Imaged deconvolution: a method for extracting high-resolution NMR spectra from inhomogeneous fields

We present a novel method for obtaining high resolution NMR spectra in the presence of grossly inhomogeneous magnetic fields, such as those encountered in one-sided access NMR. Our method combines the well-known principle of reference deconvolution with NMR imaging in order to resolve spectral features with frequency resolution orders of magnitude smaller than the prevailing line-broadening due to field inhomogeneity. We demonstrate that, in cases of inhomogeneous field line-broadening more than an order of magnitude larger than the spectral features to be resolved, rather than performing reference deconvolution on the sample as a whole, it is more favourable in terms of SNR to divide the target region of a sample into smaller sub-regions, by means of chemical shift imaging, and then to perform reference deconvolution on the individual sub-region spectra, finally summing the results In this way, significant resolution enhancements can be obtained in the presence of severe magnetic field inhomogeneity without an unacceptable loss in SNR.     

High-resolution NMR spectra in inhomogeneous and unstable fields via the three-pulse method

In modern solution nuclear magnetic resonance (NMR), the spectral resolution is mainly dependent on the spatial homogeneity and temporal stability of the magnetic field. The spectral linewidths are usually proportional to the overall field homogeneity and the stability experienced by the sample. Many high-resolution NMR methods have been developed, but few are applicable in inhomogeneous and unstable fields. In this paper, a high-resolution three-pulse method based on intermolecular zero-quantum coherences (iZQCs) is proposed. Since this method is insensitive to field inhomogeneity and instability, spectral information such as the chemical shift can be retained in the resulting spectra. In comparison with the CPMG-HOMOGENIZED method, the new method provides almost pure solvent–solute iZQC signals.     

High-resolution magnetic relaxation dispersion measurements of solute spin probes using a dual-magnet system.

The magnetic field dependence of the nuclear spin-lattice relaxation rate provides a detailed report of the spectral density functions that characterize the intra- and intermolecular fluctuations that drive magnetic relaxation. We have addressed the difficult sensitivity and resolution problems associated with low magnetic field strengths by using two magnets in close proximity and shielded from each other. The sample is stored in the high magnetic field, pneumatically driven to the variable satellite field, then returned to the high field for detection at high resolution. A magnetic shield effectively decouples the two magnets so that varying the satellite field strength has minimal effect on the field strength and shim of the high field magnet. The disadvantage of the sample-shuttle magnet-pair system is the restriction imposed on the relaxation times by the finite shuttle times. Experiments not described here have shown this rate maximum to be about 20 s(-1) for most practical solutions. However, we demonstrate here that the sensitivity gains over switched-current magnet systems permit characterization of solute inter- and intramolecular dynamics over the time scale range from tens of microseconds to less than a picosecond. This range permits investigation of a number of crucial chemical dynamics questions, while high sensitivity permits examination of a variety of solute spins. Representative data are presented for (1)H, (111)Cd, and (7)Li.     

Numerical analysis of the spectral response of an NSOM measurement

Near-field Scanning Optical Microscopy (NSOM) is a powerful tool for investigating optical field with resolution greater than the diffraction limit. In this work, we study the spectral response that would be obtained from an aperture NSOM system using numerical calculations. The sample used in this study is a bowtie nanoaperture that has been shown to produce concentrated and enhanced field. The near- and far-field distributions from a bowtie aperture are also calculated and compared with what would be obtainable from a NSOM system. The results demonstrate that it will be very difficult to resolve the true spectral content of the near-field using aperture NSOM. On the other hand, the far-field response may be used as a guide to the near-field spectrum.     

A multiplexed high‐resolution imaging spectrometer for resonant inelastic soft X‐ray scattering spectroscopy

The optical design of a two‐dimensional imaging soft X‐ray spectrometer is described. A monochromator will produce a dispersed spectrum in a narrow vertical illuminated stripe (～2 µm wide by ～2 mm tall) on a sample. The spectrometer will use inelastically scattered X‐rays to image the extended field on the sample in the incident photon energy direction (vertical), resolving the incident photon energy. At the same time it will image and disperse the scattered photons in the orthogonal (horizontal) direction, resolving the scattered photon energy. The principal challenge is to design a system that images from the flat‐field illumination of the sample to the flat field of the detector and to achieve sufficiently high spectral resolution. This spectrometer provides a completely parallel resonant inelastic X‐ray scattering measurement at high spectral resolution (～30000) over the energy bandwidth (～5 eV) of a soft X‐ray absorption resonance.     

