Algorithm for Unfolding Current from Faraday Rotation Measurement

Abstract

Various methods are described to translate Faraday rotation measurements into a useful representation of the dynamic current under investigation[1]. For some experiments, simply counting the "fringes" up to the turnaround point in the recorded Faraday rotation signal is sufficient in determining the peak current within some allowable fringe uncertainty. For many other experiments, a higher demand for unfolding the entire dynamic current profile is required. In such cases, investigators often rely extensively on user interaction on the Faraday rotation data by visually observing the data and making logical decisions on what appears to be turnaround points and/or inflections in the signal. After determining extrema, inflection points, and locations, a piece-wise, ¿I/¿t, representation of the current may be revealed with the proviso of having a reliable Verdet constant of the Faraday fiber or medium and time location for each occurring fringe. In this paper, a unique software program is reported which automatically decodes the Faraday rotation signal into a time-dependent current representation. System parameters such as the Faraday fiber's Verdet constant and number of loops in the sensor are the only user-interface inputs. The central aspect of the algorithm utilizes a short-time Fourier transform (STFT) which reveals much of the Faraday rotation's hidden detail necessary for unfolding the dynamic current measurement.