Hadamard Spectroscopy Research Articles

Microscanning in Hadamard spectroscopy.

Hadamard spectroscopy is a method of taking spectroscopic measurements suited to domains such as far infrared, where the sensor noise is dominant. Unfortunately, the signal-to-noise ratio of such a system scales poorly with the resolution. In this paper, we analyze a technique called microscanning that attempts to solve this problem by combining several lower resolution "preview" spectra to form a higher resolution spectrum. We provide a theoretical analysis of the method concerning the noise reduction and blurring. We conduct simulations based on the measured far infrared spectra of minerals in order to determine if the noise reduction can outweigh the loss in accuracy caused by the blurring effect, and we demonstrate the microscanning method in experimental conditions. We conclude that the microscanning method provides a noise reduction by a factor proportional to the number of previews and that it can be useful in far infrared spectroscopy.

Compact multichannel high-resolution micro-electro-mechanical systems-based interrogator for Fiber Bragg grating sensing

We propose a novel type of compact high-resolution multichannel micro-electro-mechanical systems (MEMS)-based interrogator, where we replace the linear detector with a digital micromirror device (DMD). The DMD is typically cheaper and has better pixel sampling than an InGaAs detector used in the 1550nm range, which leads to cost reduction and better performance. Moreover, the DMD is a 2D array, which means that multichannel systems can be implemented without any additional optical components in the interrogator. This makes the proposed interrogator highly cost-effective, particularly for multichannel systems. The digital nature of the DMD also provides opportunities for advanced programmable Hadamard spectroscopy, which, without significant penalties, can greatly improve the wavelength fit resolution. Our results show that DMDs can be used in high-resolution spectroscopy and for Fiber Bragg grating (FBG) interrogation.

Fast acquisition of multidimensional NMR spectra of solids and mesophases using alternative sampling methods

Unique information about the atom-level structure and dynamics of solids and mesophases can be obtained by the use of multidimensional nuclear magnetic resonance (NMR) experiments. Nevertheless, the acquisition of these experiments often requires long acquisition times. We review here alternative sampling methods, which have been proposed to circumvent this issue in the case of solids and mesophases. Compared to the spectra of solutions, those of solids and mesophases present some specificities because they usually display lower signal-to-noise ratios, non-Lorentzian line shapes, lower spectral resolutions and wider spectral widths. We highlight herein the advantages and limitations of these alternative sampling methods. A first route to accelerate the acquisition time of multidimensional NMR spectra consists in the use of sparse sampling schemes, such as truncated, radial or random sampling ones. These sparsely sampled datasets are generally processed by reconstruction methods differing from the Discrete Fourier Transform (DFT). A host of non-DFT methods have been applied for solids and mesophases, including the G-matrix Fourier transform, the linear least-square procedures, the covariance transform, the maximum entropy and the compressed sensing. A second class of alternative sampling consists in departing from the Jeener paradigm for multidimensional NMR experiments. These non-Jeener methods include Hadamard spectroscopy as well as spatial or orientational encoding of the evolution frequencies. The increasing number of high field NMR magnets and the development of techniques to enhance NMR sensitivity will contribute to widen the use of these alternative sampling methods for the study of solids and mesophases in the coming years.

Lab‐on‐a‐Chip Reactor Imaging with Unprecedented Chemical Resolution by Hadamard‐Encoded Remote Detection NMR

AbstractThe development of microfluidic processes requires information‐rich detection methods. Here we introduce the concept of remote detection exchange NMR spectroscopy (RD‐EXSY), and show that, along with indirect spatial information extracted from time‐of‐flight data, it provides unique information about the active regions, reaction pathways, and intermediate products in a lab‐on‐a‐chip reactor. Furthermore, we demonstrate that direct spatial resolution can be added to RD‐EXSY efficiently by applying the principles of Hadamard spectroscopy.

Lab-on-a-chip reactor imaging with unprecedented chemical resolution by Hadamard-encoded remote detection NMR.

The development of microfluidic processes requires information-rich detection methods. Here we introduce the concept of remote detection exchange NMR spectroscopy (RD-EXSY), and show that, along with indirect spatial information extracted from time-of-flight data, it provides unique information about the active regions, reaction pathways, and intermediate products in a lab-on-a-chip reactor. Furthermore, we demonstrate that direct spatial resolution can be added to RD-EXSY efficiently by applying the principles of Hadamard spectroscopy.