Probe--sample coupling in the magnetic resonance force microscope

The magnetic resonance force microscope (MRFM) provides a route to achieving scanned probe magnetic resonance imaging with extremely high spatial resolution. Achieving this capability will require understanding the force exerted on a microscopic magnetic probe by a spatially extended sample over which the probe is scanned. Here we present a detailed analysis of this interaction between probe and sample. We focus on understanding the situation where the micromagnet mounted on the mechanical resonator generates a very inhomogeneous magnetic field and is scanned over a sample with at least one spatial dimension much larger than that of the micromagnet. This situation differs quite significantly from the conditions under which most MRFM experiments have been carried out where the sample is mounted on the mechanical resonator and placed in a rather weak magnetic field gradient. In addition to the concept of a sensitive slice (the spatial region where the magnetic resonance condition is met) it is valuable to map the forces exerted on the probe by spins at various locations; this leads to the concept of the force slice (the region in which spins exert force on the resonator). Results of this analysis, obtained both analytically and numerically, will be qualitatively compared with an initial experimental finding from an EPR-MRFM experiment carried out on DPPH at 4 K.     

High-resolution NMR of static samples by rotation of the magnetic field

Mechanical rotation of a sample at 54.7 degrees with respect to the static magnetic field, so-called magic-angle spinning (MAS), is currently a routine procedure in nuclear magnetic resonance (NMR). The technique enhances the spectral resolution by averaging away anisotropic spin interactions thereby producing isotropic-like spectra with resolved chemical shifts and scalar couplings. It should be possible to induce similar effects in a static sample if the direction of the magnetic field is varied, e.g., magic-angle rotation of the B0 field (B0-MAS). Here, this principle is experimentally demonstrated in a static sample of solid hyperpolarized xenon at approximately 3.4 mT. By extension to moderately high fields, it is possible to foresee interesting applications in situations where physical manipulation of the sample is inconvenient or impossible. Such situations are expected to arise in many cases from materials to biomedicine and are particularly relevant to the novel approach of ex situ NMR spectroscopy and imaging.     

Localization microscopy (SPDM) facilitates high precision control of lithographically produced nanostructures

Nanoscale resolution in material sciences is usually restricted to scanning electron beam microscopes. Here we present a procedure that allows single molecule resolution of the sample surface with visible light. Highlighting the performance we used electron beam lithography to generate highly regular nanostructures consisting of interconnected cubes. The samples were labeled with Alexa 647 dyes. The spatial organization of the dyes on nanostructured surfaces was localized with single molecule resolution using localization microscopy. This succeeded also in an absolute spatial calibration of the localization method applied (spectral precision distance microscopy/SPDM). The findings will contribute to the field of product control for industrial applications and long-term fluorescence imaging.     

On the voxel size and magnetic field strength dependence of spectral resolution in magnetic resonance spectroscopy

While the inherent low sensitivity of in vivo MR spectroscopy motivated a trend towards higher magnetic fields, B(0), it has since become apparent that this increase does not seem to translate into the anticipated improvement in spectral resolution. This is attributed to the decrease of the transverse relaxation time, T(2)*, in vivo due to macro- and mesoscopic tissue susceptibility. Using spectral contrast-to-noise ratio (SCNR) arguments, we show that if in biological systems the linewidth (on the frequency scale) increases linearly with the field, the spectral resolution (in parts per million) improves approximately as the fifth-root of B(0) for chemically shifted lines and decreases as about B(0)(4/5) (in hertz) for a structure of J-coupled multiplets. It is also shown that for any given B(0) there is a unique voxel size that is optimal in spectral resolution, linking the spectral and spatial resolutions. Since in practical applications the spatial resolution may be dictated by the target anatomy, nomograms to determine the B(0) required to achieve the desired spectral resolution at that voxel size are presented. More generally, the scaling of the nomograms to determine the achievable spectral and spatial resolutions at any given field is described.     

High quality electromagnetically induced transparency spectroscopy of ~(87)Rb in a buffer gas cell with a magnetic field

We have studied the phenomenon of electromagnetically induced transparency(EIT) of ~(87)Rb vapor with a buffer gas in a magnetic field at room temperature. It is found that the spectral lines caused by the velocity selective optical pump effects get much weaker and wider when the sample cell is mixed with a 5-Torr N_2 gas while the EIT signal is kept almost unchanged. A weighted least-square fit is also developed to remove the Doppler broadening completely. This spectral method provides a way to measure the Zeeman splitting with high resolution, for example, the Λ-type EIT resonance splits into four peaks on the D_2 line of ~(87)Rb in the thermal 2-cm vapor cell with a magnetic field along the electric field of the linearly polarized coupling laser. The high-resolution spectrum can be used to lock the laser to a given frequency by tuning the magnetic field.     

