Free Induction Decay Research Articles

A comprehensive study on the weak magnetic sensor character of different geometries for proton precession magnetometer

The measurement precision or uncertainty of proton precession magnetometer (PPM) depends on the signal-to-noise ratio (SNR) of the free induction decay (FID) signal induced in the sensing coil. A diversity of weak magnetic measurement applications has benefited from various coils through a more comprehensive and reliable design. Likewise, numerous optimized sensors for PPM have been proposed and published in literature. However, due to lack of commonly accepted assessment measures and benchmark resources, it is hard to identify the performance of the proposed sensors and corresponding implementations. This paper investigates and categorizes sensing coils for PPM which are well used and accepted. Three state-of-the-art geometries of the coil including solenoid, toroid, and cylindric, are considered to evaluate the significance of these designs in terms of sensing signal strength analyses within their respective applications. Furthermore, the electromotive force (EMF) of FID signal is calculated as a function of sensing coils' geometrical parameters, and numerous critical factors such as the polarizing current, the orientation of the coil axis with respect to the direction of the external magnetic field, etc., are considered. Although the results of these calculations are limited by prerequisites, e.g. the sensor should be in a uniform magnetic field, it is a critical step for future sensor research. This paper aims to advance weak magnetic sensor development by establishing a comparative study to allow the optimum geometrical shapes to be chosen for different applications.

Molecular Coupling between Organic Molecules and Metal.

Molecular couplings at interfaces play important roles in determining the performance of nanophotonics and molecular electronics. In this Letter, using femtosecond sum frequency generation to trace free-induction decay of vibrationally excited aromatic thiol molecules immobilized on metal with and without the bridged methylene group(s), metal surface free electron-coupled and uncoupled phenyl C-H stretching vibrational modes were identified, with dephasing times of ∼0.28 and ∼0.60 ps, respectively. For thiols on Au with the bridged methylene group(s) (benzyl mercaptan and phenylethanethiol), both the coupled and uncoupled modes were observed; for thiol on Au without the bridged methylene group (thiophenol), only the coupled mode was observed. This indicates that the bridged methylene group(s) serving as a spacer can be used to adjust the molecular coupling between the phenyl vibration and surface free electrons. The experimental approach can be used to tune molecular couplings in advanced nanophotonics and molecular electronics.

Frequency cycling to alleviate unknown frequency offsets for adiabatic half-passage pulses in surface nuclear magnetic resonance

Adiabatic half-passage (AHP) pulses show great promise for significantly enhancing the signal-to-noise ratio of the surface nuclear magnetic resonance (NMR) free-induction decay measurement. Performing an AHP requires that the frequency sweep terminates when the transmit frequency is equal to the Larmor frequency, a condition that demands accurate knowledge of the true Larmor frequency. If the frequency sweep is terminated at an incorrect frequency, i.e., with an unknown offset between the transmit and Larmor frequency at the end of the pulse, the net excitation is affected and it can differ from that predicted by modeling that assumes a 0 Hz offset at the end of the sweep. Surface NMR surveys using a traditional single-frequency pulse have previously been shown to display degraded performance in the presence of an uncertain Larmor frequency estimate; the AHP pulse is also likely susceptible to such degraded performance. To ensure that reliable results can be produced by AHP pulses in the presence of an uncertain Larmor frequency estimate, we have developed an approach that adapts the frequency-cycling scheme for use with AHP pulses. We hypothesize that data collected using two similar AHP pulses, each with the exact same frequency sweep but where one sweeps toward the Larmor frequency from higher frequencies and the other from lower frequencies, can be stacked in such a manner that the impact of an unknown frequency offset is significantly reduced. We present synthetic and field results to demonstrate that frequency-cycling AHP pulse surface NMR data can ensure reliable performance even in the presence of an uncertain Larmor frequency estimate.

