Use of composite refocusing pulses to form spin echoes

The radiofrequency pulses used in NMR are subject to a number of imperfections such as those caused by inhomogeneity of the radiofrequency (B(1)) field and an offset of the transmitter frequency from precise resonance. The effect of these pulse imperfections upon a refocusing pulse in a spin-echo experiment can be severe. Many of the worst effects, those that distort the phase of the spin echo, can be removed completely by selecting the echo coherence pathway using either the "Exorcycle" phase cycle or magnetic field gradients. It is then tempting to go further and try to improve the amplitude of the spin-echo signal by replacing the simple refocusing pulse with a broadband composite 180° pulse that compensates for the relevant pulse imperfection. We show here that all composite pulses with a symmetric or asymmetric phase shift scheme will reintroduce phase distortions into the spin echo, despite the selection of the echo coherence pathway. In contrast, all antisymmetric composite pulses yield no phase distortion whatsoever, both on and off resonance, and are therefore the correct symmetry of composite refocusing pulse to use. These conclusions are verified using simulations and (31)P MAS NMR spin-echo experiments performed on a microporous aluminophosphate.     

DPSD在低场核磁共振回波信号检测中的应用

核磁共振回波信号幅度微弱,容易受到来自电子器件和外部环境噪声的干扰,要求回波检测方法既能实时采集回波数据,又能较好的抑制噪声. 对比分析不同微弱信号检测方法的优缺点,归纳出DPSD(Digital Phase-Sensitivity Detection)方法在回波检测应用中的优越性. 通过仿真计算, 提出适用于回波信号检测的最佳滤波器窗函数. 在自制的核磁共振仪器上进行实验,结果表明,DPSD方法在满足回波信号实时测量的同时,有效压制了噪声,能准确的提取出低场核磁共振回波信号的幅度和相位信息.     

Excitation conditions for quantitative determination of quadrupolar spins with one pulse or spin-echo sequences in solid-state NMR

One of the major problems concerning quadrupolar spins in solid-state NMR is their quantification. If the optimal excitation conditions with one radio-frequency pulse are widespread known now, this is not the case with the spin-echo sequences. This paper reports some theoretical predictions and their limitations concerning quantification with the echo obtained with spin-echo resonances. To realize that, first, the relative line intensity of a transition (m+1,m) is defined in order to allow the comparison of results, from different authors. Then results concerning one pulse excitation on a spinI=3/2 are summarized. The condition of short pulse excitation is generalized to higher spins using the Pauli matrices applied to the two extreme cases: hard pulse or non selective excitation, and selective excitation. Finally the same procedure has been followed for the spin-echo sequence involving twox-pulses. It was shown that the optimum conditions are: both the pulse length must be sufficiently short, and the interpulse delay should be taken as short as the duration of the FID provided the phase of the second pulse alternates without changing the receiver phase. In these conditions, the relative echo amplitude depends linearly on the first pulse length and quadratically on the second. The limitations are: the homonuclear magnetic dipolar interaction must be much smaller than the heteronuclear case which must be itself much smaller than the amplitude of the pulse. Furthermore, quantification with the echo requires the determination of the spin-spin relaxation time as well.     

14N Pulsed nuclear quadrupole resonance. 4. Two-pulse sequences for the determination of T1 and T2 relaxation times

A general theory, based on density matrix calculations, has been developed for the special case of a two-pulse sequence applied to spin 1 (¹⁴N) nuclear quadrupole resonance (NQR) of a powder sample. It is shown that the homolog of the NMR inversion-recovery experiment leads easily to the spin-lattice relaxation time T ₁ (associated with the diagonal elements of the density matrix) provided that an appropriate phase cycling is used. Conversely, in spite of two-step phase cycling schemes adapted to spin-spin relaxation measurements, the homolog of the NMR Hahn spin-echo sequence may pose some problems if the results are displayed in the magnitude mode. First, at short decay times, the echo may be corrupted by unwanted signals. Secondly, in that case, the amplitude of the resulting signal can evolve unexpectedly and differently as a function of the phase of the second pulse. Thirdly, at long decay times, the echo maximum occurs earlier than expected. All these problems in principle disappear with a complete four-step phase cycling scheme and the echo decay curve yields reliably the spin-spin relaxation time T ₂ (associated with off-diagonal elements). This theory allowed the exploitation of many test experiments performed at different frequencies on hexamethylenetetramine (HMT) and sodium nitrite.     

