H Barkhuijsen

Retrieval of frequencies, amplitudes, damping factors, and phases from time-domain signals using a linear least-squares procedure

Abstract A new method for quantitative analysis of time-domain signals is reported. It amounts to fitting a function consisting of exponentially damped sinusoids with arbitrary phases to the data. By invoking the principle of linear prediction (LP) the fitting can be carried out by a linear least-squares (LS) procedure, and therefore needs no starting values The LS procedure is based on singular value decomposition (SVD), which enables one to distinguish between signal and noise. The method, denoted by LPSVD, yields a list comprising the frequency, damping factor, amplitude, and phase of each retrieved sinusoid. In addition, LPSVD is insensitive to truncation at the beginning and/or the end of the signal, and in fact is capable to accurately reconstruct the missing part. Preprocessing of the data is not necessary. Finally, the method achieves higher resolution than fast Fourier transformation.

Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals

This communication is concerned with a new method of fitting a physical model function to a magnetic resonance signal, directly in the time domain. Our primary aim is analysis of the signal in quantitative terms, i.e., describing the signal in terms of physically meaningful parameters with their statistical errors. Before explaining the new method we make some remarks about the place of time-domain model fitting in spectral analysis. The notion of quantitative description just defined goes beyond constructing a spectrum from the available time-domain data. This judgment is supported by the observation that recently proposed methods for constructing a spectrum (l-3), although very useful for many purposes, have not provided values of the physical parameters involved. In fact, if the latter are wanted afterward, it is then still necessary to fit an appropriate model function to the spectrum (4, 5). Furthermore, in addition to the fitting, the degree to which the spectrum constructed approximates the “ideal” spectrum is to be assessed. On the basis of these considerations, we advocate the use of timedomain model fitting, if quantitative description of a signal is needed. On the other hand, if the primary need is to have a spectrum, one may well use methods such as proposed in Refs. (Z-3), some of which require significantly less computer time. If the signal decays exponentially, which is not uncommon in magnetic resonance, an additional advantage of remaining in the time domain emerges, namely that the fitting procedure can be made noniterative. To the best of our knowledge noniterative fitting procedures are not yet available for the frequency domain. A method of noniterative fitting has recently been devised by Kumaresan and Tufts (6) and was subsequently applied to magnetic resonance (7, 8) under the name LPSVD; see also (9) for a related method. An error analysis was given in (6, IO). We are here concerned with an alternative noniterative model fitting procedure, devised by Kung et al. (II) using the so-called state space formalism. The method can handle considerably more data points than LPSVD because polynomial rooting is avoided. At the same time, the residue of the fit is usually better than that of LPSVD. We shall indicate that the basic idea can be explained with elementary matrix algebra, without invoking the state space formalism. In addition, a formula for efficient computer implementation is given.

Measurement of hyperfine interactions with electron spin-echo spectroscopy. Application to F centers in KCl

Abstract The accuracy of spin-Hamiltonian determination via analysis of electron spin-echo nuclear modulation signals is investigated for F centers in KCl. It turns out that the accuracy matches that of ENDOR. The linewidth of the signals converted to the frequency domain also compares well with ENDOR. Parametric spectrum estimation with autoregressive modeling (maximum entropy method) yields significant further reduction of the linewidth. Analysis of the signal strength in the frequency domain appears feasible.

Observation of potassium hyperfine interactions in X-irradiated KH2AsO4 through the method of electron spin echo envelope modulation

Abstract Hyperfine interaction frequencies of 1H and 39K nuclei near the AsO4-4 radical in X-ray irradiated KH2AsO4 (KDA) have been observed through the method of electron spin echo envelope modulation (ESEEM). This method enabled us to record nuclear hyperfine interaction (ENDOR-like) spectra around the ferroelectric phase transition of KDA for the first time. The ESEEM spectrum of 39K exhibits a clear change when passing the ferroelectric phase transition temperature, but that of close protons does not. The result for close protons is in agreement with the symmetry breaking of the AsO4-4 site as observed via the EPR spectrum [5]. Finally, at 4.2 K the hyperfine interaction parameters of a 39K nucleus near the AsO4-4 unit could be determined through the ESEEM method.

Partial excitation in electron spin-echo envelope modulation spectroscopy

Abstract The existing theory of electron spin-echo envelope modulation (ESEEM) is extended to the case where a hyperfine manifold is excited only partially. The extension is important for application of ESEEM to analytical work. The theory has been worked out for three-pulse echo experiments. In a regular experiment, where one sweeps the time between the first and third pulse, partial excitation affects the amplitudes of the modulation components, but new components do not arise. When one sweeps the time between the first and second pulse, partial excitation causes new modulation components at combination frequencies. The theory can be tested by spectral analysis of the suppression effect, a phenomenon inherent to three-pulse ESEEM. Satisfactory agreement between theory and experiment is found. Data processing is done with the aid of FFT and autoregressive modeling. A preliminary result of data processing using linear prediction combined with least-squares fitting and singular value decomposition is given.

Analysis of signal intensities in electron spin echo envelope modulation spectroscopy

Abstract Unlike ENDOR, electron spin echo envelope modulation (ESEEM) spectroscopy enables one to interpret the signal intensity without knowledge of relaxation processes. The technique is put to the test through analysis of the signal from 39 K in the fifth shell around the F-centre in a single crystal of KCl. The ratio between the experimental and theoretical intensities in this case is found to be 1.06 ± 0.09.

Electron spin echo envelope modulation (eseem) in CaF2:Gd3+K+

The energy levels of the nucleus of a K+ ion near a paramagnetic Gd3+ ion, both substituted in CaF2, have been measured with the recently developed technique of electron spin echo envelope modulation, combined with an also recently developed microwave cavity, the loop-gap resonator. The results provide confirmation of the theory of lattice distortion around substituted ions.