Fractional magnetic resonance imaging based on inhomogeneous main magnetic field

The existing NMR equipment is uneven to face the main magnetic field, mostly adopts the hardware method of magnetic field compensation, such as magnetic field compensation, but it brings bad effects such as image artifact and blurred image. In view of the problem of magnetic field inhomogeneous in magnetic resonance imaging, a fractional domain magnetic resonance imaging (fMRI) method under the main magnetic field inhomogeneous is proposed. First, select a layer of living tissue to be imaged, select several points on the layer and measure the intensity of the magnetic field on the layer. Based on the principle of magnetic resonance imaging, establish the model of the magnetic field intensity distribution in the imaging area, and then establish. The polynomial model of the magnetic field can be divided into the second-order polynomial model and the higher-order polynomial model according to whether there is a significant second-order component in the measured magnetic field. Then, the two models are respectively substituted into the free-induction decay (FID) signals of the magnetic resonance. For the second-order model, the fractional Fourier transform tool can be used to solve the spin density function on one layer of the imaged object. The order model needs to obtain the spin density function at a certain level of the imaging object by solving the algebraic equation, thus establishing the MR signal model with any non-uniform main magnetic field. Experimental results show that this method achieves the same effect as the uniform main magnetic field.

Free-Induction-Decay Magnetometer Based on a Microfabricated Cs Vapor Cell

We describe an optically pumped Cs magnetometer containing a 1.5 mm thick microfabricated vapor cell with nitrogen buffer gas operating in a free-induction-decay (FID) configuration. This allows us to monitor the free Larmor precession of the spin coherent Cs atoms by separating the pump and probe phases in the time domain. A single light pulse can sufficiently polarize the atomic sample however, synchronous modulation of the light field actively drives the precession and maximizes the induced spin coherence. Both amplitude and frequency modulation have been implemented with noise floors of 3 pT / √ Hz and 16 pT / √ Hz respectively within the Nyquist limited bandwidth of 500 Hz .

Oscillating Free Induction Decay in Polymer Systems: Theoretical Analysis

It is shown that during the Anderson-Weiss transformation derivation, as applied to a reptating polymer chain, the spin system can be divided into two sub-systems: an ergodic fluctuating one and a nonergodic quasi-static one. Consequently, the free induction decay (FID) expression is factorized. The factor with a fluctuating dipole-dipole interaction for an arbitrary correlation time is transformed into the generalized Anderson-Weiss exponential, and the factor with a quasi-static dipole-dipole interaction in an isotropic polymer melt is transformed into the oscillating Fourier image of the Pake doublet. The final expression permits both describing the FID shape of a polymer melt as a function of the molecular mass and temperature below the temperature of the primitive segment quasi-static state and forecasting the temperature range in which oscillating FIDs have been observed for poly(isoprene) melt. The new approach is applicable to qualitatively describe the oscillating FID in semi-crystalline poly(ethylene).

Field-frequency lock approach for 21.3-MHz high-performance NMR relaxation analyzer

Low-field NMR (LF-NMR) relaxation analyzers have been more and more widely used in food science, biomedicine, and petroleum exploration in recent years. An LF-NMR device analyzes various interactions between sample molecules through spin relaxation, diffusion, flow, and imaging experiments. However, temporal field fluctuations in the magnet limit the scope of application. A stable magnetic field is the basic guarantee for detecting weak signals with shorter relaxation time. This paper presents an approach involving a field-frequency lock for a 21.3-MHz high-performance NMR bipolar permanent magnet. The diameter spherical volume (DSV) of the magnet is only 60 mm. The field-frequency lock system uses 19F in a micro coil integrated into the main probe as a lock detector. The required magnetic field compensation can be calculated from the lock free induction decay (FID) signal frequency, which is measured by lock spectroscopy. The compensation coils used to produce the magnetic field were designed based on Helmholtz coils. The system determines the signal frequency by detecting the lock FID signal and calculates the required compensation-coil current to stabilize the main magnetic field of the analyzer. The results of practical locking experiments in a 21.3-MHz high-performance NMR relaxation analyzer showed that this new approach helps to reduce magnetic field fluctuations from 11 ppm/3h (11 × 10–6) to 0.4 ppm/3h (0.4 × 10–6), which meets the application requirements. This approach is especially viable and effective for a permanent magnet with large field fluctuations. This paper also provides observations of the effect of these fluctuations on NMR measurements before and after installation of the field-frequency lock system.

