An investigation of errors in ellipse-fitting for cold-atom interferometers

Abstract Ellipse fitting is a technique which is used to extract differential phase in cold-atom interferometers, particularly in situations where common-mode noise needs to be suppressed. We use numerical simulation to investigate errors in the ellipse fitting process; specifically, errors due to the presence of additive noise, linear drift in ellipse offset and amplitude, as well as an error that can arise from fringe normalisation. Errors are found to manifest in two ways: bias in the ellipse phase measurement and incomplete suppression of common mode phase noise. We quantify these errors for three different ellipse fitting algorithms and discuss the applicability of these results to future cold atom sensors.