Phasing arbitrarily sampled multidimensional NMR data

The recent re-introduction of the two-dimensional Fourier transformation (2D-FT) has allows for the transformation of arbitrarily sampled time domain signals. In this respect, radial sampling, where two incremented time dimensions (t(1) and t(2)) are sampled such that t(1)=taucosalpha and t(2)=tausinalpha, is especially appealing because of the relatively small leakage artifacts that occur upon Fourier transformation. Unfortunately radially sampled time domain data results in a fundamental artifact in the frequency domain manifested as a ridge of intensity extending through the peak positions perpendicular to +/- the radial sampling angle. Successful removal of the ridge artifacts using existing algorithms requires absorptive line shapes. Here we present two procedures for retrospective phase correction of arbitrarily sampled data.     

Narrow peaks and high dimensionalities: Exploiting the advantages of random sampling

Level of artifacts in spectra obtained by Multidimensional Fourier Transform has been studied, considering randomly sampled signals of high dimensionality and long evolution times. It has been shown theoretically and experimentally, that this level is dependent on the number of time domain samples, but not on its relation to the number of points required in appropriate conventional experiment. Independence of the evolution time domain size (in the terms of both: dimensionality and evolution time reached), suggests that random sampling should be used rather to design new techniques with large time domain than to accelerate standard experiments. 5D HC(CC-TOCSY)CONH has been presented as the example of such approach. The feature of Multidimensional Fourier Transform, namely the possibility of calculating spectral values at arbitrary chosen frequency points, allowed easy examination of resulting spectrum. We present the example of such approach, referred to as Sparse Multidimensional Fourier Transform.     

Optimized angle selection for radial sampled NMR experiments

Sparse sampling offers tremendous potential for overcoming the time limitations imposed by traditional Cartesian sampling of indirectly detected dimensions of multidimensional NMR data. Unfortunately, several otherwise appealing implementations are accompanied by spectral artifacts that have the potential to contaminate the spectrum with false peak intensity. In radial sampling of linked time evolution periods, the artifacts are easily identified and removed from the spectrum if a sufficient set of radial sampling angles is employed. Robust implementation of the radial sampling approach therefore requires optimization of the set of radial sampling angles collected. Here we describe several methods for such optimization. The approaches described take advantage of various aspects of the general simultaneous multidimensional Fourier transform in the analysis of multidimensional NMR data. Radially sampled data are primarily contaminated by ridges extending from authentic peaks. Numerical methods are described that definitively identify artifactual intensity and the optimal set of sampling angles necessary to eliminate it under a variety of scenarios. The algorithms are tested with both simulated and experimentally obtained triple resonance data.     

基于傅里叶变换光谱技术的Zoom-FFT算法研究

在分析经典的Zoom-FFT算法基础上,提出一种基于傅里叶变换光谱技术的Zoom-FFT算法,用matlab仿真常规FFT算法和Zoom-FFT算法,对不同采样步长的干涉条纹进行数据处理,通过反演出的光谱曲线图和原始光谱曲线图可以看出:采样步长小于20 m时,FFT和Zoom-FFT算法都可以反演出光谱;而当采样步长大于20 m且小于33.3 m时,FFT算法未能反演出光谱,而Zoom-FFT算法仍然可以反演出光谱。     

Wavelet-based ultra-high compression of multidimensional NMR data sets

The application of a lossy data compression algorithm based on wavelet transform to 2D NMR spectra is presented. We show that this algorithm affords rapid and extreme compression ratios (e.g., 800:1), providing high quality reconstructed 2D spectra. The algorithm was evaluated to ensure that qualitative and quantitative information are retained in the compressed NMR spectra. Whilst the maximum compression ratio that can be achieved depends on the number of signals and on the difference between the most and the least intense peaks (dynamic range), a compression ratio of 80:1 is affordable even for the challenging case of homonuclear 2D experiments of large biomolecules.     

Interlaced Fourier transformation of ultrafast 2D NMR data

A new protocol for processing the data arising in ultrafast 2D NMR is discussed and exemplified, based on the interlaced Fourier transformation. This approach is capable of dealing in a single, combined fashion, with the two mirror-imaged interferograms arising in this kind of experiment as a result of the acquisition of a train of magnetic field gradient echoes. By combining all the acquired data points into a common Fourier processing procedure the spectral width along the direct-acquisition domain becomes effectively doubled, giving the opportunity of employing acquisition gradients that are approximately half as strong as hitherto required. This in turn should lead to an overall enhancement in the signal-to-noise ratio of the experiment of ca. 2, as well as to improvements in the achievable digital resolution. These expectations were tested by carrying out a series of homo- and heteronuclear ultrafast 2D NMR acquisitions, and found systematically fulfilled. The robustness and conditions that allow the interlaced numerical procedure to be implemented in routine analytical applications were explored and are briefly discussed.     

