Automatic alignment of individual peaks in large high-resolution spectral data sets

Pattern recognition techniques are effective tools for reducing the information contained in large spectral data sets to a much smaller number of significant features which can then be used to make interpretations about the chemical or biochemical system under study. Often the effectiveness of such approaches is impeded by experimental and instrument induced variations in the position, phase, and line width of the spectral peaks. Although characterizing the cause and magnitude of these fluctuations could be important in its own right (pH-induced NMR chemical shift changes, for example) in general they obscure the process of pattern discovery. One major area of application is the use of large databases of (1)H NMR spectra of biofluids such as urine for investigating perturbations in metabolic profiles caused by drugs or disease, a process now termed metabonomics. Frequency shifts of individual peaks are the dominant source of such unwanted variations in this type of data. In this paper, an automatic procedure for aligning the individual peaks in the data set is described and evaluated. The proposed method will be vital for the efficient and automatic analysis of large metabonomic data sets and should also be applicable to other types of data.     

The phase shifts leading to the broadening and shift of spectral lines

The classical theory of collisional broadening and shift parameters (β, δ) of an isolated spectral line was used to obtain simple analytical formulas for calculating both β and δ. These formulas were obtained on the assumption that the short range interaction is effective only in the broadening while the long range is effective in the shift of the spectral line. These parameters β and δ depend on the limiting phase shifts responsible for broadening η_b and shift ηδ. It was found that the values of η_b and η_δ are not equal to each other as was proposed by Weisskopf η_b=η_δ=1. The maximum and average values of η_b (η_b max, η_b av) and η_δ (η_δ max, η_δ av) were obtained by numerical evaluation, using different inverse power potentials. By introducing these parameters into the approximated formulas for β and δ using Van der Waals and Lennard-Jones potential, it was found that the results of calculations for (β and δ) with different atomic transitions perturbed by different inert gases are in close agreement with earlier results. Those results, obtained earlier, were based on the Lindholm-Foley theory especially with the average values of η_b [η_b av=0.6057] and the maximum values of η_δ [η_δ max=1.57625]. The impact parameters ρ_b and ρ_δ leading to the broadening and shift of the spectral line were also obtained for different interactions. It was found that the end parameter for the broadening ρ_b is not equal to the starting parameter for the shift ρ_δ.     

啁啾脉冲频域相移的模拟与实验研究

在超快光学瞬态相移的测量中,结合线性啁啾脉冲与频谱干涉技术,可以获得啁啾脉冲相移随频谱的变化规律。光脉冲经过光栅色散和透镜聚焦后,不同的频率成分以空间上的不同坐标展开。当两束脉冲频谱同时在空间上展开时,相同的频谱成分会产生干涉。基于傅里叶变换频谱干涉技术,从频谱干涉图中提取相移,并对其进行了数值模拟和实验研究。结果表明,通过对不同类型频域相移进行重构所得到的结果反映出了相移随脉冲频谱变化的特性。实验结果表明了这种重构算法是有效的,与模拟结果具有较好的一致性。     

Magnetic resonance spectroscopic imaging for visualization and correction of distortions in MRI: high precision applications in neurosurgery

We present a method for the quantification and correction of geometrical/intensity distortions of magnetic resonance images predominantly caused by bulk magnetic susceptibility shifts due to susceptibility heterogeneities of measured biologic tissues and shape of the object under investigation. The method includes precise and fast measurements of the static magnetic-field distribution inside the measured object and automated data processing. Magnetic-field deviations in the range −2.4; 2.6 ppm were found in the human brain at B₀ = 1.5 T. For routinely used imaging parameters, with a read gradient strength of about 1 mT/m, the magnetic-field perturbations in the human brain can cause geometrical distortions up to ±4 mm and intensity changes up to ±50%. MR images corrected by the described method are suitable for planning high precision applications in neurosurgery.     

Light-Induced shifts in the frequency of a multiphoton radiooptical SHF resonance in alkali atoms

A computation is carried out for light-induced shifts in the frequency of a multiphoton radiooptical SHF resonance in alkali atoms on the basis of the quantum formalism of spherical tensors. The components of a light-induced shift in frequency at magneto-independent 0–0– and 1,–1-transitions in⁸⁷Rb atoms under the conditions of isotopic filtration of the resonance light of pumping are calculated. The difference between the temperatures of a filter cell is discovered at which the point of zero shift in the frequency of radiooptical resonance is attained. The components of the light-induced shift of frequency in optically oriented⁸⁷Rb and¹³³Cs atoms are compared in the absence of collisional reorientation in excited state. The prevailing role of the tensor component of light-induced shift in pumping by the D₁-line of a head doublet and the effect of the orientational dependence of the frequency of a multiphoton resonance on change in the sign of the pumping source radiation polarization are noted. St. Petersburg State Polytechnical University, 29 Politekhnicheskaya Str., St. Petersburg, 195251, Russia. Translated from Zburnal Prikladnoi Spektroskopii, Vol. 65, No. 6, pp. 832–838, November–December, 1998.     

Automatic frequency alignment and quantitation of single resonances in multiple magnetic resonance spectra via complex principal component analysis

Several algorithms for automatic frequency alignment and quantitation of single resonances in multiple magnetic resonance (MR) spectra are investigated. First, a careful comparison between the complex principal component analysis (PCA) and the Hankel total least squares-based methods for quantifying the resonances in the spectral sets of magnetic resonance spectroscopy imaging (MRSI) spectra is presented. Afterward, we discuss a method based on complex PCA plus linear regression and a method based on cross correlation of the magnitude spectra for correcting frequency shifts of resonances in sets of MR spectra. Their advantages and limitations are demonstrated on simulated MR data sets as well as on an in vivo MRSI data set of the human brain.     

