Optimizing and comparing laser anemometers

Abstract

Comparisons can be made only if some single valued measure of the quality of each system can be defined. This concept is illustrated here by specifying the quality variable to be the measurement uncertainty in the mean velocity of a turbulent flow in the presence of a large background noise. The Fisher number is used as a figure of merit for some parts of the system. It is noted that in many cases of practical interest, the reciprocal Fisher number gives the actual variance of an estimator. Its principal advantage here is that it can be computed without detailed assumptions about the statistics of the estimated quantities. The concept of a Fisher number is related to the concept of information gain in a measurement. The variance of the measured mean velocity is expressed in terms of the uncertainty for the individual measurements, the measurement rate, and the velocity correlation time. Conditions are given under which the fringe and the two-spot anemometer are optimized.