Converts a sinusoidal rapid-scan time-domain EPR signal to the corresponding field-swept EPR spectrum.

rapidscan2spc(rsSignal,rsAmp,rsFreq);
rapidscan2spc(rsSignal,rsAmp,rsFreq,g);
[dB,spc] = rapidscan2spc(...);

See also the user guide on rapid-scan EPR.

rapidscan2spc converts a rapid-scan time domain signal into the corresponding EPR spectrum.

It takes three or four inputs:

rsSignal is s a vector containing the rapid-scan time-domain signal over one period of modulation. It must be complex-valued and contain the dispersion in the real part and the absorption in the imaginary part. The number of points must be even. The underlying modulation is assumed to be cosine.

rsAmp is the peak-to-peak modulation amplitude, in units of mT. rsFreq is modulation frequency, in units of kHz.

g is the g value for the field/frequency conversions needed to calculate the spectrum and the field range. If g is omitted, it is assumed to be 2.002319.

The function returns the field offset in dB (in units of mT) and the EPR spectrum in spc. spc is complex-valued: the real part is the dispersion spectrum, and the imaginary part is the absorption spectra.

For the conversion to work, the rapid-scan signals of the up- and the down-sweeps should not overlap, and the data should not be saturated. Additionally, the input signal needs to be correctly quadrature phased, time shifted to align with a cosine field modulation, and background corrected.

Here is a simple example. First, let us simulate a rapid-scan signal:

g = 2;
T1 = 4;          % microseconds
T2 = 0.5;        % microseconds
B1 = 1e-3;       % mT
deltaB0 = 0;     % mT
ModAmp_mT = 1;   % mT
ModFreq = 50;    % kHz    
[t,Mx,My,Mz] = blochsteady(g,T1,T2,deltaB0,B1,ModAmp_mT,ModFreq);
Mxy = -Mx + 1i*My;

rapidscan2spc takes Mxy and constructs the EPR spectrum

ModAmp_mT = 1;   % mT
ModFreq = 50;    % kHz    
[dB,spc] = rapidscan2spc(Mxy,ModAmp_mT,ModFreq,g);
plot(dB,real(spc),dB,imag(spc));

rapidscan2spc uses a Fourier deconvolution method (Tseitlin et al., 2011) that transforms each of the two halves of the time-domain signal (up-sweep and down-sweep) separately to obtain two spectra, which are then added.

• M. Tseitlin, G. A. Rinard, R. W. Quine, S. S. Eaton, G. E. Eaton, J. Magn. Reson. 2011, 208, 279-283. link
• M. Tseytlin, J. Magn. Reson. 2017, 281, 272-278. link

pepper, blochsteady