Voigt线型的微分消卷积

通过频域内的近似处理得到了洛仑兹线型微分消卷积的实用算符。推广到高斯、洛仑兹线型的复合情形即Ｖｏｉｇｔ线型，亦可得到它的消卷积算符。把所得算符应用于单峰、多峰情形，对各种不同的组合形式，分别得到了消卷积谱，其分辨率提高因子Ｋ与复合线型中洛仑兹成分的多少有关。     

HREELS signal processing via wavelets

In spectroscopy, the recorded spectra can often be modelled as the noisy convolution product of an instrumental function with the ‘true’ signal to be estimated. Such models have often been used for high‐resolution electron energy‐loss spectroscopy (HREELS). In this article, a new method is suggested to estimate the ‘true’ HREELS signal, i.e. the original electronic diffusion function with ‘true’ peak intensities. Our method relies upon the use of wavelets that, because they exhibit simultaneous time and frequency localization, are well‐suited for signal analysis. Firstly, a wavelet shrinkage algorithm is used to filter the noise. This is achieved by decomposing the noisy signal into an appropriate wavelet basis and then thresholding the wavelet coefficients that contain noise. This algorithm has a particular threshold related to frequency and time. Secondly, the broadening due to the instrumental response is eliminated through a deconvolution process. This step mainly rests on the existing relation between the Lipschitz regularity of the signal and the decay with scale of its wavelet coefficients and on least squares. The efficiency of this technique is highlighted by comparing the results obtained with those provided by other published methods. This work is the second in a series of three papers in this issue. The first one presents background knowledge on the wavelets required to understand the estimation methods. The third paper explores the application of wavelet filtering and deconvolution techniques to x‐ray photoelectron spectroscopy. Copyright © 2004 John Wiley & Sons, Ltd.     

Deconvolving compactly supported densities

This paper addresses the statistical problem of density deconvolution under the condition that the density to be estimated has compact support. We introduce a new estimation procedure, which establishes faster rates of convergence for smooth densities as compared to the optimal rates for smooth densities with unbounded support. This framework also allows us to relax the usual condition of known error density with non-vanishing Fourier transform, so that a nonparametric class of densities is valid; therefore, even the shape of the noise density need not be assumed. These results can also be generalized for fast decaying densities with unbounded support. We prove optimality of the rates in the underlying experiment and study the practical performance of our estimator by numerical simulations.      

Efficiency of four different techniques in coupled HPLC-UV/VIS to quantify overlapping peaks with known spectral features

Summary Four different techniques to quantify unresolved chromatographic peaks with known spectral features combined with photodiode array detection, are investigated as regards their efficiency for the accurate and precise determination of drugs in the low g-range. The comparison includes peak suppression utilising difference chromatograms, first-order derivative chromatograms, selective chromatograms, generated by the calculation of orthogonal polynomial shares, and the powerful least-squares multicomponent analysis approach. Each of these methods uses UV-spectra taken throughout, the peak. The results presented and conclusions reached should enable the chromatographer to come to a decision about the reasonable use of these options now provided by multichannel detection in HPLC.     

FTIR-spectroscopy as a highly sensitive technique to study adsorption and desorption on ionic film and single crystal surfaces

Sample/spectrum relationships are investigated using both a low resolution rapid-scanning NIR monochromator and a Fourier transform instrument capable of high resolution and are evaluated in terms of whether or not the resolution of the instrument is sufficient for measuring the natural bandwidths corresponding to the sample. Based on the sample/spectrum relationship a criterion is developed which must be followed in order to apply either derivative spectroscopy or deconvolution to enhance the resolution of overlapped bands without generating spectral artifacts.     

Effect of europium doping levels on photoluminescence and thermoluminescence of strontium yttrium oxide phosphor

