Computer Optics

13-21

Authors: Kotlyar V.V., Kovalev A.A., Porfirev A.P.

An explicit formula for the normalized orbital angular momentum (OAM) of an elliptical Hermite-Gaussian (HG) beam of orders (0, n) focused by a cylindrical lens is obtained. In modulus, this OAM can be both greater and smaller than n. If the cylindrical lens focuses not an elliptical, but a conventional HG beam, the latter will also have an OAM that can be both larger and smaller in modulus than that of an elliptical HG beam. For n = 0, this beam converts to an astigmatic Gaussian beam, but, as before, it will still have OAM. With the help of two interferograms, a phase of the astigmatic Gaussian beam is reconstructed, which is then used to calculate the normalized OAM. The values of the OAM calculated by the theoretical formula and using a hybrid method combining modeling with experiment differ only by 6 %.

28-37

Authors: Grebenyuk A.A., Klychkova D.M., Ryabukho V.P.

This paper presents an analysis of the effects occurring at the borders of the field of view in numerically focused imaging of optically defocused objects in interference microscopy systems with spatially coherent illumination of an object. Equations describing the borders of regions of different types in numerically focused images with respect to the defocus parameters are obtained. Equations for estimating the acceptable limits of defocus in numerically focused imaging are obtained. Experimental investigation of the effects, occurring at the borders of the field of view in numerically focused imaging of optically defocused objects in a digital holographic microscope with illumination in transmission is performed.

44-53

Authors: Batomunkuev Yu. Ts., Dianova A.A.

Results of calculating the radius of higher-order spherical aberrations (fifth, seventh and ninth orders) of a high-aperture focusing holographic optical element (HOE) with corrected third-order spherical aberration in the operating spectral range are discussed. As examples, high-aperture axial HOEs with relative apertures close to 1:1 in specified spectral ranges are considered. Coordinates of the point sources of a divergent reference wave and a convergent object wave of the HOE are given. It is shown that when imaging a point source emitting in the 0.250-0.281-μm and 0.500-0.563-μm spectral ranges, the use of an HOE in the first and second diffraction orders makes it is possible to correct the third-order spherical aberration on two wavelengths and the fifth- and seventh-order spherical aberrations on one wavelength. Note that these visible-spectrum wavelengths are different from the HOE's recording wavelength of 0.532 μm.

60-66

Authors: Zadorin A.S., Lukina A.A.

It is noted that the best technical characteristics of optoelectronic microwave self-oscillators (OESO) are reached in schemes employing high-Q optical microresonators (OMR) working in the traveling wave modes (TWM). A possibility of using disk OMRs excited by fundamental whispering gallery modes (WGM) has been considered. Multielement coupling devices (CD) for such resonators have been investigated. They are constructed on the basis of planar optical waveguides (POWG) located over the disk resonator surface in a region bounded by the outer and inner caustics of the WGM. Models of this device have been proposed. The corresponding calculations have been provided.

72-83

Authors: Rozhkov O.V., Piskunov D.E., Nosov P.A., Pavlov V.Yu., Khorokhorov A.M., Shirankov A.F.

Key theoretical concepts advanced by the Bauman MSTU scientific school 'Zoom lens design' are discussed. These include methods for design of both classical and laser zoom lenses, systems with linear and nonlinear relations between the displacements of components, basics of professor I. I. Pakhomov's theory of generalized parameters, a method of paraxial synthesis of multicomponent zoom systems, a method of aberration synthesis of zoom systems in the approximation of the third- and fifth-order aberrations. The effectiveness of the described methods is illustrated by examples of designing zoom systems with superior optical characteristics.

96-104

Authors: Lejhter S.V., Chukanov S.N.

We discuss a problem of comparison of two diffeomorphic images, namely, the source and target images of a diffeomorphism, which are given by two sets of points. The problem is solved on the basis of a method of constructing a minimized functional characterizing the evolution of the diffeomorphic source-to-target image transformation and a penalty for the image path deviation from the required trajectory. An algorithm for solving the diffeomorphic transformation equation is developed on the basis of the gradient descent method. The considered problem of comparison of two images can be used for constructing an optimal metamorphism of images, when there is no exact correspondence between the source and target images of the diffeomorphism.

