Mikhail V. Volkov

Solving the Coulomb scattering problem using the complex-scaling method

We present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex-scaling method, applied to a specially constructed inhomogeneous Schrodinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.

Fringe analysis for moiré interferometry by modification of the local intensity histogram and use of a two-dimensional Fourier transform method

A noise-immune method for phase retrieval of a single moire interferometric fringe pattern is presented and discussed. The method is shown to provide accurate recovery of the phase information by a combined method based on modification of the local intensity histogram and use of a two-dimensional Fourier transform of the enhanced moire fringe pattern. The principle of the method is described and the experimental results of moire interferometric measurements with submicrometre sensitivity of the in-plane displacement fields of thick carbon fibre/PEEK composite laminates are presented as an example of the application of the technique.

Phase retrieval of THz radiation using set of 2D spatial intensity measurements with different wavelengths

Using the infrared matrix of pyroelectric or other photodetectors along with THz band pass filters with pulsed or CW sources one can record the 2D intensity distribution of THz radiation with a high degree of monochromatization. This allows one to use various approaches to solving the phase problem which were developed for the visible frequencies. In this contribution we present the results of the numerical investigation of the wavefront reconstruction using THz radiation at several wavelengths and taking the intensity distribution at various distances.

The impact of sharp screening on the Coulomb scattering problem in three dimensions

The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complementary situations, firstly, when the interior part of the Coulomb potential is left in the Hamiltonian and, secondly, when the long-range tail is considered as the potential. The partial wave results are summed up to obtain the wavefunction in three dimensions. It is shown that in the domains where the wavefunction is expected to be proportional to the known solutions, the proportionality is given by an operator acting on the angular part of the wavefunction. The explicit representation for this operator is obtained in the basis of Legendre polynomials. We proposed a driven Schrodinger equation including an inhomogeneous term of the finite range with purely outgoing asymptotics for its solution in the case of the three-dimensional scattering problem with long-range potentials.

Fringe Evaluation and Phase Unwrapping of Complicated Fringe Patterns by the Data-Dependent Fringe Processing Method

Evaluation of noisy fringe patterns is important for solving problems of nondestructive testing and is widely used in moire, holographic, and speckle interferometry. In this paper, a new method of fringe pattern analysis has been proposed based on iterative estimation of local fringe amplitude, spacing, and orientation. Fringe parameter evaluation at each iteration step allows the formation of a two-dimensional (2-D) data-dependent anisotropic impulse response of a spatial filter that allows suppression of the noise influence without decreasing the fringe visibility. When the local fringe parameters are obtained, it is possible to find the phase difference at each point of the fringe pattern and at any other one within the local 2-D area. These local phase differences are utilized to recover the wrapped fringe phase at the point using a local model of the fringe pattern fitted under the criterion of root-mean-square error minimization. The high noise immunity of the proposed method was verified experimentally when processing complicated fringe patterns with 2-D fringe phase unwrapping

Video capillaroscopy clarifies mechanism of the photoplethysmographic waveform appearance

Photoplethysmography (PPG) devices are widely used in clinical practice but the origin of PPG signal is still under debating. The classical theory assumes that the PPG waveform stems from variations of blood volume in pulsating arteries. In this research we analysed high-speed video recordings of capillaries in a fingernail bed. It was found that speed of erythrocytes in capillaries has pronounced modulation in time, which follows variations of instantaneous blood pressure in arteries. However, the mean speed significantly differs even for neighbour capillaries whereas change of the speed occurs in phase for the most of capillaries. Moreover, the light intensity remitted from the papillary dermis is also modulated at the heartbeat frequency displaying significant correlation with waveforms of the RBC speed. Obtained results can hardly be explained by the classical theory of PPG signal formation. Shallow penetrating visible light acquires modulation of erythrocytes density in the capillary bed without interacting with deeper situated pulsating arteries. Therefore, the capillary bed could serve as a distributed sensor for monitor the status of deep vessels. Better understanding of the photoplethysmography basis will result in a wider range of applications of this fast growing technology in both medical and research practice.

Image reconstruction using measurements in volume speckle fields formed by different wavelengths

An iterative wavefront retrieval method based on intensity measurements formed by several wavelengths is investigated in the present contribution. This multiwavelength technique is extended to use the intensity distributions recorded in various planes of the volume speckle field. The ability to retrieve the wavefront using speckle patterns is demonstrated in experiment. Two different experimental techniques have been used. The first proposed method allows one to record three different intensity distributions corresponding to the three CCD RGB channels at single exposure. This gives the advantage in the analysis of fast processes, e.g. phase microscopy of moving biological cell-like objects investigation. The second technique involves using a large number of wavelengths of supercontinuum radiation formed by photonic-crystal fiber. This approach provides faster and more accurate convergence of the proposed method, has simple and rugged recording scheme with fiber optic elements.

Potential splitting approach to the three-body Coulomb scattering problem

The potential splitting technique is developed for solving the three-body Coulomb scattering problem. The formalism is applied to e+-H and e+-He+ scattering problems. Calculated phase shifts and the annihilation rate parameter are in fairly good agreement with the most accurate results available in the literature.

Blood Peripheral Circulation Assessment Method Based on Combined Use of the Video-Capillaroscopy, Imaging Photoplethysmography, and Electrocardiography

Parameters of blood microcirculation are revealed when obtaining in-vivo useful information by combined use of the video-capillaroscopy, imaging photoplethysmography, and electrocardiography. Different time delays were found between signal pulsations evaluated by various techniques allowing development of new blood circulation diagnostic methods.

Optimized data processing for an optical 3D sensor based on flying triangulation

We present data processing methods for an optical 3D sensor based on the measurement principle “Flying Triangulation”. The principle enables a motion-robust acquisition of the 3D shape of even complex objects: A hand-held sensor is freely guided around the object while real-time feedback of the measurement progress is delivered during the captioning. Although of high precision, the resulting 3D data usually may exhibit some weaknesses: e.g. outliers might be present and the data size might be too large. We describe the measurement principle and the data processing and conclude with measurement results.