Response functions of atom gravimeters

TL;DR

This paper models atom gravimeters as linear time-invariant systems, analyzing their impulse responses and effects of gravity gradients, and compares different types based on their filtering characteristics.

Contribution

It introduces a system-theoretic framework for atom gravimeters, characterizing their impulse responses and effects of gravity gradients, including new insights into Bloch oscillation-based devices.

Findings

Impulse responses are triangle, meander, and Dirac comb shapes.

Effective measurement height varies with gravity gradient and instrument type.

Different atom gravimeters act as first- or second-order low-pass filters.

Abstract

Atom gravimeters are equivalent to non-multi-level corner-cube gravimeters in translating the gravity signal into the measurement result. This enables description of atom gravimeters as LTI systems. The system's impulse responses by acceleration, velocity, and displacement are found to have the shape of triangle, meander, and the Dirac comb resp. The effects of inhomogeneous gravity field are studied for constant and linear vertical gradients and self-attraction of the instrument. For the constant gradient the effective measurement height is below the top of the trajectory at 1/6 and 7/24 of its length for the fountain and the release types of the instruments resp. The analysis is expanded to the gravimeters implementing the Bloch oscillations at the apex of the trajectory. In filtering the vibrations these instruments are equivalent to the first-order low-pass filters, while other atom gravimeters are equivalent to the second-order low-pass filters.