Study on water proton distribution and flow status of starch during the hydration process

The hydration process of starch significantly affects the quality of starch-based food, especially for samples with medium to low water content. In this paper, rice starch, as a representative of cereal starch, and potato starch were chosen as the samples. The proton distributions and flow status of the hydrated rice starch and potato starch with moisture contents of 20–90% and the causes of the differences between them were investigated by 1H LF-NMR. The longitudinal and transverse proton relaxation (T1 and T2) of the two starch systems was obtained using the inversion recovery (IR) sequence, the free induction decay (FID) sequence, and the multi-pulse echo CPMG sequence. Through the detection of longitudinal relaxation, two different populations were found in the two hydrated starch systems, and the changes were linearly related to the moisture content. Through the detection of transverse relaxation, two populations were distinguished in the hydrated rice starch samples with different moisture content, whereas two to four different populations were detected in the hydrated potato starch samples. Because of the differences in particle size and swelling capacity, hydrated potato starch showed greater proton freedom and more observable types of protons than hydrated rice starch.

Quantum master equation with dissipators regularized by thermal fluctuations

We report an alternate formulation of the quantum master equation (QME) to describe the dynamics of a quantum system weakly coupled to a heat bath, in the presence of weak external driving. A key feature of this approach is the introduction of an explicit Hamiltonian to model the thermal fluctuations in the heat bath. We show that the resulting time coarse-grained dynamical equation for the quantum system has dissipators with a natural regulator, which emerges from an ensemble average over the fluctuations. Importantly, such regularized dissipators arise from the second-order contributions of both the external drive as well as the system-environment coupling. We show that the second-order drive terms, regularized to time-scales set by the fluctuations, result in dynamic drive-induced frequency shifts as well as drive-dependent relaxation phenomena. Considering the specific case of an ensemble of two-level systems, subjected to a linearly polarized external drive, we derive the modified Bloch Equations with such drive-dependent shift and damping terms. The resulting drive-induced frequency shifts converge to the known forms of dynamic frequency shifts, such as the Bloch-Siegert shift or the dynamic Stark shift, in appropriate limits. The Kramers-Kronig pairs of these frequency shifts - manifest as drive-dependent damping terms in the modified Bloch Equations and help explain the Redfield limit of free-induction-decay (FID) rates as well as the non-Bloch decay of Rabi oscillations in isotropic medium. Our method predicts correct orders of magnitudes of non-Bloch decay rates in isotropic medium as well as their observed temperature dependence. The QME reported here, correctly describes all known aspects of the driven-dissipative dynamics up to second-order of an open quantum system with appropriate thermal signatures and as such is expected to provide deeper insights into the study of quantum information processing on real systems.

Diffusion effect on T2 relaxometry in triple-echo steady state free precession sequence

PurposeThe purpose of this study is to evaluate the effect of diffusion on SSFP (Steady-state Free Precession) signals in triple-echo steady state (TESS) sequence and ultimately on the accuracy of T2 relaxometry. MethodsThe extended phase graph (EPG) algorithm was used to study the effect of diffusion on SSFP signals and T2 relaxometry. The simulation results were verified by a commercial phantom and in vivo studies. Based on the simulation results, a correction scheme was proposed to correct the estimated T2 values. ResultsT2 underestimation in TESS was evident in case of small flip angle and large unbalanced gradient moment on objects with large T2 and D values. The T2 underestimation mainly originated from the diffusion sensitivity of SSFP-echo. It was also observed that SSFP-FID (Free Induction Decay) signals increased with increasing diffusion weighting under some specific conditions. The proposed correction scheme corrected the T2 underestimation, which verified that the underestimation was due to the neglect of diffusion effect. For clinical practice of TESS in tissues with short T2 such as cartilage and muscle, the diffusion effect of TESS is negligible. ConclusionThe effect of diffusion cannot be neglected during TESS T2 quantification as it is the main source of T2 underestimation when small flip angle and large unbalanced gradient moment is used, especially for objects with large T2 and D values.

A subband Steiglitz-McBride algorithm for automatic analysis of FID data.

