Treatment and interpretation of experimental data in applied spectroscopy

The paper describes current methods of treatment and interpretation of experimental data in applied spectroscopy. The issue is reduced to the solution of an inverse problem, which frequently proves to be an ill-posed problem of mathematical physics. To solve such problems one must use a priori information on the solution obtained by the experimenter (regularization of solution). The methods of solution of such one-dimensional and multidimensional problems as smoothing, differentiation (including fractional), allowance for instrument distortions, solution of Abel's and Radon's equations (emission tomography), reduction problems in plasma spectroscopy and atomic absorption, decomposition of analytical signals to elementary components (Lorentzian, Gaussian, exponential), determination of components in CARS--spectra are considered in unified terms. The efficiency of the suggested algorithms are demonstrated by a number of mathematical experiments

Regularities in the stark widths and shifts of spectral lines of singly-ionized aluminium

Based on semiclassical calculations the dependencies for singly-ionized aluminium enabling one to estimate the unknown values of the Stark line widths and shifts with an accuracy no less than 10-30% are obtained. Literature experimental data are analysed based on the AlII line widths and shifts calculated according to these dependencies. Copyright © 1996 Elsevier Science Ltd

Self-similar fluctuations in a turbulent plasma

In the paper one of possible reasons for explanation of strange transport in the turbulent plasma in the presence of a fluctuating magnetic field is discussed. A model of self-similar fluctuations in the magnetic field is investigated in terms of the microscopic theory based on a kinetic diffusion equation for plasmas. A problem of non-Markovian evolution for fluctuations in a magnetic field is discussed and the appearance of anomalous transport is illustrated. It is shown this particular class is of special interest for the description of subdiffusive process

Spectral line shape identification by using fractional derivative spectrometry

Before it is difficult to say about a peak shape without conducting additional research. Conventional nonlinear fitting methods based on the OLS approach are unsuitable to unambiguously assign the overlapped peaks. This implies that a composite band can be decomposed into elementary components of a given shape with the same integral reconstruction error with a large number of ways. A main drawback of this approach is the high variance of the spectral parameters to be estimated. This is due to the overlapping of individual components, which leads to the ambiguous fitting. In this paper we develop a simple mathematical tool in terms of fractional derivative (FD) to determine the overlapping peaks spectral parameters. It is possible due to several positive effects of FD connected with the behavior of its zero-crossing and maximal amplitude. For acquiring a stable and unbiased FD estimate we utilize the statistical regularization method. Along with the well-known distributions such as Lorentzian, Gaussian and their linear combinations the Tsallis distribution is used as a model to correctly resolve overlapped peaks. As exhaustive examples demonstrating a power of the method we estimate unresolved bands spectral parameters of synthetic and experimental infra-red spectra

Investigations of properties of opal-like photonic crystals using combined methods

We propose a technique that combines atomic force microscopy, optical spectrophotometry and diffraction method for characterization of photonic crystals. These materials are promising for the creation of various devices, as well as for the observation of new effects due to their unique properties. Photonic crystals were synthesized by self-assembly of colloidal silica particles with low deviation in size. It is shown that the developed technique allows to increase the accuracy of determining the parameters of the photonic crystal

A simple method to extract spectral parameters using fractional derivative spectrometry

The nonlinear fitting method, based on the ordinary least squares approach, is one of several methods that have been applied to fit experimental data into well-known profiles and to estimate their spectral parameters. Besides linearization measurement errors, the main drawback of this approach is the high variance of the spectral parameters to be estimated. This is due to the overlapping of individual components, which leads to ambiguous fitting. In this paper, we propose a simple mathematical tool in terms of a fractional derivative (FD) to determine the overlapping band spectral parameters. This is possible because of several positive effects of FD connected with the behavior of its zero-crossing and maximal amplitude. For acquiring a stable and unbiased FD estimate, we utilize the statistical regularization method and the regularized iterative algorithm when a priori constraints on a sought derivative are available. Along with the well-known distributions such as Lorentzian, Gaussian and their linear combinations, the Tsallis distribution is used as a model to correctly assign overlapping bands. To demonstrate the power of the method, we estimate unresolved band spectral parameters of synthetic and experimental infra-red spectra. © 2003 Elsevier B.V. All rights reserved

Determination of the size of. Nanoparticles in photonic nanostructures from AFM images

© Published under licence by IOP Publishing Ltd. In this paper we propose a relatively simple algorithm for determining the size of ellipsoidal particles on atomic force microscopy (AFM) image. The proposed algorithm frees researchers from the «manual» measuring of the size of a large number of particles. This algorithm is based on a three-dimensional approximation of the segmented images by ellipsoids and it has several advantages over similar methods. One of important advantages is the ability to determine the parameters of particles the surface of which is not completely visible on the image. Proposed method has been tested on simulated images as well as on the experimentally obtained AFM images of silica particles. Especially the method is very useful for the study of opal-like photonic crystals, in which the particles are packed tightly

Regularities for stark widths of spectral lines of singly ionized aluminum

A dependence for evaluating Stark widths of spectral lines of singly ionized aluminum atoms is proposed. On the basis of linewidths calculated by this dependence, experimental data available in the literature are analyzed

Fractional derivative for finding width, amplitude and shape of overlapping peaks

This work describes a technique based on fractional derivative for finding the overlapping peaks spectral parameters. This is due to positive effects of the fractional derivative caused by the behavior of its zero-crossing and maximal amplitude. A power of the method is demonstrated for synthetic data by using the well-known distributions such as Lorentzian, Gaussian ones and for experimental infra-red spectra coming from molecular spectroscopy. It is shown that recorded spectra are approximated with the Tsallis distribution in the best way, compared to the distributions above mentioned

Regularities for stark widths of spectral lines of singly ionized aluminum

A dependence for evaluating Stark widths of spectral lines of singly ionized aluminum atoms is proposed. On the basis of linewidths calculated by this dependence, experimental data available in the literature are analyzed