一种降低井下核磁共振振铃的新方法

核磁共振（NMR）测井仪在测量过程中,振铃噪声幅度一般很高,会影响回波信号的检测. 常用的交叉相位对脉冲序列（PAPS）虽然能有效地降低振铃影响,但由于振铃与频率有关,使PAPS叠加只能在同频率之间展开,大大降低了NMR测井的纵向分辨率. 利用回波信号和振铃噪声的相位特征,设计了一种脉冲序列,采用PAPS和回波间叠加相结合的方式降低振铃噪声. 研究表明,相对于PAPS技术,提高了测量效率,同时提高了回波串的信噪比和NMR测井的纵向分辨率.     

Nuclear spin echo model based on Floquet–Lyapunov theory

The method of nuclear spin-echo amplitude calculation based on the density matrix technique is improved. The Floquet–Lyapunov theorem for a system of the ordinary differential equations with coefficients periodically dependent on time is used to find the solution of the Schrödinger equation for the time-evolution operator which describes behavior of a nuclear spin in the presence of a radiofrequency pulsed magnetic field. NQR spin echo for the case of nuclear spin I?=?1 and NMR spin echo for I?=?1/2 are considered as the simplest illustrations of the approach. The appearance of multiple spin echoes is predicted in the case of strong radiofrequency field.     

19F Magnetic resonance imaging of perfluorooctanoic acid encapsulated in liposome for biodistribution measurement

The tissue distribution of perfluorooctanoic acid (PFOA), which is known to show unique biological responses, has been visualized in female mice by (19)F magnetic resonance imaging (MRI) incorporated with the recent advances in microimaging technique. The chemical shift selected fast spin-echo method was applied to acquire in vivo (19)F MR images of PFOA. The in vivo T(1) and T(2) relaxation times of PFOA were proven to be extremely short, which were 140 (+/- 20) ms and 6.3 (+/- 2.2) ms, respectively. To acquire the in vivo (19)F MR images of PFOA, it was necessary to optimize the parameters of signal selection and echo train length. The chemical shift selection was effectively performed by using the (19)F NMR signal of CF(3) group of PFOA without the signal overlapping because the chemical shift difference between the CF(3) and neighbor signals reaches to 14 kHz. The most optimal echo train length to obtain (19)F images efficiently was determined so that the maximum echo time (TE) value in the fast spin-echo sequence was comparable to the in vivo T(2) value. By optimizing these parameters, the in vivo (19)F MR image of PFOA was enabled to obtain efficiently in 12 minutes. As a result, the time course of the accumulation of PFOA into the mouse liver was clearly pursued in the (19)F MR images. Thus, it was concluded that the (19)F MRI becomes the effective method toward the future pharmacological and toxicological studies of perfluorocarboxilic acids.     

Secondary Nuclear Spin Echo Signals in Thin Yttrium Iron Ferrite Garnet Films

The results are presented of experimental and theoretical study of the phenomenon of secondary nuclear spin echo in magnetically ordered materials in which the formation of additional echo signals is due to dynamic hyperfine coupling. Numerical simulation of the effect of the amplitude (ω1) and the durations of the first (t1) and the second (t2) exciting pulses on the echo signals is performed. It is found that the maximum amplitude of the secondary echo is formed under the conditions ω1t1 = 0.5π and ω1t2 ≈ 0.6π. It is shown that secondary echo signals can be observed upon inhomogeneous excitation of the spectral line ω1 ≤ Δω, where Δω is the inhomogeneous spectral line width. At a temperature of T = 4.2 K, additional double-pulse spin 3τ-echo signals from iron nuclei are experimentally observed in an epitaxial yttrium ferrite garnet film enriched with 57Fe magnetic isotope to 96%. The experimentally observed phase relationships between the primary and secondary echo signals, as well as the dependence of the echo signal amplitude on the amplitude and duration of the exciting pulses, are in good agreement with the results of numerical simulation of the dynamics of nuclear magnetization with regard to the dynamic hyperfine coupling. It is shown that the secondary echo exhibits the effect of spectral line narrowing, and the amplitude of the secondary echo is proportional to the nuclear magnetic resonance (NMR) enhancement factor in magnets, η. In the case of 57Fe NMR in an yttrium iron garnet (YIG) film, the amplitude of the 3τ-echo is two to three orders of magnitude smaller than the amplitude of the primary 2τ-echo, which corresponds to η ≈ 440. The detection of weak secondary echo signals proves to be possible due to the use of a phase-coherent NMR spectrometer with digital quadrature detection at the carrier frequency and signal accumulation.     

