Fourier self-deconvolution in coherent anti-Stokes Raman scattering spectrum analysis

Coherent anti-Stokes Raman scattering (CARS) microscopy is rapidly developing into a unique microscopic tool in biophysics, biology and the material sciences. The nonlinear nature of CARS spectroscopy complicates the analysis of the received spectra. There were developed mathematical methods for signal processing and for calculations spectra. Fourier self-deconvolution is a special high pass FFT filter which synthetically narrows the effective trace bandwidth features. As Fourier self-deconvolution can effectively reduce the noise, which may be at a higher spatial frequency than the peaks, without losing peak resolution. The idea of the work is to experiment the possibility of using wavelet decomposition in spectroscopic for background and noise removal, and Fourier transformation for linenarrowing.

Selecting Wavelet Filter for Compression of Spectra from Multispectral Images

The problem of selecting anappropriate wavelet filter is always present in signal compression based on thewavelet transform. In this report, we propose a method to select a wavelet filter from a predefined set of filters for the compression of spectra from a multispectral image. The wavelet filter selection is based on the Learning Vector Quantization (LVQ). In the training phase for the test images, the best wavelet filter for each spectrum has been found by a careful compression-decompression evaluation. Certain spectral features are used in characterizing the pixel spectra. The LVQ is used to form the best wavelet filter class for different types of spectra from multispectral images. When a new image is to be compressed, a set of spectra from that image is selected, the spectra are classified by the trained LVQand the filter associated to the largest class is selected for the compression of every spectrum from the multispectral image. The results show, that almost inevery case our method finds the most suitable wavelet filter from the pre-defined set for the compression.

On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.

Investigation and data adaptive analysis of CARS spectra

In this diploma work advantages of coherent anti-Stokes Raman scattering spectrometry (CARS) and various methods of the quantitative analysis of substance structure with its help are considered. The basic methods and concepts of the adaptive analysis are adduced. On the basis of these methods the algorithm of automatic measurement of a scattering strip size of a target component in CARS spectrum is developed. The algorithm uses known full spectrum of target substance and compares it with a CARS spectrum. The form of a differential spectrum is used as a feedback to control the accuracy of matching. To exclude the influence of a background in CARS spectra the differential spectrum is analysed by means of its second derivative. The algorithm is checked up on the simulated simple spectra and on the spectra of organic compounds received experimentally.

Mössbauer spectra of iron oxides in the bulk and nanocrystalline states

Magnetic nanoparticles are very important in modern industry. These particles are used in many different spheres of life. Nanoparticles have unusual physical and chemical properties connected both with quantum dimensional effects and with the increased role of the surface atoms. Most clearly the difference between the properties of bulk materials and nanoparticles can be seen in the magnetic properties of these materials. The most typical magnetic properties of nanomaterials are superparamagnetism with the size of the cluster from 1 to 10 nm; single-domain magnetic state of nanoclusters and nanostructures up to 20 nm; magnetization processes connected with magnetic cluster ordering and with its forms and sizes; quantum magnetic tunneling effects when magnetization changes by jumps and giant magnetoresistance effects. For research of the magnetic properties of iron-containing nanostructures, it is convenient to apply Mӧssbauer spectroscopy. In this work a number of nano-sized samples of iron oxides were examined by Mössbauer spectroscopy. The Mössbauer spectra of nanoparticles with various sizes were obtained. Mössbauer spectra of iron oxide nanoparticles were compared with the spectra of bulk samples. It was shown how the spectra of iron oxide nanoparticles change depending on the particle sizes.

Side peaks in Nb and NbTi point-contact spectra

Superconductor – normal metal point contacts were investigated, using different combinations of Cu, brass, Nb and NbTi. The resulting spectra contained side peaks. The currents at which these side peaks appeared, depended on the radii of the contacts. For contacts with Nb this dependence was quadratic, while for contacts with NbTi it was linear. Based on this, we argue that the side peaks in the case of the Nb contacts are due to the critical current density being exceeded. In contrast, side peaks of the NbTi contacts are caused by the self-magnetic field exceeding the lower critical field of NbTi. The NbTi contacts did not show the expected contribution from the vanishing Maxwell resistance of the superconductor, a question which remained open.

Detection of Illicit Drugs and Drug Precursors with Cantilever-Enhanced Photoacoustic Spectroscopy

In this study, cantilever-enhanced photoacoustic spectroscopy (CEPAS) was applied in different drug detection schemes. The study was divided into two different applications: trace detection of vaporized drugs and drug precursors in the gas-phase, and detection of cocaine abuse in hair. The main focus, however, was the study of hair samples. In the gas-phase, methyl benzoate, a hydrolysis product of cocaine hydrochloride, and benzyl methyl ketone (BMK), a precursor of amphetamine and methamphetamine were investigated. In the solid-phase, hair samples from cocaine overdose patients were measured and compared to a drug-free reference group. As hair consists mostly of long fibrous proteins generally called keratin, proteins from fingernails and saliva were also studied for comparison. Different measurement setups were applied in this study. Gas measurements were carried out using quantum cascade lasers (QLC) as a source in the photoacoustic detection. Also, an external cavity (EC) design was used for a broader tuning range. Detection limits of 3.4 particles per billion (ppb) for methyl benzoate and 26 ppb for BMK in 0.9 s were achieved with the EC-QCL PAS setup. The achieved detection limits are sufficient for realistic drug detection applications. The measurements from drug overdose patients were carried out using Fourier transform infrared (FTIR) PAS. The drug-containing hair samples and drug-free samples were both measured with the FTIR-PAS setup, and the measured spectra were analyzed statistically with principal component analysis (PCA). The two groups were separated by their spectra with PCA and proper spectral pre-processing. To improve the method, ECQCL measurements of the hair samples, and studies using photoacoustic microsampling techniques, were performed. High quality, high-resolution spectra with a broad tuning range were recorded from a single hair fiber. This broad tuning range of an EC-QCL has not previously been used in the photoacoustic spectroscopy of solids. However, no drug detection studies were performed with the EC-QCL solid-phase setup.

Spin-electromagnetic waves spectra in multiferroic heterostructures

This work devotes to the theoretical investigations of spin-electromagnetic waves (SEW) propagating in a thin-film multiferroic structures that were composed of a slot-line and structures with several ferrite films. In contrast to earlier works, the spin-electromagnetic waves in the investigated structures are originated from two different electrodynamics coupling. The first one is coupling of the electromagnetic wave localized mainly in the slot-line with the spin wave excited mostly in the ferrite film. The second one is coupling of two spin waves in the different ferrite films separated by a thin ferroelectric film. For theoretical analysis of SEWs propagation in such kind of structures theories of their eigen-wave spectra were developed. Spectra of SEW in the investigated structures were calculated and analyzed. The range of electric and magnetic tunability of dispersion characteristic were investigated. Spectra of SEW in the investigated multiferroic structures are used for investigation of transfer function of periodic structures.