Shape of spectral lines emitted from a gas in the presence of a condensed phase

The shape of emission lines from a spatially inhomogeneous gas containing particles of a condensed phase is discussed. Monochromatic scattering from particles and the walls limiting the infinite slab was taken into account, as well as emission and absorption by atoms, particles and walls. The Sobolev probabilistic method was used to obtain an exact solution of the equation of transfer. The intensity of the radiation emitted from the slab is expressed in terms of the fundamental functions. The final expressions may be used for calculations of emission line shapes.     

High resolution measurements of hyperfine structure and isotope shifts in 9 spectral lines of Nd I

Nine transitions in Nd I, originating from various levels belonging to the 4f ⁴6s ² ground state configuration, have been studied with high resolution using an actively stabilized C.W. ring dye laser in a crossed laser-atomic-beam set-up. Accurate values for the isotope shifts in all transitions as well as for the hyperfine structure constants of 7 excited states have been obtained.     

Electronic and nuclear properties from the analysis of the isotope shifts in the spectral lines of lead

Isotope shifts in the 623.7 nm line of Pb I have been measured. Then, in a spectral range of nm the optical isotope shifts in 24 lines of neutral and singly ionized lead have been analyzed using a combined model-independent method. From the combination of the optical isotope shifts data with elastic electron scattering, muonic X-ray and electronic K_α X-ray data, we were able to determine the two contributions to the total isotope shift, namely the mass and the field shifts, and to obtain the values of several nuclear factors for a long chain of lead isotopes.     

Change in the frequency and intensity of the spectral lines of a hydrogen-like atom in the field of a point charge

The changes in the wave functions and the energies of a hydrogen-like atom in the static field of a structureless charged particle are calculated in the asymptotic approximation. The corrections to the energy of states, as well as to the dipole matrix elements of radiative transitions caused by the interaction of the atom with the point charge at long range are calculated using the perturbation theory and the Sturm series for a reduced Coulomb Green’s function in parabolic coordinates. The analytical expressions are derived and tables of numerical values of the coefficients of asymptotic series that determine the corrections to the matrix elements and the intensities of transitions of the Lyman and Balmer series are presented.     

Real-time phase measurement and correction of dynamic multimode beam using a single spatial light modulator

In this Letter,a novel system for adaptively correcting the phase of a dynamic multimode beam is proposed.While using merely one spatial light modulator,the phase measurement of the first-order diffraction pattern and the correction of the zeroth diffraction order are simultaneously realized.The real-time experimental result is obtained at a control rate of 10 Hz.The power-in-the-bucket value is improved from 38.5%to 61.8%,even with fundamental mode content that is consistently below 30%.To the best of our knowledge,this is the first implementation of real-time adaptive correction of the entire multimode beam.     

Laser-induced shifts and splittings of hyperfine structure lines in electron spin resonance spectra of 35Cl atoms

Laser-induced shifts and splittings of the hyperfine structure (hfs) lines in the electron spin resonance (ESR) spectra of ³⁵Cl atoms have been studied using both dressed-atom theory and semiclassical dispersion theory. In resonant cases, the calculated results by the dressed-atom theory of the ac Stark effect indicate that laser-induced hfs ESR shifts of ³⁵Cl atoms in the ground state 3p^{5 2}P⁰ _3/2 can be more than 1 MHz W^?1 cm², and a single ESR hfs line is split into four lines under the action of a laser beam with intensity 10 W cm^?2. In non-resonant cases, the two theories give similar results for the shifts. The laser-induced broadening of the ESR hfs lines is also calculated and is less than the shifts. The laser-induced shifts in ESR can be observable within the resolution of ESR experiments.     

Using the broadening and shifts of the spectral lines of cesium for determining the concentrations of charged particles and neutral atoms in a dc arc plasma

Experimental contours of several of the spectral lines of the cesium atom were obtained and the concentrations of charged particles and neutral atoms in a dc arc plasma were calculated. The Stark constants were computed precisely and the limiting charged particle concentrations measurable on the basis of the various lines were established.The authors are sincerely grateful to M. A. El'yashevich for discussing our paper and making valuable comments.     

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory. The relative positions of these features are well-known and they play an important role in fitting experimental data. However, there has been relatively little discussion of how high the steps are, so we present explicit formulae for these heights. This gives a full characterization of the features in this lineshape which can lead to an analysis of the spectrum without the usual laborious powder average.The transition frequency, as a function of the orientation angles, shows critical points: maxima, minima and saddle points. The maxima and minima correspond to the step discontinuities and the saddle points generate the singularities. Near a maximum, the contours are ellipses, whose dimensions are determined by the second derivatives of the frequency with respect to the polar and azimuthal angles. The density of points is smooth as the contour levels move up and down, but then drops to zero when a maximum is passed, giving a step. The height of the step is determined by the Hessian matrix—the matrix of all partial second derivatives. The points near the poles and the saddle points require a more detailed analysis, but this can still be done analytically. The resulting formulae are then compared to numerical simulations of the lineshape.We expand this calculation to include a relatively simple case where there is chemical shielding anisotropy and use this to fit experimental ¹³⁹La spectra of La₂O₃.     

有振幅调制和相位畸变光束的远场光谱移动与光谱开关

基于瑞利衍射公式,研究了被光阑衍射的具有振幅调制和相位畸变光束的远场光谱变化规律。结果表明,有振幅调制和相位畸变光束在远场也会出现光谱异变现象和光谱开关效应,光阑截断参数、光束的相位畸变参数、振幅调制参数、光强调制参数对远场光谱的跃迁量和光谱开关产生影响。通过数值计算结果分析讨论了光阑截断参数及光束各参数影响远场光谱的规律。