113-117

Authors: Mikherskii R.M.

The suitability of artificial immune systems for recognizing visual patterns is discussed. A new algorithm and software implementation of an artificial immune system have been proposed based on which real-time pattern recognition can be done using a Web camera. It has been shown experimentally that this system can be successfully used to recognize both human faces and any other objects. An issue of using an artificial immune system in high-performance parallel computing systems is discussed. The advantages of the developed artificial immune system include the ability to teach the system a new image in a fast manner at any moment during run-time. These advantages open up a possibility of creating artificial intelligence systems for real-time learning.

128-140

Authors: Kamaev A.N., Urmanov I.P., Sorokin A.A., Karmanov D.A., Korolev S.P.

In this paper, a method for estimating the volcano visibility in the images is presented. This method includes algorithms for analyzing parametric edges of objects under observation and frequency characteristics of the images. Procedures for constructing parametric edges of a volcano and their comparison are considered. An algorithm is proposed for identifying the most persistent edges for a group of several reference images. The visibility of a volcano is estimated by comparing these edges to those of the image under analysis. The visibility estimation is maximized with respect to a planar shift and rotation of the camera to eliminate their influence on the estimation. If the image quality is low, making it hardly suitable for further visibility analysis, the estimation is corrected using an algorithm for analyzing the image frequency response represented as a vector of the octave frequency contribution to the image luminance. A comparison of the reference frequency characteristics and the characteristics of the analyzed image allows us to estimate the contribution of different frequencies to the formation of volcano images. We discuss results of the verification of the proposed algorithms performed using the archive of a video observation system of Kamchatka volcanoes. The estimates obtained corroborate the effectiveness of the proposed methods, enabling the non-informative imagery to be automatically filtered off while monitoring the volcanic activity.

149-158

Authors: Savchenko A.V.

In this paper we study image recognition tasks in which the images are described by high dimensional feature vectors extracted with deep convolutional neural networks and principal component analysis. In particular, we focus on the problem of high computational complexity of a statistical approach with non-parametric estimates of probability density implemented by the probabilistic neural network. We propose a novel statistical classification method based on the density estimators with orthogonal expansions using trigonometric series. It is shown that this approach makes it possible to overcome the drawbacks of the probabilistic neural network caused by the memory-based approach of instance-based learning. Our experimental study with Caltech-101 and CASIA WebFace datasets demonstrates that the proposed approach reduces the error rate by 1–5 % and increases the computational speed by 1.5 – 6 times when compared to the original probabilistic neural network for small samples of reference images.

167-174

Authors: Parfenov V.I., Golovanov D.Y.

An algorithm for estimating time positions and amplitudes of a periodic pulse sequence from a small number of samples was proposed. The number of these samples was determined only by the number of pulses. The performance of this algorithm was considered on the assumption that the spectrum of the original signal is limited with an ideal low-pass filter or the Nyquist filter, and conditions for the conversion from one filter to the other were determined. The efficiency of the proposed algorithm was investigated through analyzing in which way the dispersion of estimates of time positions and amplitudes depends on the signal-to-noise ratio and on the number of pulses in the sequence. It was shown that, from this point of view, the efficiency of the algorithm decreases with increasing number of sequence pulses. Besides, the efficiency of the proposed algorithm decreases with decreasing signal-to-noise ratio. It was found that, unlike the classical maximum likelihood algorithm, the proposed algorithm does not require a search for the maximum of a multivariable function, meanwhile characteristics of the estimates are practically the same for both these methods. Also, it was shown that the estimation accuracy of the proposed algorithm can be increased by an insignificant increase in the number of signal samples. The results obtained may be used in the practical design of laser communication systems, in which the multipulse pulse-position modulation is used for message transmission.