相位调制信号的全光再生技术

介绍了差分相移键控信号的全光再生技术.研究了多进制相位调制信号的全光再生技术.对适用于正交相移键控和差分正交相移键控信号的全光再生器进行了仿真.研究结果表明,这种再生器可以显著抑制信号的幅度噪音和相位噪音,使40 Gb/s RZ差分正交相移键控系统在误码率为10－12条件下的传输距离延长至2 000 km以上.     

PGSTE-WATERGATE: an STE-based PGSE NMR sequence with excellent solvent suppression

A new stimulated-echo based pulsed gradient spin-echo NMR diffusion sequence incorporating WATERGATE solvent suppression, PGSTE-WATERGATE, is presented. The sequence provides superb solvent suppression without any phase distortions. The sequence is simple to set up and particularly suited to measuring diffusion coefficients in aqueous solution such as is commonly required in pharmaceutical and combinatorial applications. The utility of the sequence is demonstrated on samples containing lysozyme and sucrose. Importantly, the high degree of phase-distortion suppression allows more complicated selective pi pulses to be used to enhance the selectivity of solvent suppression.     

Resonant excitation of single-pulse nuclear spin echo in magnetically ordered media

An analytical expression for a single-pulse nuclear echo signal in magnetically ordered materials has been obtained taking into account inhomogeneous broadening of the spectroscopic transition and non-uniform distribution of the enhancement factor. The signal has been shown to result from superimposing the nuclear magnetic moment oscillations of the same amplitude and phase that arise upon termination of a radio-frequency pulse. The cause for the effective suppression of oscillations of nuclear magnetic moments in the initial phase of the free precession signal has been determined analytically. The single-pulse echo signal amplitude has been found as a function of the external variable magnetic field strength, the exciting pulse duration, the inhomogeneous NMR line broadening, and the distribution width of the enhancement factor. The results have been compared with experimental data observed in a Co₂MnSi ferromagnetic polycrystalline sample. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 387–394, May–June, 2009.     

Noise suppression properties of an interferometer-based regenerator for differential phase-shift keying data

We studied the amplitude and phase noise suppression properties of an all-optical regenerator for differential phase-shift keying data. A detailed analytical investigation is performed and compared with numerical simulations for different working points. The results show that both amplitude and phase can be regenerated. However, simultaneous amplitude and phase noise suppression is possible only if the phase degradation is stronger than the amplitude degradation, for instance, due to nonlinear phase noise.     

Microscopic displacement imaging with pulsed field gradient turbo spin-echo NMR

We present a pulse sequence that enables the accurate and spatially resolved measurements of the displacements of spins in a variety of (biological) systems. The pulse sequence combines pulsed field gradient (PFG) NMR with turbo spin-echo (TSE) imaging. It is shown here that by ensuring that the phase of the echoes within a normal spin-echo train is constant, displacement propagators can be generated on a pixel-by-pixel basis. These propagators accurately describe the distribution of displacements, while imaging time is decreased by using separate phase encoding for every echo in a TSE train. Measurements at 0.47 T on two phantoms and the stem of an intact tomato plant demonstrate the capability of the sequence to measure complete and accurate propagators, encoded with 16 PFG steps, for each pixel in a 128 x 128 image (resolution 117 x 117 x 3,000 microm) within 17 min. Dynamic displacement studies on a physiologically relevant time resolution for plants are now within reach.     

Application of phase consistency to improve time efficiency and image quality in dual echo black-blood carotid angiography

There is a considerable similarity between proton density-weighted (PDw) and T2-weighted (T2w) images acquired by dual echo fast spin-echo (FSE) sequences. The similarity manifests itself not only in image space as correspondence between intensities of PDw and T2w images, but also in phase space as consistency between phases of PDw and T2w images. Methods for improving the imaging efficiency and image quality of dual echo FSE sequences based on this feature have been developed. The total scan time of dual echo FSE acquisition may be reduced by as much as 25% by incorporating an estimate of the image phase from a fully sampled PDw image when reconstructing partially sampled T2w images. The quality of T2w images acquired using phased array coils may be significantly improved by using the developed noise reduction reconstruction scheme, which is based on the correspondence between the PDw and T2w image intensities and the consistency between the PDw and T2w image phases. Studies of phantom and human subject MRI data were performed to evaluate the effectiveness of the techniques.     

