The basics of registration and features of nuclear magnetic resonance in the Earth magnetic field are described in detail, for example, in the monograph [1]. In 1957 D. Elliot and R. Schumacher obtained the 1H signal from fluorobenzene in the Earth magnetic field [2], using the method of M. Packard and R. Varian [3, 4], and observed “slow beats” in the decay of the signal. They estimated the frequency of these beats and concluded that the J-coupling constant for the 19F nuclei and protons is 5.8 Hz. This was one of the first attempts to obtain the information about NMR spectrum by pulse method. However, already in the next 1958 in Russia at the Faculty of Physics of the Leningrad (now St. Petersburg) State University, F. Skripov and co-workers managed to obtain the proton spectrum of tributyl phosphate in the Earth magnetic field via the Fourier transform of a free induction decay (FID) [5]. However, they calculated the spectrum manually using electromechanical counting machines for many days and this circumstance explains the fact that their work did not attract the attention of contemporaries (see details in [6]).
With the advent of the possibility of creating magnetic systems with high field homogeneity, the interest of researchers to low-field NMR decreased significantly. The lack of chemical shifts in NMR spectra in weak fields such as the Earth’s one and the low signal-to-noise ratio were also superimposed on this. Nevertheless, the works of P. Callaghan [7, 8] and S. Appelt [9-11] stand out, showing that despite of the absence of chemical shifts, NMR spectra can be informative, as they carry information about J-coupling constants. To obtain them, the high homogeneity of a static magnetic field is required, which is possessed only by very expensive and sophisticated devices, but in the Earth field narrow spectral lines can be obtained using home-built equipment. However, P. Callaghan limited himself to the study of fluorine-containing liquids with a high natural abundance of 19F magnetic nuclei (100%), the interaction with which split proton spectra. S. Appelt used a strong Halbach magnet for pre-polarization of nuclei and manually transferred the sample in the NMR sensor, losing 1-2 seconds, but obtaining proton spectra contained lines due to J-coupling with 29Si (4.7%) and 13C (1.1%) nuclei of natural abundance.
The main problem of such a study is the ineffectiveness of signal accumulation due to fluctuations of the Earth magnetic field because of magnetic interferences from laboratory equipment and other magnetic field sources. The original solution to the problem was proposed by J. Stepišnik and co-workers [12], who suggested using a second sensor to monitor changes of the resonance frequency caused by fluctuations in the Earth field. They used a signal from the second sensor with a water sample for the quadrature detection of a signal from the test sample. The authors [12] used their approach for MRI in the Earth field and the duration of the water signal was sufficient for the detection of short signals in the gradient field. We improved this method for the high-resolution NMR spectroscopy in the Earth field [13] by suggesting that after simultaneous recording of signals from both sensors one can determine the resonance frequency using the signal from the reference sensor and then forming a “infinite” reference signal at this frequency it is possible to detect the signal from the studied substance. However, taking into account the fact that generally in the Earth magnetic field proton-containing liquids have spectra with a central strong line, a simpler method has been found to neutralize the Larmor frequency fluctuations. The frequency of this line can be determined and then the total NMR signal can be processed using the reference signal with obtained frequency. After the fast Fourier transform (FFT) the individual spectra can be accumulated to increase the signal-to-noise ratio. The results of the application of this simple technique, combined with conventional NMR signal processing, are presented in the article.
Notations
The following notations will be applied within the scope of the article:
Xk
|
-th element of an any array
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F
|
An array of discrete frequencies of a spectrum
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A (ReA, ImA)
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An array of discrete complex amplitudes of a spectrum
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V
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An array of discrete amplitudes of a signal
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Signal processing
First, it is necessary to perform the FFT of a NMR signal (FID), and then the region of the spectrum with a strong line is selected and its frequency is calculated. However, the "straightforward" determination of the dominant frequency is not accurate enough. To achieve the necessary precision, it is necessary to perform the inverse FFT (IFFT) of a narrow segment of the spectrum with the strong line, thereby performing the narrow-band filtering of the signal, and then calculate the frequency. After that, the quadrature detection can be used for the original signal with the reference signal at the calculated frequency and it is possible to perform the FFT again. Thus, the NMR frequency of the strongest line in a spectrum shifts to zero. All subsequent signals processed in this way can be accumulated in the traditional manner (see Fig. 1). A demonstration of the prospects for registering spectra using the proposed algorithm for neutralizing fluctuations in the Earth magnetic field is shown in Figure 2.
Note that the spectrum does not have to contain only one strong line. If there are several strong lines in a spectrum, it is also possible to use one of the strong spectral lines to neutralize the frequency fluctuations.
The NMR signal in the Earth magnetic field is recorded not immediately after the end of polarization (in the case of the Packard-Varian method [2, 3]) or after the 90-degree RF-pulse, but after the so-called "dead time" (time of receiver insensitivity). The problem is especially important in the case of the Earth field because of a very low resonance frequency (about 2 kHz) and, as a result, a long transient process in the receiving path ("dead time" is about 30-50 ms). In this case, the loss of the initial phase of a signal (FID) leads to the distortion of a spectrum. This effect varies for different frequencies, so it is impossible to align lines simultaneously for corrected spectrum element Ck using the traditional method:
where φ is the handpicked variable. It is necessary to take into account the phase shift, which occurs due to the introduction of “dead time” in Eq. (1):
where td is the “dead time”. But in this case, oscillations are observed in the spectrum even if the apodization of a signal is done (as after adding zeros to a signal in the absence of apodization, see the details in Ref. [14]). The fact is that introducing the variable td in Eq. (2) is equivalent to adding zeros at the beginning of a signal, emulating the segment of the “dead time” td. Fig. 3 (left) shows the “raw” spectrum of 2,2,2 trifluoroetanol, and Fig. 3 (right) shows the spectrum after applying Eq. (2). In other words, the oscillations appeared in the spectrum because entering td into formula (2), we had actually shifted a signal along the time axis to the right, and zeros appeared in the time interval from zero to the beginning of a signal. This means that there is now a sharp front at the beginning of a signal, which causes the oscillations in the spectrum.
To increase the resolution in the spectrum, it is necessary to supplement the signal with zeros (see, for example, [1]). However, due to the presence of noise in the signal, a front appears at the boundary of the signal with the "zero part", causing oscillations in the spectrum (similar to Fig. 3, right). To eliminate this effect, the signal apodization procedure is used, which consists in multiplying the signal by a function that decreases to zero. Possible variants of these functions are described in Ref. [14].