Janusz Chrzanowski

New technique in plasma polarimetry: Evolution equations for angular parameters ‘amplitude ratio–phase difference’ of polarization ellipse

New technique is suggested in plasma polarimetry: Differential equations for angular parameters of polarization ellipse, characterizing the amplitude ratio and the phase difference between orthogonal components of the wave field. Equations for angular variables ‘amplitude ratio–phase difference’ are derived, which allow direct calculation of the parameters of polarization ellipse, omitting solutions for the Stokes vector. The simplest analytical solutions are presented for the pure Faraday and the pure Cotton–Mouton effects. Behavior of angular parameters in the homogeneous and inhomogeneous plasmas is illustrated by numerical modeling in conditions when the Faraday and Cotton–Mouton effects are large enough and comparable in strength.

Accuracy of Cotton-Mouton polarimetry in sheared toroidal plasma of circular cross-section

The Cotton-Mouton effect in sheared plasma with helical magnetic lines is studied on the basis of the equation for complex amplitude ratio (CAR). A simple model for helical magnetic lines in sheared plasma of toroidal configuration is suggested. The equation for CAR in the sheared plasma is solved by perturbation method, using the small shear angle deviations as is characteristic for tokamak plasma. It is shown that the inaccuracy in polarization measurements caused by deviations of the sheared angle amounts to some percentage of the shearless Cotton-Mouton phase shift. One suggested method is to subtract the “sheared” term, which may improve the accuracy of the Cotton-Mouton measurements in the sheared plasma.

Application of polarimetry to test the models of thermonuclear plasma and determination the safety factor profile

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP

Conditions for observation of the enhanced backscattering phenomenon in a turbulent atmosphere

Influence of enhanced backscattering effect on laser measurements of dust and aerosols content in a turbulent atmosphere is discussed. It is shown that doubling of the backscattered light intensity, characteristic for enhanced backscattering, leads to overestimating dust content in the air. To avoid undesirable effect of overestimation, it is recommended to displace receiving aperture sidewise relatively to laser source. Other method to eliminate overestimation is to use wider laser beam and extended receiving aperture as compared to coherence radius of the scattered wave field.

Photoelectric effect in aspect of electron waves interaction

The interaction of electromagnetic waves with metal surface is analyzed in terms of electrons waves and quasiparticles theory. Work function for any metal is presented in dependence on electrons density and Fourier transform of potential due to single electron. Influence of different factors on change of work function value is considered.

Influence of the electromagnetic wave polarization on surface impedance of metal

Our results consider the surface impedance of a metallic half space in the presence of the external magnetic field perpendicular to the surface. We consider a weak magnetic field and the strong one separately. The presented results include of Fermi liquid effects (the quasiparticles interaction), consequently they are valid only in low temperatures when the elastic electron scattering on the impurities is predominant. The shape of the integral terms of the impurity scattering operator allows distinguishing the difference between the transport mean free path from the mean free path. Because we take into account the kind of polarization of the electromagnetic wave, all calculations are made in the circular coordinates. Each part of the surface impedance has been separated to express exactly the influence of magnetic field and kind of polarization on the real part of impedance and on the imaginary one. All considerations are restricted to the isotropic metal model because the anisotropic case may be a matter of purely numerical calculations only.

Interaction of Cotton-Mouton and Faraday effect under different initial polarization state of incident beam

The evolution of polarization along the ray in homogeneous plasma is analyzed in situation when Faraday and Cotton-Mouton effects are not small and comparable with each other. On the basis of the quasi-isotropic approximation of geometrical optics method authors find the numerical solution for azimuthal and ellipticity angles of polarization ellipse and analyze how the initial state of the incident beam affects obtained results. Numerical modeling is performed for plasma parameters comparable with those acceptable for the ITER project.

Surface impedance in the anomalous skin effect regime

An analytical solution of the surface impedance is obtained using the kinetic equation with the collision integral that takes into account the Fermi liquid effects. It is assumed that the reflection of electrons is purely diffusive. Particular attention is paid to the influence of external magnetic field and polarization of the incident wave on the real and imagine part of the surface impedance.

Investigation of the relations between the dust granularity and pollution concentration

Mechanism of light interaction with particles of dusts was presented in quantum aspect by analyzing differential cross section onto scattering. For rotational symmetry the differential scattering cross section was related with angle of scattering. One pointed on relation between the shape of indicatrix of scattering with size of scattered particles. Next a model of devices was introduced which makes possible a measurement of concentration of dustiness of the air oe gases and defines the sizes of dust grains on the basis of measurement of the scattered light stream.

Application of amplitude changes of monochromatic scattered light to investigation of dust grain composition

The light beam crossing the dust area meets with the loss of energy. We know by experience that the scattering indikatrix depends on the size of the dust particles. The measurement of the light energy scattered into given solid angle enables to identify and specification of the grain composition of the dust particles. Basis on the research a special head has been made to step change of the location of the photodetectors and in result to measure a specific or even desirable dust fraction for the sake of technology. In this paper the graphs of the grain dust distribution are presented with regard to the materials which are transported most frequently by Polish merchant marine.