Fast, accurate, and automatic extraction of parameters of nuclear magnetic resonance free induction decay (FID) signal for chemical spectroscopy is a challenging problem. Recently, the Steiglitz-McBride algorithm has been shown to exhibit superior performance in terms of speed, accuracy, and automation when applied to the extraction of T2 relaxation parameters for myelin water imaging of brain. Applying it to FID data reveals that it falls short of the second objective, the accuracy. Especially, it struggles with the issue of missed spectral peaks when applied to chemical samples with relatively dense frequency spectra. To overcome this issue, a preprocessing stage of subband decomposition is proposed before the application of Steiglitz-McBride algorithm to the FID signal. It is demonstrated that by doing so, a considerable improvement in accuracy is achieved. But this is not gained at the cost of the first objective, the speed. An adaptive subband decomposition is employed in conjunction with the Bayesian information criteria to carry out an efficient decomposition according to spectral content of the signal under investigation. Furthermore, adaptive subband decomposition and the Bayesian information criteria also serve to make the resulting algorithm independent of user input, which also fulfills the third objective, the automation. This makes the proposed algorithm favorable for fast, accurate, and automatic extraction of FID signal parameters.

Time-domain measurement of optical activity by an ultrastable common-path interferometer.

We introduce a novel configuration for the broadband measurement of the optical activity of molecules, combining time-domain detection with heterodyne amplification. A birefringent common-path polarization-division interferometer creates two phase-locked replicas of the input light with orthogonal polarization. The more intense replica interacts with the sample, producing a chiral free-induction decay field, which interferes with the other replica, acting as a time-delayed phase-coherent local oscillator. By recording the delay-dependent interferogram, we obtain by a Fourier transform both the circular dichroism and circular birefringence spectra. Our compact, low-cost setup accepts ultrashort light pulses, making it suitable for measurement of transient optical activity.

Effects of the pulse-driven magnetic field detuning on the calibration of coil constants while using noble gases

In the calibration of coil constants using the Free Induction Decay (FID) signal of noble gases, we analyse the effects of the pulse-driven magnetic field detuning on the calibration results. This method is based on the inverse relation between the π/2 pulse duration and its amplitude. We confirmed that obtaining a precise frequency is a prerequisite for ensuring the accuracy of research using the initial amplitude of the FID signal. In this paper, the spin dynamics of noble gases and its time-domain solution under the driving pulse have been discussed with regard to different detuning ranges. Experimental results are in good agreement with our theoretical predictions, which indicate the correctness of our theoretical deduction. Therefore, the frequency of the pulse-driven magnetic field is an important factor to the calibration of coil constants, it should be determined with a high degree of accuracy.

Correlated Signals of Free Induction Decay in CdSe–CdS Nanostructures Under Two- and Three-Photon Excitation by Crossed Femtosecond Laser Beams

The possibility and conditions of a generation of the correlated free induction decay signals in CdSe–CdS nanostructures under two- and three-photon excitation by crossed femtosecond beams of the Ti:sapphire laser radiation are considered. It is shown that these correlated signals will be emitted in two opposite directions. The information contained in the temporal shapes and wavefronts of these signals will be correlated.

Determining the oil and water content of single olives using magnetic resonance imaging (MRI) spectroscopy

The nuclear magnetic resonance (NMR) spectra of olives are dominated by oil and water. Chemical shift imaging (CSI), a specialized version of magnetic resonance imaging (MRI), was examined as a noninvasive technique to determine both oil and water content. To make the method quantitative, internal oil and water standards were used. CSI was used to spatially separate the oil and water signals from the olive from known masses of oil and water. Single intact Olea europaea 'Mission' olives were examined to test the method. In principle, the ratio of the integrals of the oil and water signals at the olive position to the integrals at the phantom (oil and water controls) positions in CSI images will give the oil and water contents of the olive. We found that both oil and water in an olive have short spin lattice relaxation times (T2 of 28 and 13 ms, respectively). We also found that the spin echo version of CSI was required, since the free induction decay method lost significant signal due to sample heterogeneity. Moreover, short T2 requires a fit of a series of CSI images to determine oil and water content. Intensities versus echo times were fitted to an exponential, and extrapolation to zero echo time gave the absolute masses of water and oil in the olive. The same olives were subsequently analyzed by classical Soxhlet extraction. The Soxhlet values correlated poorly with the NMR values, and this may have been due to the difficulty of accurately extracting single olives. For the NMR data, shimming, phasing and choice of CSI integration limits as possible sources of error were also considered.

