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An analysis of simulators and tracking systems for laser Doppler velocimeters

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Abstract

Analogue and digital techniques are proposed for the simulation of signals arising in laser Doppler velocimeters. Their merits are evaluated.

Of special interest is the estimation of the instantaneous frequency of the Doppler signal from the zero crossing rate. An analysis is presented whereby the biases introduced in this estimation method are derived for two optical configurations of the velocimeter. This analysis is extended to the case of additive Gaussian noise on the signal, and the cumulative effect of additive noise on the zero crossing rate is determined.

The so called “drop-out problem” which pervades the frequency estimation of the instantaneous Doppler signal is next considered, and expressions are derived for mean drop-out rate and the mean interval between drop-outs in terms of an arbitrary signal threshold. These should facilitate choice of threshold detection for given rms Doppler signal levels, and in achieving relative compromises in terms of signal bandwidth. Finally a novel form of frequency tracking system is discussed and its performance critically assessed.

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Abbreviations

A 1,2 :

Weighting constant for Doppler signal arising from different velocimeter configurations

E :

Expectation operator

{itH(t)}:

Envelope of Doppler signal

H 0 :

Doppler signal threshold level

K 1,2 :

Bandwidth ratio

N i :

Total input additive noise power

R(τ) :

Autocorrelation function for lagτ

W(t) :

Weighting function associated with velocimeter set-up

p(.):

Probability density function of random variable (.)

x(t),y(t) :

Bandpass filtered Doppler signal

Φ(f):

Power spectral density function at frequencyf

ψ i :

Total input signal power

η i :

Input signal-to-noise ratio

λ :

Zero crossing rate

ρ(τ):

Normalized autocorrelation function for lag (τ)

μ :

Normalized threshold level

(ω 0)f 0 :

(Angular) central frequency of Doppler signal

(ω 1)f 1 :

(Angular) central frequency of bandpass filter.

References

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Authors and Affiliations

  1. Department of Electronics, University of Southampton, UK

    T. S. Durrani & T. H. Wilmshurst

  2. Fluid Dynamics Unit, Physics Department, University of Edinburgh, UK

    C. Greated

Authors
  1. T. S. Durrani
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  2. T. H. Wilmshurst
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  3. C. Greated
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Durrani, T.S., Wilmshurst, T.H. & Greated, C. An analysis of simulators and tracking systems for laser Doppler velocimeters. Opto-electronics 5, 71–89 (1973). https://doi.org/10.1007/BF01421903

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  • DOI: https://doi.org/10.1007/BF01421903

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