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

Abstract

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 Cramér-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.