Signal processing efficiency of Doppler global velocimetry with laser frequency modulation

Abstract

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 Cramér 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 Cramér–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.