Signal processing efficiency of Doppler global velocimetry with laser frequency modulation

Novel Doppler global velocimeters using laser frequency modulation can optically measure flow velocity fields and offer promising perspectives but so far unknown limits for achieving low measurement uncertainties One approach e g is based on sinusoidal frequency modulation and a harmonic signal analysis In order to determine the minimum achievable measurement uncertainty the known theorem of Cramer and Rao is applied to a derived signal model initially excluding the harmonic signal analysis For a typical scattered light power of 1 nW and a desired temporal resolution of 16 ms the calculated minimum velocity standard deviation amounts to 0 02 and 0 06 m/s for signal dependent (quantum shot) noise and signal Independent (thermal and dark current) noise respectively It is subsequently investigated how efficient the harmonic signal analysis extracts the Fisher information content The ratio of the Cramer-Rao lower bound and the estimated measurement uncertainty where the signal processing is taken into account was found to be >75% in terms of standard deviations in the entire measurement range of about +/- 250 m/s For the challenge of measuring velocity fields in turbomachine flows (requirements 5 kHz measurement rate <= 1% statistical error velocities (50-240) m/s) the presented results indicate a necessary minimum scattered light power of 1 5 nW which seems feasible (C) 2009 Elsevier GmbH All rights reserved