Uncertainty analysis for absorption and first-derivative EPR spectra

Electron paramagnetic resonance (EPR) experimental techniques produce absorption or first-derivative spectra. Uncertainty analysis provides the basis for comparison of spectra obtained by different methods. In this study it was used to derive analytical equations to relate uncertainties for integrated intensity and line widths obtained from absorption or first-derivative spectra to the signal-to-noise ratio (SNR), with the assumption of white noise. Predicted uncertainties for integrated intensities and line widths are in good agreement with Monte Carlo calculations for Lorentzian and Gaussian lineshapes. Conservative low-pass filtering changes the noise spectrum, which can be modeled in the Monte Carlo simulations. When noise is close to white, the analytical equations provide useful estimates of uncertainties. For example, for a Lorentzian line with white noise, the uncertainty in the number of spins obtained from the first-derivative spectrum is 2.6 times greater than from the absorption spectrum at the same SNR. Uncertainties in line widths obtained from absorption and first-derivative spectra are similar. The impact of integration or differentiation on SNR and on uncertainties in fitting parameters was analyzed. Although integration of the first-derivative spectrum improves the apparent smoothness of the spectrum, it also changes the frequency distribution of the noise. If the lineshape of the signal is known, the integrated intensity can be determined more accurately by fitting the first-derivative spectrum than by first integrating and then fitting the absorption spectrum. Uncertainties in integrated intensities and line widths are less when the parameters are determined from the original data than from spectra that have been either integrated or differentiated.