Fundamental Measurement Uncertainty Limits of Doppler Global Velocimetry with Laser Frequency Modulation

摘要

A Doppler Global Velocimetry system with sinusoidal laser frequency modulation (FM-DGV) for the purpose of measuring velocity fields in fluid flows is described. It consists of a frequency modulated laser diode emitting at 852.3 nm, a caesium absorption cell to convert Doppler freqency shifts to intensity changes and a fibre-coupled avalanche photo diode array as detecting unit. The fundamental limits of the measurement uncertainty are analysed to understand and overcome current system limitations. Therefore, a simplified signal and a noise model are derived. The considered noises are Poisson distributed photon noise and Gaussion distributed detector noise. Using these models, the theory of Cramer and Rao can be applied, calculating the minimum achievable measurement uncertainty. The calculations show, that 0.02 m/s minimum standard deviation of the velocity are achievable with e.g. 20 nW scattered light power and 260 fW/VHz minimum noise equivalent power of the detector. This agrees well with the measured value of 0.03 m/s. Furthermore, we found that the influence of detector noise is of big importance for flow measurements, that are low scattered light powers. As a result, one strategy for FM-DGV system improvements is the optimisation of the detectors. A comparison between the fundamental measurement uncertainty limit of FM-DGV and conventional DGV shows, that in principle approximately the same velocity resolutions can be achieved. However, two large system immanent errors (image misalignment error and beam splitting error) reducing the performance of conventional DGV using two detector units are eliminiated with FM-DGV technique. Thus, it is a promising tool for measuring the flow velocity e.g. around a truncated cylinder or the velocity spectrum for turbulence analysis with low measurement uncertainty and instantaneously at multiple points.