For the investigation of turbulent flows, the measurement of Lagrangian acceleration is of great interest as it represents a direct component of the Navier–Stokes equations. The presented sensor is based on the common laser Doppler technique, but offers in addition combined high spatial resolution in the micrometre range and the possibility of measuring the velocity component along the optical axis. As a result of the sensor setup, signals of particles with inclined trajectories show frequency modulation within a single burst similar to the signal of an accelerated particle. A model-based approach to distinguish between both quantities is presented, and a signal processing technique based on the Hilbert transform has been developed. The processing is comparatively fast and showed good agreement with preset values, even for signals of poor quality. The variance of velocity and acceleration measurements nearly reaches the Cramér–Rao lower bound. Experimental verification is done by the measurement of a harmonic oscillator with known parameters and a stagnation flow within a free jet.
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Bayer et al. (2008) studied this question.