Computer Optics

926-935

Authors: I.P. Lukin

Theoretical research of coherent properties of vortex conic waves propagating in a turbulent atmosphere was developed. The analysis was based on the analytical solution of the equation for the transverse second-order mutual coherence function of a light field. The following characteristics of coherence of vortex conic waves were considered: the coherence degree, the coherence radius, the root-mean-square and the integral scale of coherence degree. Dependence of these characteristics on the parameters of optical radiation and turbulent atmosphere was analyzed. Unlike the coherence radius, the root-mean-square and integral scales of the coherence degree of vortex conic waves were found to be highly sensitive to the influence of atmospheric turbulence.

946-955

Authors: L.L. Doskolovich, E.A. Bezus, D.A. Bykov, R.V. Skidanov, N.L. Kazanskiy

A method for calculating a “spectral” diffractive lens, which ensures the preservation of the focal position at several prescribed wavelengths is proposed. The method is based on minimizing the function characterizing the difference between the complex transmission functions of the spectral lens for given wavelengths and the complex transmission functions of diffraction lenses calculated separately for each of the given wavelengths. As examples, spectral diffractive lenses are calculated for three and seven wavelengths. The simulation results of the calculated lenses confirm good performance of the proposed method.

968-975

Authors: A.A. Mingazov, L.L. Doskolovich, D.A. Bykov, N.L. Kazanskiy

The article deals with a problem of calculating two reflecting surfaces that form a given irradiance distribution with a flat wavefront, provided that a point source of light is used. A notion of a weak solution for the said problem is formulated and the equivalence of this problem and the Monge–Kantorovich mass transfer is proven.

983-991

Authors: V.Kh. Bagmanov, A.Kh. Sultanov, A.R. Gizatulin, I.K. Meshkov, I.A. Kuk, E.P. Grakhova, G.I. Abdrakhmanova, I.L. Vinogradova

In this paper, using a modified model of slowly varying amplitudes, a process of optics-to-THZ-conversion of vortex beams based on the nonlinear difference frequency generation in a medium with second-order susceptibility is considered. A theoretical substantiation of the law of topological charge conversion of vortex beams is given – the topological charge of the output THz vortex beam is equal to the difference of the topological charges of the input optical vortex beams. A simulation model of the processes under consideration is implemented.

1001-1007

Authors: A.N. Ruchay, K.A. Dorofeev, V.V. Kalschikov

In this paper, we propose a novel switching bilateral filter for depth map from a RGB-D sensor. The switching method works as follows: the bilateral filter is applied not at all pixels of the depth map, but only in those where noise and holes are possible, that is, at the boundaries and sharp changes. With the help of computer simulation we show that the proposed algorithm can effectively and fast process a depth map. The presented results show an improvement in the accuracy of 3D object reconstruction using the proposed depth filtering. The performance of the proposed algorithm is compared in terms of the accuracy of 3D object reconstruction and speed with that of common successful depth filtering algorithms.

1021-1029

Authors: S.V. Eremeev, D.E. Andrianov, V.S. Titov

A problem of automatic comparison of spatial objects on maps with different scales for the same locality is considered in the article. It is proposed that this problem should be solved using methods of topological data analysis. The initial data of the algorithm are spatial objects that can be obtained from maps with different scales and subjected to deformations and distortions. Persistent homology allows us to identify the general structure of such objects in the form of topological features. The main topological features in the study are the connectivity components and holes in objects. The paper gives a mathematical description of the persistent homology method for representing spatial objects. A definition of a barcode for spatial data, which contains a description of the object in the form of topological features is given. An algorithm for comparing feature barcodes was developed. It allows us to find the general structure of objects. The algorithm is based on the analysis of data from the barcode. An index of objects similarity in terms of topological features is introduced. Results of the research of the algorithm for comparing maps of natural and municipal objects with different scales, generalization and deformation are shown. The experiments confirm the high quality of the proposed algorithm. The percentage of similarity in the comparison of natural objects, while taking into account the scale and deformation, is in the range from 85 to 92, and for municipal objects, after stretching and distortion of their parts, was from 74 to 87. Advantages of the proposed approach over analogues for the comparison of objects with significant deformation at different scales and after distortion are demonstrated.

1041-1052

Authors: V.V. Myasnikov

The paper deals with the reconstruction of implicitly defined functions or digital images. Functions are defined using observations, each of which is the result of a pairwise comparison of the function values for two random arguments. The analysis of the current state of research for particular statements of this problem is presented: the method of pairwise comparisons used in decision-making for a finite set of alternatives; reconstruction of preference/utility function in multicriteria tasks; sign representations of images used for the description and analysis of digital images. A unified approach to reconstructing functions and images according to their sign representations is proposed, based on mapping in a high-dimensional space and constructing a linear (when reconstructing a function and images) or non-linear (including non-parametric) classifier (when reconstructing preferences). For a number of classification algorithms, experimental studies have been conducted to evaluate the effectiveness of the proposed approach using the example of the reconstruction of the utility function in problems of decision theory and reconstruction of the brightness function of real images.

1064-1071

Authors: N.V. Fetisova

The paper presents a modified multicomponent model of ionospheric parameter time series. The model describes regular variations and anomalous changes of a multi-scale structure that characterize the occurrence of ionospheric irregularities. Identification of the model components is based on a combined application of the wavelet transform and autoregressive-integrated moving average models. An algorithm for analyzing ionospheric parameters has been developed on the basis of the proposed model. The algorithm allows the intensive ionospheric anomalies characterizing the occurrence of strong ionospheric storms to be detected on-line. Results of the evaluation of the algorithm performance are presented. The evaluation is performed by the example of processing and analyzing hourly and 15-minute data on the ionospheric critical frequency (foF2) during magnetic storms in 2015 – 2017. The performed estimations showed the efficiency of the algorithm and the possibility of its application for space weather forecasting.

1079-1083

Authors: M.A. Butt, S.N. Khonina, N.L. Kazanskiy

Silicon photonics is gaining substantial impulse because it permits optical devices to be realized inexpensively using standard semiconductor fabrication techniques and integrated with microelectronic chips. In this paper, we designed few optical elements such as optical power splitter, polarization beam splitter and Bragg grating based on silicon platform simulated using finite element method.

1088-1092

Authors: V. Ukleev

The hybrid input-output algorithm is a phase retrieval method that provides solution for the phase problem of coherent X-ray diffraction imaging of micro- and nano-objects from the diffraction pattern alone without using any focusing optics. In this paper, we have studied a tolerance of this algorithm to missing information at the center of the diffraction pattern, which is a frequent problem in problems of small-angle scattering. We considered the particular problem of the stability of the algorithm in the case of scattering from an ordered structure and provided a qualitative and quantitative description of the degradation of image reconstruction with an increase in the amount of missing information.

1098-1102

Authors: A.A. Kovalev, V.V. Kotlyar, D.S. Kalinkina

For a light field with both phase and polarization singularities at its center, expressions are obtained that describe the distribution of the spin angular momentum (SAM) density in the sharp focal spot of an aplanatic system. These expressions include the radial, azimuthal, and longitudinal SAM components. As special cases, focusing of optical vortices with radial, azimuthal, and saddle polarizations is studied. Using the Bessel beam as an example, it is shown that in some areas in the focal plane the longitudinal SAM component is zero (resulting in a photonic wheel), while in others it is an order of magnitude less than the transverse component.