Hyperpolarized Hadamard Spectroscopy Using Flow NMR

The emergence of the dissolution dynamic nuclear polarization (D-DNP) technique provides an important breakthrough to overcome inherent sensitivity limitations in nuclear magnetic resonance (NMR) experiments. In dissolution DNP, only a small amount of frozen sample is polarized, dissolved, and injected into an NMR spectrometer. Although substantially enhanced NMR signals can be obtained, the single scan nature of this technique a priori impedes the use of correlation experiments, which represent some of the most powerful applications of NMR spectroscopy. Here, an alternative method for multiscan spectroscopy from D-DNP samples utilizing a flow NMR probe is described. Multiple hyperpolarized segments of sample are sequentially injected using a purpose designed device. Hadamard spectroscopy can then be applied for obtaining chemical shift correlation information even from a small number of scans. This capability is demonstrated with a four-scan data set for obtaining the [(13)C,(1)H] correlations in the test molecule 1-butanol. Because of the effects of spin-lattice relaxation and concentration gradients in the D-DNP experiment, the subtractive process for Hadamard reconstruction requires an additional step of intensity scaling. For this purpose, a reconstruction procedure was developed that uses entropy maximization and is robust with respect to noise and signal overlap. In a broader sense, the multiscan NMR as described here is amenable to various correlation NMR experiments, and increases the versatility of D-DNP in small-molecule characterization.

Parallel receivers and sparse sampling in multidimensional NMR

The recent introduction of NMR spectrometers with multiple receivers permits spectra from several different nuclear species to be recorded in parallel, and several standard pulse sequences to be combined into a single entity. It is shown how these improvements in the flow and quality of spectral information can be significantly augmented by compressive sensing techniques – controlled aliasing, Hadamard spectroscopy, single-point evaluation of evolution space (SPEED), random sampling, projection-reconstruction, and hyperdimensional NMR. Future developments of these techniques are confidently expected to mitigate one of the most serious limitations in multidimensional NMR – the excessive duration of the measurements.

Application of Hadamard spectroscopy to automated structure verification in high‐throughput NMR

Combined verification using 1-D proton and HSQC has been proved to be quite successful; the acquisition time of HSQC spectra, however, can be limiting in its high-throughput applications. The replacement with Hadamard HSQC can significantly enhance the throughput. We hereby propose a protocol to optimize the grouping of the predicted carbon chemical shifts from the proposed structure and the associated Hadamard frequencies and bandwidths. The resulting Hadamard HSQC spectra compare favorably with their Fourier-transformed counterparts, and have demonstrated to perform equivalently in terms of combined verification, but with several fold enhancement in throughput, as illustrated for 21 commercial available molecules and 16 prototypical drug compounds. Further improvement of the verification accuracy can be achieved by the cross validation from Hadamard TOCSY, which can be acquired without much sacrifice in throughput.

Spin state selective Hadamard encoding during transfer periods using multiple selective CW-HCP

Hadamard spectroscopy today represents an alternative to conventional Fourier transform spectroscopy. The selective inversion of several narrow frequency bands is typically achieved by taylored inversion pulses in place of t 1-evolution periods. However, band-selective inversion can also be achieved during coherence transfer steps, thereby shortening the period during which the magnetization is in the transverse plane. Using CW heteronuclear cross polarization (CW-HCP) as an example for highly selective coherence transfer, the implementation of Hadamard encoding within a transfer step is presented. Transfer characteristics, the preparation of multiple frequency selective CW-HCP and the possibility of acquiring spin state selective spectra are discussed in detail. The theoretical results are verified on two examples involving a cyclic pentapeptide and ubiquitin.

Hadamard NMR spectroscopy for two-dimensional quantum information processing and parallel search algorithms

Hadamard spectroscopy has earlier been used to speed-up multi-dimensional NMR experiments. In this work, we speed-up the two-dimensional quantum computing scheme, by using Hadamard spectroscopy in the indirect dimension, resulting in a scheme which is faster and requires the Fourier transformation only in the direct dimension. Two and three qubit quantum gates are implemented with an extra observer qubit. We also use one-dimensional Hadamard spectroscopy for binary information storage by spatial encoding and implementation of a parallel search algorithm.