Uniaxial Diffusional Narrowing of NMR Lineshapes for Membrane Proteins Reconstituted in Magnetically Aligned Bicelles and Macrodiscs

Structure and dynamics of membrane proteins can be effectively studied by oriented-sample solid-state nuclear magnetic resonance (NMR) techniques when the lipid bilayers are macroscopically aligned with respect to the main magnetic field. Magnetic alignment of the protein-containing membrane bilayer results from the negative susceptibility anisotropy of the lipid hydrocarbon interior yielding perpendicular sample alignment. At this orientation, while the uniformity of alignment represents an essential prerequisite for obtaining high-quality NMR spectra, further line narrowing is obtained by uniaxial motional averaging of the azimuthal parts of the chemical shift anisotropies and dipolar couplings. The motional averaging is brought about by uniaxial rotational diffusion of the protein molecules about the normal to the membrane surface, which is perpendicular to the magnetic field. Uniaxial averaging is efficient when the motion about the axis of alignment becomes sufficiently fast (on the timescale of the dipolar couplings and chemical shift anisotropies). Line narrowing under uniaxial rotation can be theoretically modeled using the stochastic Liouville equation. In this mini-review, we illustrate the method of uniaxial averaging for the relatively small Pf1 coat protein which exhibits excellent resolution in magnetically aligned bicelles due to its fast uniaxial diffusion and even superior resolution in large (30 nm) nanodiscs (macrodiscs) stabilized by a belt peptide. Spectra of Pf1 coat protein in polymer-stabilized macrodiscs, an alternative and more robust alignment media, are presented. We also report on preliminary spectra of a much larger protein—uniformly ¹⁵N labeled M1-M4 domain for the human acetylcholine receptor. While some spectral resolution is apparent, significantly broader linewidths emphasize the need for creating fast rotating discoidal membrane mimetics.     

Real-Time in Vitro Drug Dissolution Studies of Tablets Using Volume-Localized NMR (MRS)

An approach to measure in vitro drug dissolution rates employing spatially resolved nuclear magnetic resonance (NMR) is reported, as a complement to standard United States Pharmacopeia protocols. Measurements are performed under conditions that mimic the physiological (pH 1, temperature 37° C). In order to register realistic dissolution rates, the sample is stirred in the magnetic field, employing a setup that is described. While the stirrer in the sample cell does degrade spectral resolution even in volume-localized mode, it proves possible nevertheless to acquire ‘high resolution??information. Measurements are performed employing ‘point resolved spectroscopy??(PRESS) by tracking drug concentration in a selected voxel in the dissolution medium as a function of time. The dissolution of the tablets in vitro follows first-order kinetics under the non-sink conditions of these experiments, the measured rate constants reflecting characteristic differences in dissolution rates of different formulations. We supplement this study with diffusion-weighted imaging of water ingress into the tablets, confirming the trends.     

A rapid,spatially dispersive frequency comb spectrograph aimed at gas phase chemical reaction kinetics

This New Views article will highlight some recent advances in high sensitivity gas detection using direct infrared absorption frequency comb laser spectroscopy, with a focus on frequency comb use in chemical reaction kinetics and our own contribution to this field. Our recently implemented detection technique uses a combination of a 12.9?GHz free spectral range virtually imaged phased array and diffraction grating to spatially disperse the mid-infrared frequency comb onto a camera. Individual frequencies or ‘comb teeth’ of a 250?MHz repetition-rate frequency comb are able to be resolved. High molecular sensitivity is achieved by increasing the interaction path length using a Herriott multipass cell. High spectral resolution, broadband spectral coverage, and high molecular sensitivity are all achieved on an adjustable 1–50 µs timescale, making this frequency comb apparatus ideal for measuring chemical reaction kinetics where multiple absorbing species can be monitored simultaneously. This New Views article will also discuss some of the challenges and decisions that chemists might face in implementing this advanced physics technology in their own laboratory.

Spatially dispersed 250 MHz mid-infrared frequency comb laser, with absorption of some frequencies by a dilute sample of methane.     

Maghemite in basalt studied by Mössbauer spectroscopy in external magnetic field

In the present study, we investigate the feasibility of detecting and determining the presence of maghemite in rock samples, by obtaining Mössbauer spectra in an external magnetic field of 1.6 T at room temperature. The interaction of the external magnetic field and the magnetic moments of the sublattices will induce differential shifts in the peak positions. By this method, we can assign some lower limit of the amount of maghemite in the sample. The results are compared with a model for a mixture of maghemite and stoichiometric magnetite.     