Hadamard frequency-encoded SOFAST-HMQC for ultrafast two-dimensional protein NMR

We demonstrate the feasibility of recording (1)H-(15)N correlation spectra of proteins in only one second of acquisition time. The experiment combines recently proposed SOFAST-HMQC with Hadamard-type (15)N frequency encoding. This allows site-resolved real-time NMR studies of kinetic processes in proteins with an increased time resolution. The sensitivity of the experiment is sufficient to be applicable to a wide range of molecular systems available at millimolar concentration on a high magnetic field spectrometer.     

Recent Fourier and Laplace perspectives for multidimensional NMR in porous media

Multidimensional NMR techniques used in the measurement of molecular displacements, whether by diffusion or advection, and in the measurement of nuclear spin relaxation times are categorised. Fourier-Fourier, Fourier-Laplace and Laplace-Laplace methods are identified, and recent developments discussed in terms of the separation, correlation and exchange perspective of multidimensional NMR spectroscopy.     

An alternative approach for recording of multidimensional NMR data based on frequency dependent folding mechanism

A new scheme for obtaining HSQC spectra with improved resolution or in a shorter time called SHARC (Shaped Arrayed data aCquisition protocol) is proposed, which uses region selective RF pulses and allows the sweep width to be adjusted individually for each region. It thus bypasses the problems with the Nyquist theorem associated with other method suggested for this purpose. Assignment of the cross-peaks to their respective region is achieved by manipulating the phases of the RF pulses and/or their frequencies. SHARC NMR can be applied without any previous knowledge of the chemical shift distribution, but can be further optimized on the basis of a quick overview spectrum.     

Laser and Fourier transform emission spectroscopy of TaCl

The emission spectrum of TaCl has been recorded at high resolution in the 3000-35 000 cm⁻¹ region using a Fourier transform spectrometer. The bands were observed by microwave excitation of a mixture of TaCl₅ vapor and 3.0 Torr of He. Several TaCl bands have also been recorded using the laser ablation/molecular beam source at the University of New Brunswick. A rotational analysis of a number of bands has been obtained and the majority of the stronger bands have been classified into three groups with different lower state spectroscopic constants. The three lower states have been identified as having Ω″ = 0⁺, Ω″ = 2, and (tentatively) Ω″ = 3. The Ω″ = 0⁺ and Ω″ = 2 states are very close in energy and one of these two states is the ground state of TaCl.     

The rotational spectrum of epifluorohydrin measured by chirped-pulse Fourier transform microwave spectroscopy

The rotational spectrum of epifluorohydrin measured by chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy is presented. A new CP-FTMW spectrometer capable of measuring the entire 7.5-18.5 GHz spectrum with a single polarizing pulse is described briefly. The CP-FTMW spectrometer takes advantage of recent advances in digital electronics by utilizing a 4.2 GS/s arbitrary waveform generator as a frequency source and a 12 GHz digital oscilloscope to digitize the down converted molecular free induction decay (FID). Signal averaging in the time domain is used to increase the signal-to-noise ratio. The rotational constants of three unique conformers of epifluorohydrin were measured, as well as the rotational constants of the three unique ¹³C isotopomers and the ¹⁸O isotopomer (in natural abundance) of the most stable conformer. The rotational constants of the two less stable conformers differ significantly from those previously reported [F.G. Fujiwara, J.L. Painter, H. Kim, J. Mol. Struct. 41 (1977) 169-175]. Ab initio calculations were performed for all three conformations and are compared to experimental values.     

高分辨率傅里叶变换成像光谱仪光谱重建并行算法

高分辨率傅里叶变换成像光谱仪具有高空间分辨率和高光谱分辨率的特点,但光谱重建时间冗长。通过对傅里叶变换光谱重建流程分析,为研制的1024pixel(光谱维)×1024piexl(像宽)×1024piexl(像高)高分辨率紫外傅里叶变换成像光谱仪的数据立方体反演,设计了一种并行优化算法。实验表明,在6核处理器上对512M和2G的数据立方体进行变换,时间分别只需88.33s和489.75s,加速比分别为3.70和3.04,大幅度提高了运算效率。如将该算法应用到更多内核处理器上,可得到更高的加速比和更少的运算时间。     

Fractional Fourier transform of Cantor sets: further numerical study

This paper is a further work of the authors＇ paper published previously （Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316）. The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method （WTMM）. An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.     

