Bias correction for individual realisation LDA measurements

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Abstract
The case where every particle which passes through the ellipsoidal probe volume produces one and only one velocity measurement is examined. The implications of this simplification are considered in detail. It is shown that it is usually possible to arrange the system parameters so as to justify this assumption, especially if frequency shifting is used for highly turbulent flows. The method of bias correction described applies to a one-dimensional LDA which does not measure particle residence times. This method involves fitting a theoretical biased probability density function of velocity to the experimental velocity histogram, and the mean and root mean square velocities are obtained by the maximum likelihood estimation procedure. This method requires estimates of two other properties of the turbulent velocity field, but it is shown that the results are not very sensitive to the values of these estimates.