Optimized signal deduction procedure for the MIEZE spectroscopy technique

TL;DR

This paper introduces an efficient algorithm for phase and amplitude reconstruction in MIEZE spectroscopy that enhances data acquisition speed and maintains accuracy, surpassing traditional fitting methods in speed and bias.

Contribution

The paper presents a novel, less computationally intensive reconstruction method for sinusoidal event rates in MIEZE spectroscopy, improving data throughput and accuracy over existing techniques.

Findings

Reconstruction method is unbiased and efficient for phase estimation.

Increases potential time resolution by a factor of four.

Reconstruction error is about 10% higher for contrast compared to traditional fitting.

Abstract

We report a method to determine the phase and amplitude of sinusoidally modulated event rates, binned into four bins per oscillation, based on data generated at the resonant neutron spin-echo spectrometer RESEDA. The presented algorithm relies on a reconstruction of the unknown parameters. It omits a calculation intensive fitting procedure and avoids contrast reduction due to averaging effects. It allows the current data acquisition bottleneck at RESEDA to be relaxed by a factor of four and thus increases the potential time resolution of the detector by the same factor. We explain the approach in detail and compare it to the established fitting procedures of time series having four and 16 time bins per oscillation. In addition we present the empirical estimates of the errors of the three methods and compare them to each other. We show that the reconstruction is unbiased, asymptotic, and efficient for estimating the phase. Reconstructing the contrast increases the error bars by roughly 10% as compared to fitting 16 time binned oscillations. Finally, we give heuristic, analytical equations to estimate the error for phase and contrast as a function of their initial values and counting statistics.