Limitations on Threshold Sensitivity and Measurement Errors in Pulsed Optical Fiber Accelerometers

Abstract

Estimation of the ultimate metrological performance of precision digital accelerometers with pulsed optical fiber transducer carried out in [1] was based on an idealized model in which the authors deliberately neglected a number of factors that restrict performance. In this paper, we consider the effect of the natural limitations of threshold sensitivity and of the minimally attainable acceleration measurement errors that are due to the effect of temperature on the modulator sensitive element of the optical fiber transducer and also to the instability of the period of revolution of the modulator which is a real self-oscillating system with finite quality factor. In thermal equilibrium, the atoms of the modulator are in chaotic oscillatory motion. Assuming that the modulator is an ensemble of atoms described by statistical laws, one can consider its average thermal energy whose fluctuations are added to the total mechanical energy. Starting from the equipartition law [2], we assume that the number of degrees of freedom is i = 2 (kinetic and potential energy). According to [2], the uncertainty of the total energy of the sensitive element of the modulator is taken to be kΘ (where k is the Boltzmann constant and Θ is absolute temperature); this will be seen to determine the corresponding degree of instability of the oscillations. Let us estimate it.