Computer Optics

5-11

Authors: V.V. Kotlyar, S.S. Stafeev, A.G. Nalimov

Using Richards-Wolf formulas, we show that an axisymmetric circularly polarized vortex-free field can be focused into a sharp subwavelength focal spot, around which there is a region where the light energy flow propagates along a spiral. This effect can be explained by the conversion of the spin angular momentum of the circularly polarized field into the orbital angular momentum near the focus, although the on-axis orbital angular momentum remains zero. It is also shown that a linearly polarized optical vortex with topological charge 2 forms near the focal plane an on-axis reverse energy flow (defined by the negative longitudinal component of the Poynting vector) whose amplitude is comparable with the direct energy flow.

22-28

Authors: R.V. Skidanov, L.L. Doskolovich, S.V. Ganchevskaya, V.A. Blank, V.V. Podlipnov, N.L. Kazanskiy

The paper presents results of the experimental investigation of “spectral” diffractive lenses the same focus position for several given wavelengths. Two spectral diffractive lenses designed to focus radiation of three and five specified wavelengths in the visible spectrum were investigated. Using a method of direct laser writing in photoresist with iterative correction of writing parameters, we fabricated a diffractive microrelief of the spectral lenses with the height deviation from the designed relief of less than 30 nm. Using a pinhole located at the focus of the fabricated lenses, we estimated the operation wavelengths. The point spread functions of the spectral lenses at the designed wavelengths were measured with the use of a tunable laser. The imaging properties of the spectral lenses were illustrated by the images of a reference color table.

34-39

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

Here we study theoretically and numerically a Gaussian beam with multiple optical vortices with unitary topological charge (TC) of the same sign, located uniformly on a circle. Simple expressions are obtained for the Gaussian beam power, its orbital angular momentum (OAM), and TC. We show that the OAM normalized to the beam power cannot exceed the number of vortices in the beam. This OAM decreases with increasing distance from the optical axis to the centers of the vortices. The topological charge, on the contrary, is independent of this distance and equals the number of vortices. The numerical simulation corroborates that after passing through a random phase screen (diffuser) and propagating in free space, the beams of interest can be identified by the number of local intensity minima (shadow spots) and by the OAM.

53-59

Authors: S.N. Khonina, S.G. Volotovskiy, M.S. Kirilenko

It is proposed to use the random field generation in the numerical simulation of the propagation of radiation through a random medium using method based on the Karhunen–Loeve expansion with various types of correlation operators to describe turbulence simulators. The properties of the calculated simulators of a random medium with a Gaussian correlation function were investigated in modeling the propagation of Laguerre-Gaussian vortex beams. The simulation results showed that an increase in the order of the optical vortex leads, as in the experiment, to lower stability of the phase singularity of the beams to random optical fluctuations. The similarity of the simulation results and the optical experiments indicates the promise of the proposed approach for the synthesis of random environment simulators.

67-73

Authors: A. Makovetskii, S. Voronin, V. Kober, A. Voronin

An efficient algorithm for registration of two non-rigid objects based on geometrical transformation of the template object to target object is proposed. The transformation is considered as warping of the template onto the target. To choose the most suitable transformation from all possible warps, a registration algorithm should satisfy deformation constraints referred to as regularization of non-rigid objects. In this work, we use variational functionals for affine transformations. With the help of computer simulation, the proposed method for searching the optimal geometrical transformation is compared with that of common algorithms.

82-91

Authors: A.E. Sulavko

The paper addresses a problem of highly reliable biometric authentication based on converters of secret biometric images into a long key or password, as well as their testing on relatively small samples (thousands of images). Static images are open, therefore with remote authentication they are of a limited trust. A process of calculating the biometric parameters of voice and handwritten passwords is described, a method for automatically generating a flexible hybrid network consisting of various types of neurons is proposed, and an absolutely stable algorithm for network learning using small samples of “Custom” (7-15 examples) is developed. A method of a trained hybrid "biometrics-code" converter based on knowledge extraction is proposed. Low values of FAR (false acceptance rate) are achieved.

101-108

Authors: M.V. Gashnikov

An adaptive multidimensional signal interpolator is proposed, which selects an interpolating function at each signal point by means of the decision rule optimized in a multidimensional feature space using a decision tree. The search for the dividing boundary when splitting the decision tree vertices is carried out by a recurrence procedure that allows, in addition to the search for the boundary, selecting the best pair of interpolating functions from a predetermined set of functions of an arbitrary form. Results of computational experiments in nature multidimensional signals are presented, confirming the effectiveness of the adaptive interpolator.

117-126

Authors: D.A. Tarasov, O.B. Milder

In modern printing, a large number of tasks are associated with the mutual transformation of color spaces. In particular, the most common pair of hardware-dependent color spaces is RGB and CMYK, the mutual transformation of colors in which is ambiguous, which creates significant problems in color reproduction. To solve this problem, we propose using color space invariants — gradation trajectories and gradation surfaces, which are analogs of gradation curves for initial colorants and their binary overlays, constructed in the absolute color space of the CIE Lab. Invariants are introduced on the basis of the mathematical apparatus of the differential geometry of spatial curves and surfaces. Practical application of color space invariants involves certain difficulties associated with their complex analytical description; moreover, for most practical problems, the high accuracy of the model is redundant. For the practical application of invariants, we propose a simpler approach using natural color sampling in digital printing systems. As an example, the procedure for determining the gray balance for an electrophotographic printing press is given.

133-136

Authors: A.I. Zhdanov, Y.V. Sidorov

The article presents a novel algorithm for calculating generalized normal solutions of underdetermined systems of linear algebraic equations based on special extended systems. The advantage of this method is the ability to solve very poorly conditioned (possibly sparse) underdetermined linear systems of large dimension using modern versions of the iterative refinement method based on the generalized minimum residual method (GMRES - IT). Results of applying the considered algorithm to solve the problem of balancing chemical equations (mass balance) are presented.