторов, в частности с DAISY и SID. Численные эксперименты, анализ и физическая интерпретация результатов в условиях реально существующих радиометрических различий в экспозиции или освещении стереопар изображений показали преимущество нового подхода перед известными.

An approach to depth map reconstruction from stereo pairs of color images in visualization of three-dimensional objects is proposed and substantiated for the first time. The approach makes use of a novel local image descriptor based on visual primitives and relations between them, namely, cocolority, coplanarity, distance, and angle. The new approach is compared with other well-known descriptors, such as DAISY and SID. Numerical experiments and an analysis and physical interpretation of their results obtained in the case of actual radiometric differences in the exposition or illumination of stereo image pairs have shown that the new approach is superior to other existing descriptors.

The possibility of efficiently using metamaterials in acousto-optics has been demonstrated. Diffraction reflection and transmission curves of metamedia with a nonuniform spatial distribution of nanoparticles have been studied taking into account absorption of light. The influence of size (geometric) effects of nanoparticles on diffraction reflection and transmission curves has been shown. In particular, it has been shown that the variation of the concentration of dielectric nanoparticles in a medium allows completely removing extraneous oscillations and suppressing the “tails” of the diffraction reflection curve. It has been demonstrated that the response function of acousto-optical devices can be controlled by varying the material, concentration, size, shape, and spatial orientation of inclusions, as well as the polarization of incident radiation.

The paper presents an analysis of electronic amplifiers for modern acousto-optical spectrometers, based on two-crystal sequential diffraction of incident radiation by acoustic waves propagating in each acousto-optical (AO) cell. Such a diffraction scheme has a higher spectral resolution, retaining all the other advantages of traditional AO spectrometers. A description of the functional block diagram of a two-crystal AO spectrometer is given, and the necessary requirements for electronic units are indicated. The results of joint use of the signal power amplification device and a previously developed wideband frequency synthesizer for exciting sound waves in AO cells are presented; output amplitudes of amplified signals are obtained.

A new computer-aided detection (CAD) system for lung nodule detection and selection in computed tomography scans is substantiated and implemented. The method consists of the following stages: preprocessing based on threshold and morphological filtration, the formation of suspicious regions of interest using a priori information, the detection of lung nodules by applying the fractal dimension transformation, the computation of informative texture features for identified lung nodules, and their classification by applying the SVM and AdaBoost algorithms. A physical interpretation of the proposed CAD system is given, and its block diagram is constructed. The simulation results based on the proposed CAD method demonstrate advantages of the new approach in terms of standard criteria, such as sensitivity and the false-positive rate.

A method for synthesis of digital low-pass filter (LPF) based on spectra of atomic functions $${{{\text{h}}}_{a}}(x)$$ is first proposed. Compactly supported function $${{{\text{h}}}_{a}}(x)$$ is a solution to the problem of partition of unity, which makes it possible to consider a sum of its $$S$$ shifts $${{h}_{{S,a}}}(x)$$ as a perfect frequency response of LPF. Truncation of the spectrum of function $${{{\text{h}}}_{{S,a}}}(x)$$ is used to obtain digital filters with rapidly decaying coefficients. Formulas for estimation of deviations of frequency responses in the passband and stopband are derived. Application of new filters in multirate signal processing is considered.

The Bragg diffraction problem in the Fabry-Perot resonator formed by two dynamic acousto-optic mirrors is considered. It is shown that the intensity of incident wave in anisotropic crystal can be enhanced by extremely large factor.