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.

Fig. 1

Comparison of the filter functions |D₁(u)| to |D₅(u)| calculated for a modulation amplitude, h_m, of 3 G (solid lines), with the Fourier transforms of first derivative lineshapes with peak-to-peak linewidths of 1 G (dashed line) or 9 G (dot-dashed line).

Fig. 2

Ratio of the S/N for f(B) to S/N for s₁(B) as a function of the ratio of the modulation amplitude (h_m) to the peak-to-peak first derivative linewidth (ΔH_pp) for the LiPc sample. Blue solid lines with error bars represent experimental results for three measurements and dashed red lines are results of numerical simulations. The S/N comparison was made for f(B) spectra reconstructed from N_H=5 (a) and N_H=10 (b) harmonics and s₁(B) obtained at constant low modulation amplitude.

Fig. 3

Comparison of the traditional first harmonic EPR spectrum s₁(B) of LiPc measured with h_m/ΔH_pp ~ 0.5 (red line) and f(B) reconstructed from N_H=10 with h_m/ΔH_pp ~2.4 (blue dashed line).

Fig. 4

Comparison of s₁(B) measured with h_m = 0.13 G (solid green) with f(B) (dashed blue) recovered from spectra at harmonics n = 1 to 10, measured with h_m = 1.12 G (s₁(B), solid black). To facilitate comparison of the lineshapes the amplitude of the over-modulated s₁(B) spectrum measured with h_m = 1.12 G is decreased by a factor of 3.