An automated method to find the proper modulation phase in continuous wave EPR spectroscopy

Abstract

Modulation of the do magnetic field is universally employed in the acquisition of continuous wave electron paramagnetic resonance spectra, which includes linear and saturation transfer (ST) EPR spectra. Modem two-channel lock-in analyzers produce two components which are at angles θ and θ + 90° with respect to the modulation reference. Experimentally it is often desired to choose θ such that the quadrature signal is “minimized,” so that the in-phase signal exhibits the maximum signal-to-noise ratio. This is called phase nulling. In this paper we provide a quantitative definition to the concept of a “minimized quadrature signal,” using a least-squares criterion, and derive a formula which enables computation of θ which is then used to generate proper in-phase and quadrature signals. Furthermore, an expression is derived for the error in θ which is of particular interest when acquiring STEPR spectra. The formulas are noniterative and can be easily programmed to rapidly and automatically phase null signals after acquisition.