Spectral unraveling by space-selective Hadamard spectroscopy

Spectral unraveling by space-selective Hadamard spectroscopy (SUSHY) enables recording of NMR spectra of multiple samples loaded in multiple sample tubes in a modified spinner turbine and a regular 5 mm liquids NMR probe equipped with a tri-axis pulsed field gradient coil. The individual spectrum from each sample is extracted by adding and subtracting data that are simultaneously obtained from all the tubes based on the principles of spatially resolved Hadamard spectroscopy. The well-known Hadamard spectroscopy has been applied for spatial selection and the method utilizes standard configuration of NMR instrument hardware. The SUSHY method can be easily incorporated in multi-dimensional multi-tube NMR experiments. This method combines the excitation multiplexing, natural advantage of FTNMR, and sample multiplexing and offers high-throughput by reducing the total experimental time by up to a factor of four in a 4-tube mode.

New methods for fast multidimensional NMR.

Considerable excitement has been aroused by recent new methods for speeding up multidimensional NMR experiments by radically modifying the normal time-domain sampling protocols. These new schemes include the filter diagonalization method, GFT-NMR, the single-scan two-dimensional technique, Hadamard spectroscopy, and a proposal based on projection-reconstruction of three-dimensional spectra. All these methods deliver appreciable improvements in the speed of data acquisition and show promise for speeding up multidimensional NMR of proteins. This perspective aims to describe these important new procedures in simple terms and to comment on their advantages and possible limitations.

NMR analysis of the trisaccharide 2′‐fucosyllactose by heteronuclear trans‐glycosidic coupling constants and molecular simulations

Abstract1H, 13C NMR coupling constants across the glycosidic linkages were measured for the trisaccharide α‐L‐Fucp‐(1→2)‐β‐D‐Galp‐(1→4)‐D‐Glcp from human milk and its reduced analogue α‐L‐Fucp‐(1→2)‐β‐D‐Galp‐(1→4)‐D‐Glucitol employing one‐dimensional multiple‐site 13C excitation experiments. Hadamard spectroscopy and pulsed field gradients were also used with or without band‐selective 1H decoupling during the acquisition period. The experimental scalar coupling constants were compared to those calculated from Langevin dynamics simulations employing different molecular mechanics force fields. An analysis of 3J(C,H) values determined with this NMR technique on di‐ and trisaccharides is also performed. Copyright © 2001 John Wiley & Sons, Ltd.

Molecular Dynamics Simulation and Nuclear Magnetic Resonance Studies of the Terminal Glucotriose Unit Found in the Oligosaccharide of Glycoprotein Precursors

The trisaccharide α-d-Glcp-(1 → 2)-α-d-Glcp-(1 → 3)-α-d-Glcp-OMe, a model for the terminal glucotriose in Glc3Man9GlcNAc2 in glycoprotein precursors, has been investigated by computer simulations and NMR spectroscopy. Molecular dynamics simulations were performed for 1 ns in aqueous solution and 20 ns in vacuo using the CHARMM-based force fields PARM22 and CHEAT95. An additional Monte Carlo simulation with the HSEA force field was also carried out. Experimental NMR data in water solution was obtained from measurement of long-range 1H,13C heteronuclear trans-glycosidic coupling constants, 3JH,C, using one-dimensional Hadamard spectroscopy. Calculation of the 3JH,C values from the simulations showed a varying degree of agreement to experimental data. It could be shown from simulation that the φ torsion angles differed, which was corroborated by the NMR measurements. Analyses were done of radial distribution functions and of hydrogen bonds. It was suggested that intermolecular hydrogen bonds were present, but in contrast to simulation the results from NMR spectroscopy did not support any major contribution. Hence, their influence on the conformation of the trisaccharide is rather small. Comparison of 1H NMR chemical shifts for the trisaccharide and the glucotriose in Glc3Man8GlcNAc revealed high similarity. However, the derived conformation of the model substance in this work differed at one glycosidic torsion angle compared to the glucotriose on a large oligosaccharide.

