Statistics of laser Doppler velocimeter signals: frequency measurement

Abstract

The statistical properties of laser Doppler velocimeter signals are derived and used to obtain the signal zero crossing statistics for steady flows and high scattering particle concentrations. The results are applied to a model of a zero crossing counter, and expressions for the power spectrum and autocorrelation of the output signal are given in terms of the input signal autocorrelation. The RMS value of the fluctuations in the zero crossing counter output is calculated as a function of the optical system bandwidth and the counting time for infinite and finite input signal-to-noise ratios, and simple asymptotic expressions are found for large counting times and infinite signal-to-noise ratio. For finite input signal-to-noise ratios and large counting times bounds are derived for the output of a zero crossing counter preceded by a tracking filter, and the effects of the tracking filter are discussed.