Reconstruction of the first-derivative EPR spectrum from multiple harmonics of the field-modulated continuous wave signal

Abstract

Selection of the amplitude of magnetic field modulation for continuous wave electron paramagnetic resonance (EPR) often is a trade-off between sensitivity and resolution. Increasing the modulation amplitude improves the signal-to-noise ratio, S/N, at the expense of broadening the signal. Combining information from multiple harmonics of the field-modulated signal is proposed as a method to obtain the first derivative spectrum with minimal broadening and improved signal-to-noise. The harmonics are obtained by digital phase-sensitive detection of the signal at the modulation frequency and its integer multiples. Reconstruction of the first derivative EPR line is done in the Fourier conjugate domain where each harmonic can be represented as the product of the Fourier transform of the 1st derivative signal with an analytical function. The analytical function for each harmonic can be viewed as a filter. The Fourier transform of the 1st derivative spectrum can be calculated from all available harmonics by solving an optimization problem with the goal of maximizing the S/N. Inverse Fourier transformation of the result produces the 1st derivative EPR line in the magnetic field domain. The use of modulation amplitude greater than linewidth improves the S/N, but does not broaden the reconstructed spectrum. The method works for an arbitrary EPR line shape, but is limited to the case when magnetization instantaneously follows the modulation field, which is known as the adiabatic approximation.

Multiharmonic electron paramagnetic resonance for extended samples with both narrow and broad lines

“…The data analysis for multiharmonic EPR is described in [2,3,7]. This method does not require prior knowledge of the signal lineshape.…”

“…Combining information from multiple harmonics of the field modulation frequency has been shown to give the first-derivative spectrum with minimal broadening up to modulation amplitudes that are several times the linewidths [2]. The amplitude at the fundamental and at higher harmonics can be obtained by digital phase-sensitive detection of the signal at the modulation frequency and at its integer multiples [3]. As the modulation amplitude is increased, the intensities at the higher harmonics of the modulation frequency increase, which can be used to improve the signal-to-noise of the spectrum for modulation amplitudes up to about 1.2 times linewidths, provided that sufficient harmonics are included in the data analysis [3].…”

“…The amplitude at the fundamental and at higher harmonics can be obtained by digital phase-sensitive detection of the signal at the modulation frequency and at its integer multiples [3]. As the modulation amplitude is increased, the intensities at the higher harmonics of the modulation frequency increase, which can be used to improve the signal-to-noise of the spectrum for modulation amplitudes up to about 1.2 times linewidths, provided that sufficient harmonics are included in the data analysis [3]. Accurate reconstruction of the spectrum from the higher harmonics requires that the modulated magnetic field is uniform over the sample.…”

“…Accurate reconstruction of the spectrum from the higher harmonics requires that the modulated magnetic field is uniform over the sample. In the initial reports the samples were very small because the magnetic field uniformity that could be obtained with commercial modulation coils was adequate for multiharmonic spectroscopy only over a small region of space and with limited modulation amplitudes [2,3]. The larger scan coils that have been developed for rapid scan EPR improve the magnetic field homogeneity over larger samples [4] relative to what can be achieved with conventional modulation coils.…”

“…In addition, the rapid scan coil driver can generate larger modulation amplitudes [5] than conventional modulation coil drivers. In the initial reports [2,3] the multiharmonic reconstruction method was applied to samples with single relatively narrow linewidths that could be over-modulated with modest modulation amplitudes. The samples selected for study in this report have more complicated lineshapes that include both narrow and broad lines and require larger modulation amplitudes to achieve overmodulation.…”