Fourier transform spectroscopy of NbS

Emission bands attributed to the NbS radical have been observed in the near infrared and visible regions with FTS techniques using an electrodeless 2450 MHz discharge as a source. Transitions within the doublet and quartet manifolds were recorded at high resolution. The present paper gives the first rotational analysis of this molecule. Numerous bands within the doublet and quartet manifolds have been analyzed, resulting in the characterization of seven different electronic states, three in the doublet and four in the quartet manifold. The states have been labeled in analogy with NbO. The analyzed electronic states are: X⁴Σ⁻, C⁴Σ⁻, A′⁴Φ, D⁴Δ, a²Δ, c²Π, and e²Φ. Four additional substates in the doublet manifold have also been analyzed. In all, 27 vibrational sublevels have been included in the analysis, the total number of rotational lines being about 18 000. The positions of the analyzed transitions are: C⁴Σ⁻ → X⁴Σ⁻ near 15 670 cm⁻¹, D⁴Δ → A′⁴Φ near 7740 cm⁻¹, c²Π → a²Δ near 5850 cm⁻¹ and e²Φ → a²Δ near 8500 cm⁻¹. The overall picture is consistent with the corresponding analysis of NbO. However, three energy separations could not be derived from the experimental data in the case of NbS, i.e., the a²Δ− X⁴Σ⁻, A′⁴Φ− X⁴Σ⁻ and a²Δ_5/2-a²Δ_3/2 splittings. These were set to 4992, 5490, and 992 cm⁻¹, respectively, from preliminary ab initio calculations. In this way, a tentative energy level scheme could be drawn. The first order spin-orbit parameter of the A′⁴Φ state was indeterminable from the experimental data and was set to the value 170 cm⁻¹, derived from the same calculations.     

Fourier transform emission spectroscopy of some new bands of ReN

The emission spectrum of ReN has been reinvestigated in the visible region using a Fourier transform spectrometer. Two new bands have been identified with band origins near 22 110 and 22 224 cm⁻¹. These bands have a common lower state and have been assigned as the 0⁺–A1 and 0⁻–A1 transitions. After rotational analysis it was noted that the new 0⁺–A1 transition also has its upper state in common with the upper state of the [24.7]0⁺–X0⁺ transition reported previously [W.J. Balfour, J. Cao, C.X.W. Qian, S.J. Rixon, J. Mol. Spectrosc. 183 (1997) 113–118.]. This observation provides T₀₀ = 2616.26 cm⁻¹ for the A1 state. It is likely that the A1 and X0⁺ states are two spin components of the ³Σ⁻ ground state.     

Fourier transform microwave spectroscopy of aluminum hydrosulfide, AlSH

Pure rotational transitions of three isotopic species of aluminum hydrosulfide, AlSH, have been measured with a cavity pulsed jet Fourier transform microwave spectrometer. AlSH was prepared by the reaction of laser ablated Al metal with H₂S, and was stabilized in pulsed supersonic free jets of Ar. For each species the transition 1₀₁-0₀₀ was measured; hyperfine structure due to the nuclear spin of ²⁷Al was observed for the first time and analyzed. For Al³²SH and Al³²SD, the rotational constants are in excellent agreement with published values. For the third species, Al³⁴SH, this is the first observation, and its rotational constants are consistent with the published geometry. Information on the electronic structure of the molecule has been obtained using the ²⁷Al nuclear quadrupole coupling constants and nuclear spin-rotation constants. The latter have been used to evaluate ²⁷Al NMR shielding parameters, which are compared with those of other ²⁷Al compounds. These shieldings have been found to be in excellent agreement with theoretical predictions. The results should also help facilitate astrophysical searches for the molecule.     

窗扫型成像光谱仪数据处理及误差校正研究

窗扫型傅里叶变换成像光谱仪具有高光通量和无动镜等特点,同时也增加了数据处理的难度,需要对采集的原始干涉图进行重组。通过对其数据处理流程特点的分析,设计了一种归一化算法,对由干涉图重组时产生的误差进行了校正,并对在数据采集过程中干涉图的中心暗纹位置的采样误差进行了二次曲线拟合校正。整个数据处理过程实现了从干涉数据立方体到光谱数据立方体的变换。从理论分析和实验结果的比较中验证了误差校正方法的有效性。     

Emission Fourier transform spectroscopy for the remote sensing of the atmosphere

Fourier transform spectrometers (FTS), thanks to their intrinsic advantages of high throughput, high spectral resolution and multiplex acquisition of spectral channels, offer a powerful tool for the characterisation of the Earth's atmosphere. The use of photon noise limited detectors in FTS instruments operating in the middle/far infrared spectral region permits high sensitivity emission spectroscopy measurements, without the limitations arising from the use of an external radiation source. The wide operating spectral range of FTS instruments makes possible simultaneous detection of different atmospheric chemical species that show rotational and vibrational spectral bands in the middle/far infrared region.Spatially resolved measurements of the concentration of the interesting species are of fundamental interest in the study of local phenomena in atmospheric chemistry and physics, and can be obtained through the use of various observation and data inversion techniques. Among these, the best results in terms of vertical resolution are achieved through the limb sounding observation technique from airborne platform.As an example of possibilities offered by the above considered technique, results obtained from the SAFIRE-A (Spectroscopy of the Atmosphere using Far InfraRed Emission-Airborne) during the Antarctic campaign APE-GAIA (Airborne Polar Experiment-Geophysica Aircraft In Antarctica, Ushuaia, Argentina, September–October, 1999) are presented.