Long-range proton-carbon coupling constants in conformational analysis of oligosaccharides

Long-range heteronuclear coupling constants, 3J(C,H), were measured across glycosidic linkages in β-linked disaccharides and also for vicinally disubstituted trisaccharides. One-dimensional multiple-site 13C excitation experiments using Hadamard spectroscopy and band-selective 1H decoupling during the acquisition period were used in conjunction with pulsed field gradients for coherence selection in the 1H detected experiment. For one dihedral angle the 3J(C,H) value could only be unambiguously determined utilizing the band-selective 1H decoupling. The 2D EXSIDE was also used for the measurement of 3J(C,H) values and the results showed excellent agreement with those of the 1D measurements. The influence of solvent, water and water–dimethyl sulfoxide (7:3), on conformation was investigated, but showed only small changes in 3J(C,H) values. In general, the long-range heteronuclear coupling constants related to the ϕ dihedral angles (3.6–4.3 Hz) were smaller than those of the ψ dihedral angles (4.3–5.3 Hz). A comparison with 3J(C,H) values from Monte Carlo or Langevin dynamics simulations showed better agreement for the ψ dihedral angles than for the ϕ dihedral angles as calculated using a Karplus relationship. © 1998 John Wiley & Sons Ltd.

Hadamard spectroscopy with a two-dimensional detecting array

In a conventional grating spectrograph consisting of a single entrance slit, a grating, and a multichannel (imaging) detector, considerable light throughput advantage can be realized by replacement of the single entrance slit with a mask. This replacement can yield a signal-to-noise ratio increase because of increased light collection over an extended area of the mask when compared with a single slit. The mask produces a spectrum on the detector, which is the convolution of the mask pattern and the spectral distribution of the light source. To retrieve the spectrum, the spectrum has to be inverted. In special cases in which emission spectra are superimposed on weak backgrounds, the signal-to-noise advantage is preserved through the inversion process. Thus this technique is valuable in the observation of light sources that are produced by atomic or molecular emissions such as aurora, airglow, some interstellar emission, or laboratory spectra. Considerable signal-to-noise advantages can also be realized when the background noise of the imaging detector is not negligible. The spectral mixing of the light from the mask on the detector causes high photon fluxes on the detector, which tend to swamp the detector noise. This is a particularly important advantage in the application of CCD's as detectors because they can have significant background noise. The technique was demonstrated by computer simulations and laboratory tests.

Fast delta Hadamard transform

In many fields (e.g., spectroscopy, imaging spectroscopy, photoacoustic imaging, coded aperture imaging) binary bit patterns known as m sequences are used to encode (by multiplexing) a series of measurements in order to obtain a larger throughput. The observed measurements must be decoded to obtain the desired spectrum (or image in the case of coded aperture imaging). Decoding in the past has used a technique called the fast Hadamard transform (FHT) whose chief advantage is that it can reduce the computational effort from N(2) multiplies to N log(2) N additions or subtractions. However, the FHT has the disadvantage that it does not readily allow one to sample more finely than the number of bits used in the m sequence. This can limit the obtainable resolution and cause confusion near the sample boundaries (phasing errors). We have developed both 1-D and 2-D methods (called fast delta Hadamard transforms, FDHT) which overcome both of the above limitations. Applications of the FDHT are discussed in the context of Hadamard spectroscopy and coded aperture imaging with uniformly redundant arrays. Special emphasis has been placed on how the FDHT can unite techniques used by both of these fields into the same mathematical basis.

Errors in Hadamard spectroscopy or imaging caused by imperfect masks

An analysis is given of the errors in Hadamard spectroscopy that are caused by transparent slits in the mask being systematically wider or narrower than they should be. It is shown that if the input spectrum consists of a single line, the distorted spectrum that is actually calculated consists of this line, plus four small blips. When the transparent slits are too wide, these blips are of equal height and the same sign, one pair surrounding the line, and another pair displaced a certain distance from it. When the slits are too narrow, the displaced blips have the same amplitude, but are negative. The response to an arbitrary input spectrum is then determined from this. The same method of analysis may also be used to handle other types of errors.

Hadamard Spectroscopy

The basic concept of Hadamard spectroscopy is presented. General methods are given for the construction of cyclic measurement matrices. A new algorithm, which permits adaptation of the fast Hadamard transform to the calculation of spectral intensities when the measurement matrices are cyclic, is introduced. Some applications are also briefly discussed.