# Optoelectronics, Instrumentation and Data Processing (v.46, #3)

Estimation of the velocity vector of a moving object with unknown intensities of its image and background by A. P. Trifonov; R. V. Kutsov; S. O. Baranov

*(207-214)*. A maximum likelihood algorithm for estimating the velocity vector of a moving object from its image of unknown intensity against an applicative background whose intensity may be unknown a priori was designed and analyzed.

**Keywords:**applicative model; moving object; estimate; velocity vector; unknown intensities; maximum likelihood algorithm; anomalous errors

Modeling images with specified fractal characteristics by B. N. Grudin; V. S. Plotnikov; N. A. Smol’yaninov

*(215-221)*. Algorithms for modeling images with fractal characteristics based on generalized spatial frequency filtering are proposed in which the phase or sign of the amplitude of the corresponding orthogonal transformation of the original image is retained and the modulus of the amplitude decreases exponentially for the entire generalized spectrum of the image or for the integral frequency characteristic of the spectrum. For the model images, fractal measures in a spatial region are proposed, which, similarly to the integral frequency characteristic, are invariant under multiplicative reduction in scale.

**Keywords:**fractal images; generalized spatial frequency filtering; integral frequency characteristic of spectrum; invariance under multiplicative reduction in scale; orthogonal transformations; energy spectra; fractal measures

Method of detecting the absorption of gamma rays propagating in a nitrogen-containing compound by A. G. Vostretsov; A. V. Burdakov; S. E. Radchenko; A. S. Kuznetsov; Yu. S. Sulyaev

*(222-228)*. An algorithm for detecting spectral peak absorption in the secondary radiation from an object containing nitrogen compounds is proposed. The algorithm is based on the statistical invariance principle and has the property of automatically adjusting to signal-noise parameters. The algorithm was tested by simulation modeling and was shown to be applicable to real secondary-radiation spectra. The algorithm and the associated experimental hardware make it possible to implement a fundamentally new method for the automatic detection of nitrogen-containing compounds.

**Keywords:**energy spectrum; spectral analysis; secondary gamma radiation; absorption; processing of measurement results

Algorithm for estimating the state vector of controlled plants based on the Kotel’nikov theorem by V. Yu. Bulychev; Yu. G. Bulychev; A. P. Lapsar’

*(229-236)*. An algorithm for estimating the state vector of controlled plants in the class of band-limited functions with a cutoff regularizing function is proposed which is more effective and accurate than available algorithms. The effect of errors in assigning samples of the differentiated functions on the estimate quality is evaluated, and the methodical error of the algorithm is analyzed.

**Keywords:**Kotel’nikov theorem; band-limited function; regularizing function; methodical error

Object selection under random geometric image transformations by P. V. Babayan

*(237-242)*. The problem of object selection in the presence of random geometric transformations of the observed images due to the movement of the image sensor and random atmosphere fluctuations is solved. An analytical and simplified algorithms of for solution of the problem are developed. Results of statistical investigation of the algorithms are presented.

**Keywords:**object selection; geometric transformations; Johnson distribution

Analysis of asymptotic properties of nonparametric estimate of the equation of the separation surface in a two-alternative problem of pattern recognition by A. V. Lapko; V. A. Lapko

*(243-247)*. Quantitative relations between the approximation properties of nonparametric estimates of the separation-surface equation and the nonuniformity of the distribution of the learning-sample elements between the classes are studied in a two-alternative problem of pattern recognition.

**Keywords:**nonparametric statistics; pattern recognition; asymptotic properties; learning sample; decision function

Methods of modeling interaction of atoms with polarized radiation by K. A. Nasyrov

*(248-255)*. Methods of the numerical solution of equations that describe the resonant interaction of polarized radiation with alkali atoms are presented. Some procedures of converting these equations to a form reducing the calculation time are given. Typical simplifying assumptions used in solving these equations are discussed. Based on comparisons of magnetic-optical resonances for Rb

^{87}with various simplifying assumptions, a conclusion is made on applicability of these approximations and possible inherent errors.**Keywords:**optical Bloch equations; elliptical polarization of radiation; magnetic-optical resonance

Experimental study and modeling of holographic photonic crystals with defects of the spatial and band-gap structures by E. F. Pen; I. G. Shatalov; V. V. Shelkovnikov

*(256-263)*. Results of experimental studies and modeling of holographic photonic crystals (PCs) with defects of their spatial and band-gap structures and also of studying quasi-crystals are presented. Thicklayer photopolymer materials with a hybrid matrix formed on the basis of the sol-gel technology are used for PC production. A method of obtaining delocalized defects is proposed and implemented. A code is written for computer modeling of the spatial PC structure, which offers a clear idea about the appearance of the synthesized crystal and the expected spectral characteristics.

