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.

Accuracy analysis of major signal processing techniques in laser Doppler velocimetry

“…This kind of zero analysis was considered first by R. Adrian in Ref. 2 and later on by H.Mishina and T.Asakura in Ref. 3 .…”

“…Currently, three major techniques are employed for signal processing in Doppler velocimetry [1][2][3] : Doppler spectral shift measurement, which is most often used; correlation measurement and zero crossings measurement. In the present paper we do a comparative accuracy analysis of these three major techniques.…”

Static and dynamic light scattering by aerosols in a controlled environment

“…Experiments such as laser light near threshold (Jakeman et al, 1970b), motions of particles in turbulent fluids (Diporto et al, 1969;Bourke et al, 1970), and light scattering from small number of particles undergoing Brownian motions (Schaefer and Berne, 1972;Schaefer and Pusey, 1972;Adrian, 1972) follow non-Gaussian statistics. Schaefer and Berne (1972) showed that non-Gaussian concentration fluctuations arise at low concentrations because the particles in the scattering volume have a Poisson distribution.…”

Optical sum-frequency generator based on coupled waveguides

“…We refer to g,(z) as the 'normalised' conditional zero density. (20gN (7) corresponds to the density g(r) defined in Adrian (1972). )…”