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Results of an analytical study of the properties of a diffraction interferometer with the general path of noninverted wavefronts are presented. The interferometer is based on the Fresnel zone plate and designed to control the shapes of surfaces and second-order mirrors. It is shown that application of the theory of pupils and windows allows an essential simplification of consideration of optical systems, visual analysis of the shape of interference fringes, and calculation of the optimum design of an interferometer. The obtained formulas, which relate the positions of pupils and windows (entrance, intermediate, and exit ones) to the zone plate focus and the mirror curvature radius, can be useful in the development of diffraction interferometers of various designs.

Results of a study of elements of solid-state electronics by holographic interferometry are presented. Examples of measurement of thermal strains of real products and control of engineering processes in the production of static induction transistors (SITs) and ultra-high frequency hybrid integrated circuits are given.

A new approach to the wavefront (phase) reconstruction from interferograms is proposed based on the classical method of fringe tracing using a sample of interferograms with different numbers and orientations of interference fringes. Wavefronts reconstructed from individual interferograms are averaged, and the test surface quality is judged by the data obtained. Averaging the phase by several interferograms makes it possible to reduce the variance of the phase reconstruction error caused by random noise and inhomogeneities in aperture illumination and interference fringe distribution, as well as to reduce the effect of instability of external conditions.

The interaction of ultrashort pulses and their bound states in fiber lasers with a saturable absorber are analyzed by numerical simulation. It is shown that the distance between two interacting pulses in the lasing mode established after a transient process can take a set of quantized values in which neighboring pulse separations correspond to steady bound states of opposite parity. Characteristic changes in the established states with a change in the parameters of the laser system are demonstrated. The developed model of passive laser mode locking and the results presented in the paper can be used to describe and interpret the lasing modes of fiber lasers with nonlinear losses due to different nanomaterials (media with quanta wells, nanotubes, graphene, etc.).

Specific features of operation of a two-capacitor generator based on overflow of the charge accumulated in capacitors through a load resistance between two capacitors with antiphase modulated capacitances by means of a lateral or planar shift of the electrode plates by applying a mechanical force to moving electrodes are analyzed. Numerical solutions for all generator operation modes are obtained, and they are found to be universal. Analytical estimates of the maximum power of the generator as a function of the capacitance modulation factor are derived. Experimental investigations of a twocapacitor rotor generator show that its characteristics are consistent with the analysis performed and that this analysis can be used to describe all specific features of operation of particular generators.

A method is proposed for constructing noise-resistant mask differentiating filters minimizing systematic errors in estimating directional fields by a gradient algorithm. A comparative analysis of the accuracy of gradient algorithms was performed by computer modeling It is shown that a decrease in the systematic error leads to a considerable increase in the accuracy of directional field estimation.

An algorithm is proposed for discriminating between random image signals and non-Gaussian impulse noise with a uniform brightness distribution which is based on a new optimality criterion combining the minimization of weighted unconditional probabilities of wrong decisions of the first and second kind and maximization of the probabilities of making correct decisions. Results of numerical studies of the proposed and the well-known Bayes algorithms are given showing that the use of the new algorithm reduces the discrimination error under conditions of complete a priori uncertainty of the image signal distribution.

A possibility of application of the algorithm of compensation for linear distortions in solving systems of linear algebraic equations with banded matrices is considered. Relations necessary for the procedure of stage-by-stage searching for the solution are derived, and conditions of correctness of their application are determined.

The proposed algorithm calculates its own filtration factor for each coefficient of the wavelet expansion of a noisy signal. The optimal filtration factor depends on the signal-to-noise ratio, which is estimated with a specially constructed iterative procedure. The limit points of this procedure are determined. A computational experiment performed shows that the proposed approach can be effectively used in problems of filtration and compression of noisy signals and images.

This paper considers the problem of determining the rotation parameters such as the direction vector of the rotation axis and the rotation angle of a three-dimensional image whose surface points are specified by vectors. The initial and rotated vectors are considered known. An approach using a quaternion representation of vectors is proposed, whose computational efficiency is severalfold higher than the efficiency of known approaches. The mechanism of the effect of noise on the accuracy of determination of the parameters is studied, and recommendations on error minimization are given. Features of the solution of the inverse problem of rotation as applied to the image recognition system are considered.