A new ellipse fitting method of the minimum differential-mode noise in the atom interference gravimeter

Abstract

Ellipse fitting is a useful tool to obtain the differential signal of two atom interference gravimeters. The quality standard of ellipse fitting should be the deviation between the true phase and the fitting phase of the interference fringe. In this paper, we present a new algorithm to fit the ellipse. The algorithm is to minimize the differential noise of two interference gravimeters and obtain a more accurate value of the gravity gradient. We have theoretically derived the expression of the differential-mode noise and implemented the ellipse fitting in the program. This new algorithm is also compared with the classical methods.

Position fixing with cold atom gravity gradiometers

“…The standard ellipse fitting approach described in reference 45 has been extended and enhanced 46,47 . However, again for simplicity, we use the standard method where the phase difference is found from fitting an ellipse of the form 45 ,…”

“…The pairs of measurements lie on an ellipsebecause the phase of the reference laser is unknown and varies over time. The gradient is found by fitting an ellipse to a set of measurements [45][46][47] . This presents a potential problem for the use of this method when the gradiometer is moving relative to the reference field.…”

A vibration correction system for cold atom gravimeter

“…A commercial software is used to correct the measured transfer function of the seismometer, obtaining the actual motion of the mirror. Experimental results have demonstrated that it improved the measurement sensitivity of absolute gravimeters by 3-4 times [20,21]. The National University of Defense Technology in China conducts a detailed analysis of the measurement noise introduced by vertical and horizontal coupling-induced vibration.…”

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

“…Various methods for fitting ellipses can be found in the literature [15][16][17][18][19]. One can distinguish between geometric fitting methods, which minimise the distance between the data points and the fitted ellipse (in the x-y plane), and algebraic methods, which minimise a certain function of x and y.…”

“…However, geometric methods have the advantage of minimising the error between the fit and the data in a more satisfactory manner; for detailed discussions of the issues involved the reader is referred to references [1,[16][17][18].…”