The present paper deals with the effect of europium (Eu³⁺) doping concentration (0.1–2.5 mol%) on photoluminescence (PL) and thermoluminescence (TL) of strontium yttrium oxide (SrY₂O₄) phosphor. The sample was prepared by the modified solid state reaction method, which is the most suitable method for large-scale production. The prepared phosphor sample was characterized by using X-ray Diffraction (XRD), field emission gun scanning electron microscopy, fourier transform infrared spectroscopy, high resolution transmission electron microscopy, photoluminescence, thermoluminescence and commission internationale de I׳Eclairage techniques. The PL emission was observed in the range of 410–630 nm for the SrY₂O₄ phosphor doped with Eu³⁺. Excitation spectrum was found at 254 and 325 nm, sharp peaks were found around 593, 615 and 625 nm with high intensity. From the XRD data, using Scherrer׳s formula, calculated average crystallite size of Eu³⁺ doped SrY₂O₄ phosphor is around 32 nm. Thermoluminescence study was carried out for the phosphor with UV and gamma irradiation. The TL response of SrY₂O₄:Eu³⁺ phosphor for two different radiations was compared and studied in detail. The present phosphor can act as a single host for white light emission in display devices. The detailed process and possible mechanisms for PL and TL are studied and discussed. For the variable concentration of Eu³⁺ on PL studies the PL intensity increases with increasing the concentration of dopant and the concentration quenching found after 2 mol% of Eu³⁺ the optimized concentration was 2 mol%, which is suitable for the display device application. In TL glow curve the optimized concentration was 1 mol% for the UV irradiated sample and 0.2 mol% of Eu³⁺ for the gamma irradiated sample and beta irradiated sample for 10 Gy dose. The kinetic parameters were calculated by the computerized glow curve deconvolution (CGCD) technique.     

A mathematical and physical Study of multiscale deconvolution models of turbulence

This work presents a rigorous analysis of mathematical and physical properties for solutions of multiscale deconvolution turbulence models. We show that solutions of these models exactly conserve model quantities for the integral invariants of fundamental physical importance: kinetic energy, helicity, and (in two dimensions) enstrophy. The kinetic energy conservation is the key that allows us to next apply the phenomenology of homogeneous, isotropic turbulence to establish the existence of a model energy cascade and, in particular, that the cascade exhibits enhanced energy dissipation in a secondary accelerated cascade, which ends at the model's microscale (which we establish is larger than the Kolmogorov microscale). We also prove that the model dissipates energy at the same rate as true turbulent flow, ～ O(U³ ∕ L), independent of Reynolds number. Lastly, we prove the existence of global attractors for the model solutions; the proof of which also shows that solutions are actually one degree of regularity higher than previously known. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental shift allowance in the deconvolution of SIMS depth profiles

We study the deconvolution of the secondary ion mass spectrometry (SIMS) depth profiles of silicon and gallium arsenide structures with doped thin layers. Special attention is paid to allowance for the instrumental shift of experimental SIMS depth profiles. This effect is taken into account by using Hofmann's mixing‐roughness‐information depth model to determine the depth resolution function. The ill‐posed inverse problem is solved in the Fourier space using the Tikhonov regularization method. The proposed deconvolution algorithm has been tested on various simulated and real structures. It is shown that the algorithm can improve the SIMS depth profiling relevancy and depth resolution. The implemented shift allowance method avoids significant systematic errors of determination of the near‐surface delta‐doped layer position. Copyright © 2013 John Wiley & Sons, Ltd.     

Spectral analysis of Sr 3d XPS spectrum in Sr-containing hydroxyapatite

The Sr 3d X-ray photoelectron spectroscopy (XPS) spectrum of Sr-containing hydroxyapatite (SHAp) overlaps completely with the P 2p spectrum. Thus, the chemical state identification of Sr in SHAp is a challenging task. In this work, the Sr 3d spectrum was isolated from the overlapping spectra for analyzing the chemical state of Sr using a generic peak-fitting method. The SHAp layers containing various Sr concentrations were produced on a Ti substrate using a chemical treatment process with a calcium phosphate slurry that included Sr (NO₃)₂. The distribution of the constituent elements changed according to the Sr concentration, implying that the chemical state of Sr varied with concentration. The isolation of the Sr 3d XPS spectrum was conducted via spectral deconvolution using the P 2p spectrum corresponding to HAp. The isolated Sr 3d spectrum revealed that the chemical state of Sr was in SrO and Sr-substituted HAp states, and their ratio varied with the Sr concentration in the layer. The SrO to Sr-substituted HAp ratios affected the Sr ion releasing behavior from the SHAp layer, supporting the validity of the obtained analytical results.     

Generalization of Strang's Preconditioner with Applications to Toeplitz Least Squares Problems

In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices A_n. The th column of our circulant preconditioner Sn is equal to the th column of the given matrix A_n. Thus if A_n is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix A_n has decaying coefficients away from the main diagonal, then is a good preconditioner for An. Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min ∥ b - Ax∥₂. Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.