Unilateral MRI using a rastered projection

Unilateral magnetic resonance techniques, where magnet and radio frequency (RF) coil are placed on one side of the sample, can provide valuable information about a sample which otherwise cannot be accommodated in conventional high spectral resolution magnetic resonance systems. A unilateral magnetic resonance imaging approach utilizing the stray field from a disc magnet and a butterfly geometry RF coil is described. The coil excites spins in a volume centered around an arc through the sample. Translating the RF coil relative to the magnet and recording the signal at each translational location creates a projection of the signal in a tomographic slice through the sample. Rotating the RF coil relative to the sample and repeating the translation creates projections through the sample at different angles. Backprojecting this information yields an image. A proof of concept device operating on this principle at 12.4 MHz was constructed and characterized. Projections through three phantoms are presented with a 1.2-4 cm field of view, thickness of 102 microm, and at a distance of 3mm from the RF coil and 14 mm from the magnet. The edge spread function (ESF) was measured resulting in a 4mm full width at half maximum (FWHM) line spread function (LSF) estimation using a Gaussian model. An example of one reconstructed image is presented.     

The harmonic inversion of the field-swept fixed-frequency resonance spectrum

When the spin Hamiltonian is a linear function of the magnetic field intensity the resonance fields can be determined, in principle, by an eigenfield equation. In this report, we show a new technical approach to the resonance field problem where the eigenfield equation leads to a dynamic equation or, more specifically, to a first order differential equation of a variable L(x), where x is associated with the magnetic field h. Such differential equation has the property that: its stationary solution is the eigenfield equation and the spectral information contained in L(x) is directly related to the resonance spectrum. Such procedure, known as the "harmonic inversion problem" (HIP), can be solved by the "filter diagonalization method" (FDM) providing sufficient precision and resolution for the spectral analysis of the dynamic signals. Some examples are shown where the resonance fields are precisely determined in a single procedure, without the need to solve eigenvalue equations.     

Micrometer scale resolution of materials by stray-field Magnetic Resonance Imaging

As Magnetic Resonance Imaging devices are becoming more and more powerful, resolutions as small as 10 μm can now be obtained. But, this is only possible when systems with slow transverse relaxation rates, like living tissues, are investigated. In this case, the time available for gradients space-encoding is long, and high k values can be reached in the Fourier domain. However, numerous materials have fast relaxation rates, thus limiting the spatial resolution to a few hundreds of microns. The Stray Field Imaging technique has solved this problem by using a very high (typically 5000 G/cm) static gradient. Consequently, the trajectory in k space is accelerated and it is possible, in principle, to reach a micrometer resolution in a few hundreds of microseconds. Most of the time, however, only resolutions in the millimeter range can be achieved due to mispositioning of the sample within the static magnetic field. Here, we show that by finely mapping the magnetic field and precisely positioning the sample, it is possible with a standard spectrometer to reach a micrometer resolution even on very fast relaxing materials.     

隧穿磁电阻效应磁场传感器中低频噪声的测量与研究

基于隧穿磁电阻效应(TMR)的磁场传感器具有很高的磁场灵敏度, 但同时噪声也较大,有效抑制TMR磁场传感器的噪声, 尤其是低频噪声的抑制对于其在高灵敏度要求场合的应用具有重要的意义. 本文采用高精度数据采集卡搭建了噪声测量系统, 测量了全桥结构TMR磁场传感器的噪声频谱图, 发现TMR传感器的噪声在低频段表现为1/f特性, 同时噪声功率谱密度与工作电流平方成正比关系; 低频噪声在自由层翻转区间内噪声急剧增大, 证明了1/f噪声主要来源于磁噪声, 这一结果为TMR磁场传感器的噪声特性优化指明了方向.     

时间分辨电子显微镜的数值模拟

对时间分辨电子显微镜进行了数值模拟。通过求解从样品透射出来的电子在静态磁场和动态电场的混合场中的运动,评价时间分辨电子显微镜的动态时空特性。根据该数值模拟,时间分辨电子显微镜能够在荧光屏上获得样品在不同时刻的6幅显微分幅图像。     

Magnetic relaxation dispersion probe

The magnetic field dependence of nuclear spin-lattice relaxation rates provides a powerful approach to characterizing intra and intermolecular dynamics. NMR spectrometers that provide extensive magnetic relaxation dispersion profiles may switch magnetic field strengths rapidly by either moving the sample or by changing the current in an electromagnet. If the sample is moved, the polarization and detection fields may be very high, which provides both high sensitivity and resolution. This report summarizes the design of a pneumatic sample transport system for glass sample containers that may be used in either a dual magnet spectrometer or in a single magnet system that exploits the fringe field as the secondary magnetic field.