Accuracy of the frequency and phase measurement concerning different noise sources for phase Doppler Anemometry

The measurement accuracy of the estimation of the Doppler frequency and the signal phase difference in Phase Doppler Anemometry (PDA) systems is investigated in this paper by taking into account the effect of the particle trajectory via the measurement volume and the different noise sources. Both the signal dependent (quantum shot) noise and the signal independent (thermal and dark current) noise are considered. The minimum achievable measurement uncertainty of the phase shift estimation for the signal independent noise is determined by employing the 2D model of the Doppler Burst Signal with the Gaussian envelope and compared with the performance of the correlation method. Additionally, the Cramér-Rao lower bound (CRLB) of the frequency estimation concerning the quantum shot noise is calculated. The numerical examples show the performance of the correlation method with various parameter configurations compared with the derived CRLB. The numerical results confirm the validity of the analysis in terms of the relative effect of the particle trajectory, relative measurement time, size of the volume and signal-to-noise ratio on the accuracy of the estimation.