Tunable feedback loop for suppression of relaxation oscillations in a diode-pumped Nd: laser

An optoelectronic noise suppression circuit connected to the RF input of a commercial diode laser mount is presented. Adjustable phase shift and amplitude control enable efficient suppression of the relaxation oscillations of a diode laser-pumped Nd:YVO₄ laser at variable frequencies between a few hundred kHz and 1.8 MHz. At least 25 dB reduction of the relaxation oscillations at 500 kHz and 1.5 MHz noise peaks is demonstrated.     

Evaluation of the susceptibility effect on gradient echo phase images in vivo: a sequential study of intracerebral hematoma.

Susceptibility effect of intracerebral hematoma was estimated on the phase images of gradient echo (GrE). Thirty-five hematomas were studied 3 hr to 5 yr after the onset, a total of 72 times with use of phase and magnitude images of GrE, as well as T1-, T2-, and density-weighted spin-echo (SE) images at 1.5 T. On the basis of the theory of electromagnetism, phase shift to hematoma was calculated for simplified models with concentric distribution of paramagnetic susceptibility. All hematomas were well visualized by the phase images, the pattern of which changed sequentially. The distribution of paramagnetic susceptibility could be estimated by correlating the observed phase shifts with the calculated one. SE images were necessary to presume the type of magnetic substances. A probable hypothesis of the evolution of intracerebral hematoma is proposed.     

"Development of REDOR rotational-echo double-resonance NMR" by Terry Gullion and Jacob Schaefer [J. Magn. Reson. 81 (1989) 196-200

The popularity of rotational-echo double-resonance (REDOR) NMR arises from its ability to measure weak dipolar couplings and long-range heteronuclear distances accurately. This ability was not anticipated in the first REDOR experiments and resulted from the effectiveness of a simple radiofrequency phase alternation scheme to suppress amplitude and phase distortions in echo trains even after hundreds of pi pulses.     

Comparative study of motions in dimethylsulfone by noise excitation and solid echo spectroscopy

2H NMR spectra of dimethylsulfone were measured with noise excitation and solid echo NMR spectroscopy in the temperature range from 125 to 355 K. Besides the known fact that broad NMR spectra can be measured with both methods, in comparable times it is shown that for noise excitation, the signal loss is negligible compared to echo spectroscopy in the regime when the correlation times of the motions are of the order of magnitude of the echo pulse spacing. For simulating the dynamic NMR spectra acquired with noise excitation, only the motional process must be taken into account and relaxation can be neglected. Furthermore, the problem of restricted acquisition bandwidth in noise NMR spectroscopy is discussed.     

Observation of a new coherent transient in NMR — Two-pulse nutational stimulated echo in the angular distribution of gamma-radiation from oriented nuclei

A new coherent transient in NMR, the two-pulse nutational stimulated echo is reported for the ferromagnetic system⁵⁰CoFe, observed by monitoring the nuclear spin dynamics as a function of the second pulse duration via anisotropic gamma quanta from thermally oriented radioactive nuclei,⁶⁰Co. The mechanism of echo formation under strong Larmor inhomogeneous broadening and the secondary but important role of inhomogeneity associated with the rf amplitude (Rabi freqeuncy) due to skin-effect are investigated via the method of concatenation of perturbation factors in the statistical tensor formalism. For those experiments performed on time scales short compared with irreversible relaxation the theoretical predictions and subsequent experimental time-domain signals are in excellent accord. Remarkable constancy of amplitude of the new gamma-detected two-pulse echo with increase of interpulse time interval is observed, the longitudinal relaxation being manifest in the off-echo signals. Comparisons are made with NMRON four-pulse stimulated off-echo decay (analogous with conventional NMR three pulse stimulated echo) which is also sensitive to longitudinal relaxation, and with three-pulse on-echo decay (analogous with conventional NMR two-pulse Hahn echo) which measures transverse relaxation.     

高精度多脉冲激光测距回波检测技术

针对远距离激光测距机回波信号脉宽强度特征和噪声的统计特性,提出了一种高精度多脉冲激光测距机的回波信号检测技术。采用时钟移相分配方式实现了400 MHz高速信号采集及数字化处理,提高了回波脉冲的检测精度。采用ARM嵌入式高速核处理器进行数据算法处理,完成了滤波降噪、自适应门限检测和多帧相关检测等功能,使回波信噪比提高了7.6 dB,达到远距离精确获取目标距离信息的目的。