Defining parametric dependencies for the correct interpretation of speckle dynamics in photon Doppler velocimetry

Laser speckle dynamics manifest themselves in photon Doppler velocimetry (PDV) data as low-frequency amplitude fluctuations, and analysis of these fluctuations provides insight into the transverse speed of the surface under observation. We previously demonstrated that a single measurement probe is capable of simultaneously measuring (1) axial motion, through frequency analysis of Doppler shifts, and (2) transverse speed, through analysis of the speckle's coherence time. However, the performance of this technique hinges on a correct understanding of the speckle pattern's response to surface motion. In this paper, we model the origination of the speckle pattern, and we describe a methodology for calculating the speckle's coherence time from the autocorrelation of a noisy signal. We then test a suite of optical probes over a range of standoff distances, demonstrating a significant reduction in the speckle's coherence time, which correlates to the increase in speckle boiling when the target surface is located near a probe's focal length. We show that spatial regions of decreased coherence time may be predicted a priori by a probe's parameters, since they stem from boiling dominance. We analyze this result as a function of probe parameters for a surface-scattering target and a volume-scattering target. Although the coherence time's behavior in the focal plane makes velocity extraction difficult, far from the probe's focal lengths, we are able to measure rigid body transverse speeds exceeding 20  m/s with an absolute accuracy of ±15% using the speckle dynamics measured by a PDV setup.