Frequency-domain analysis of absolute gravimeters

An absolute gravimeter is analysed as a linear time-invariant system in the frequency domain. Frequency responses of absolute gravimeters are derived analytically based on the propagation of the complex exponential signal through their linear measurement functions. Depending on the model of motion and the number of time-distance coordinates, an absolute gravimeter is considered as a second-order (three-level scheme) or third-order (multiple-level scheme) low-pass filter. It is shown that the behaviour of an atom absolute gravimeter in the frequency domain corresponds to that of the three-level corner-cube absolute gravimeter. Theoretical results are applied for evaluation of random and systematic measurement errors and optimization of an experiment. The developed theory agrees with known results of an absolute gravimeter analysis in the time and frequency domains and can be used for measurement uncertainty analyses, building of vibration-isolation systems and synthesis of digital filtering algorithms.