Derivation and comparison of fundamental uncertainty limits for laser-two-focus velocimetry, laser Doppler anemometry and Doppler global velocimetry

Laser-2-focus velocimetry (L2F), laser Doppler anemometry (LDA) and Doppler global velocimetry (DGV) are common measurement techniques for flow analysis, but a fundamental comparison of their minimum achievable measurement uncertainties is still missing. In order to reveal the measurement principle with the lowest uncertainty, the Cramer-Rao lower bounds (CRLB) are derived analytically regarding two inevitable fundamental disturbances: photon shot noise and thermal detector noise. The CRLB results are compared with each other assuming equal temporal resolutions. For both noise sources, a relative uncertainty limit results for L2F and LDA, and an absolute uncertainty limit for DGV. Hence, DGV seems to be appropriate for investigating high-speed flows. However, the threshold velocities strongly depend on the possible viewing angles. The CRLBs are calculated and compared with each other for typical conditions in turbomachinery as an example. (C) 2010 Elsevier Ltd. All rights reserved.