Signature of reptation in the long-time behavior of the deuteron NMR Free Induction Decay in high molecular mass polymer melts

The classical tube-reptation (TR) model is based on the assumption, that in entangled polymer melts diffusion takes place inside the effective tubes having a conformation of ideal chains and being stable on the time scale of the terminal relaxation time τt, the latter being strongly molar mass (M) dependent. We argue, that this assumption leads for high M to a characteristic, strongly non-exponential time dependence of the deuteron Free Induction Decay, or likewise of the Hahn Echo amplitude. This holds for times t satisfying the condition τe≪T2<t≪τt, where T2is an effective spin-spin relaxation time andτe is the entanglement time.

Characterization of the hyperfine interaction of the excited D05 state of Eu3+:Y2SiO5

We characterize the Europium (Eu$^{3+}$) hyperfine interaction of the excited state ($^5$D$_0$) and determine its effective spin Hamiltonian parameters for the Zeeman and quadrupole tensors. An optical free induction decay method is used to measure all hyperfine splittings under weak external magnetic field (up to 10 mT) for various field orientations. On the basis of the determined Hamiltonian we discuss the possibility to predict optical transition probabilities between hyperfine levels for the $^7$F$_{0} \longleftrightarrow ^5$D$_{0}$ transition. The obtained results provide necessary information to realize an optical quantum memory scheme which utilizes long spin coherence properties of $^{151}$Eu$^{3+}$:Y$_2$SiO$_5$ material under external magnetic fields

Spatially resolved control of fictitious magnetic fields in a cold atomic ensemble.

Effective and unrestricted engineering of atom-photon interactions requires precise spatially resolved control of light beams. The significant potential of such manipulations lies in a set of disciplines ranging from solid-state to atomic physics. Here we use a Zeeman-like ac-Stark shift caused by a shaped laser beam to perform rotations of spins with spatial resolution in a large ensemble of cold rubidium atoms. We show that inhomogeneities of light intensity are the main source of dephasing and, thus, decoherence; yet, with proper beam shaping, this deleterious effect is strongly mitigated allowing rotations of 15rad within one spin-precession lifetime. Finally, as a particular example of a complex manipulation enabled by our scheme, we demonstrate a range of collapse-and-revival behaviors of a free-induction decay signal by imprinting comb-like patterns on the atomic ensemble.

Gaining insight into the $T\,_2^*$–T 2 relationship in surface NMR free-induction decay measurements

Gaining insight into the $T\,_2^*$–<i>T</i> <b>2</b> relationship in surface NMR free-induction decay measurements

New Formulation of Magnetization Equation for Flowing Nuclear Spin Under Nuclear Magnetic Resonance/Magnetic Resonance Imaging Excitation

We have obtained from the Bloch nuclear magnetic resonance (NMR) equations the correct dependence of the single component My and Mz at resonance (NMR/magnetic resonance imaging (MRI)) on relaxation times, rf B1 field (pulsed or continuous), blood(nuclear spin) flow velocity, etc., in the rotating frame of reference. We find that the new formulation for the first time uniquely describes the true relationship between individual single component My or Mz of magnetization of flowing nuclear spin with the above quantities (excluding diffusion and gradient fields) during NMR/MRI excitation. The equations are applicable for both continuous wave (CW) and pulsed NMR experiments with or without flow of spins. Our approaches can be extended easily to include gradient fields and diffusion of spins, if needed in NMR/MRI experiments. We also discuss the application of our equations to a specific case of magnetic resonance (MR) excitation scheme: Free induction decay. The new equations and further equations that can be derived with the methodologies used here can advance the techniques of noninvasive blood flow estimation by MR and also accurate extraction of parameters of clinical importance by enabling accurate simulation of the MR images (of blood flow and tissue) and comparison with experimental MR images. The detailed simulations from the equations will be published in the next paper.