**Keywords:**holographic lithography; photopolymers; photonic crystals; band-gap structure; modeling

Effect of the eye pupil diameter and the phase shift in the diffraction structure on bifocal properties of diffractive-refractive intraocular lenses by G. A. Lenkova

*(264-273)*. As the eye pupil decreases, the bifocal properties of the intraocular lens (IOL), which is an artificial eye lens, can be violated. To avoid it, a phase shift is introduced into the structure of the IOL diffractive component. Results of an analytical study of the light intensity distribution on the axis of a bifocal IOL for different values of the eye pupil and phase shift in the diffractive component with a focal power of 4.2 D (diopters) are presented. Because of broadening and asymmetry of the intensity distribution function arising at small pupil diameters, the foci of orders 0 (far vision) and +1 (near vision) of the bifocal IOL are demonstrated to affect each other: they come closer or farther, become separated or overlapped. The total intensity distribution may be continuous or have a dip whose magnitude depends on the pupil diameter and phase shift. It is noted that the optimal phase shift at which separation of the foci (bifocality) begins from the pupil diameter of ∼0.9 mm and is not violated with further pupil expansion is 180° (

*π*radian).**Keywords:**intraocular lens; artificial eye lens; diffractive-refractive lens; bifocal lens

Multifocal displays, diffractive depth of focus, and visual comfort by A. M. Kovalev

*(274-281)*. Volumetric displays with numerous fronto-parallel planes-images stimulating eye accommodation are considered. The depth of the focal field is determined as a function of the axial intensity distribution. Results of interpolation of images between the planes are presented. It is shown that the best resolution and visual comfort are reached if the distance between the planes does not exceed the diffractive depth of focus.

**Keywords:**multifocal displays; accommodation; depth of focus; visual discomfort

Correlation method for processing speckle patterns of dynamic light scattering by small particles based on spatial averaging of data by Yu. N. Kul’chin; O. B. Vitrik; A. D. Lantsov; N. P. Kraeva

*(282-286)*. A correlation method for processing dynamic light scattering patterns resulting from laser radiation propagation through solutions and suspensions is proposed which is based on spatial averaging of measurement data on the correlation functions of the intensity of light scattered by small particles.

**Keywords:**speckle pattern; nanosize particle; dynamic light scattering; spatial averaging of data; correlation function; translation of speckle patterns

Low-voltage element of a field-programmable dynamic diffraction grating by E. G. Kostsov; V. S. Sobolev

*(287-293)*. A new element of a field-controlled diffraction grating [Grating Light Valve™ diffractive MOEMS device (GLV)] is described, which differs from known similar elements by the physical principle of operation and its structure; other distinctive features are the lower control voltage, the absence of the hysteresis, and the possibility of operation in the analog mode. Experimental characteristics of the GLV element are presented.

**Keywords:**microelectronics; microelectromechanics; microoptoelectromechanics; microoptics; diffraction grating; electrostatics

Small-size terahertz spectrometer using the second harmonic of a femtosecond fiber laser by V. D. Antsygin; A. A. Mamrashev; N. A. Nikolaev; O. I. Potaturkin

*(294-300)*. Possible implementations of a small-size terahertz spectrometer with a subpicosecond resolution on the basis of a femtosecond fiber laser are considered. An experimental sample of a spectrometer is fabricated. This spectrometer employs the method of optical rectification in a ZnTe nonlinear crystal and the Dember (photodiffusion) effect on the InAs semiconductor surface to generate terahertz radiation and the polarization-optical method to detect radiation. System operation is demonstrated by an example of measuring the terahertz absorption spectrum of water and determining the refractive index of the

*β*-BBO crystal. The basic spectrometer parameters are found: spectral range, spectral resolution, and dynamic range of the terahertz spectrum amplitude.**Keywords:**terahertz spectroscopy; optical rectification; polarization-optical detection