Full cycle rapid scan EPR deconvolution algorithm.

Rapid scan electron paramagnetic resonance (RS EPR) is a continuous-wave (CW) method that combines narrowband excitation and broadband detection. Sinusoidal magnetic field scans that span the entire EPR spectrum cause electron spin excitations twice during the scan period. Periodic transient RS signals are digitized and time-averaged. Deconvolution of absorption spectrum from the measured full-cycle signal is an ill-posed problem that does not have a stable solution because the magnetic field passes the same EPR line twice per sinusoidal scan during up- and down-field passages. As a result, RS signals consist of two contributions that need to be separated and postprocessed individually. Deconvolution of either of the contributions is a well-posed problem that has a stable solution. The current version of the RS EPR algorithm solves the separation problem by cutting the full-scan signal into two half-period pieces. This imposes a constraint on the experiment; the EPR signal must completely decay by the end of each half-scan in order to not be truncated. The constraint limits the maximum scan frequency and, therefore, the RS signal-to-noise gain. Faster scans permit the use of higher excitation powers without saturating the spin system, translating into a higher EPR sensitivity. A stable, full-scan algorithm is described in this paper that does not require truncation of the periodic response. This algorithm utilizes the additive property of linear systems: the response to a sum of two inputs is equal the sum of responses to each of the inputs separately. Based on this property, the mathematical model for CW RS EPR can be replaced by that of a sum of two independent full-cycle pulsed field-modulated experiments. In each of these experiments, the excitation power equals to zero during either up- or down-field scan. The full-cycle algorithm permits approaching the upper theoretical scan frequency limit; the transient spin system response must decay within the scan period. Separation of the interfering up- and down-field scan responses remains a challenge for reaching the full potential of this new method. For this reason, only a factor of two increase in the scan rate was achieved, in comparison with the standard half-scan RS EPR algorithm. It is important for practical use that faster scans not necessarily increase the signal bandwidth because acceleration of the Larmor frequency driven by the changing magnetic field changes its sign after passing the inflection points on the scan. The half-scan and full-scan algorithms are compared using a LiNC-BuO spin probe of known line-shape, demonstrating that the new method produces stable solutions when RS signals do not completely decay by the end of each half-scan.