Simulating translation-induced laser speckle dynamics in photon Doppler velocimetry

Historically, single-beam optical velocimetry has been limited to measuring only the component of velocity along the beam. However, theoretical work and recent experimental results have shown that laser speckle dynamics may be exploited to measure lateral motion, thereby gaining information about surface dynamics across an additional degree of freedom. In the use of photon Doppler velocimetry (PDV), this new information is considered "free" in that it is already contained within the PDV signal, needing only to be extracted and interpreted correctly. In this manuscript, we relate speckle dynamics to the lateral motion of a planar scattering surface in the PDV coordinate system via the space-time correlation function of the diffracted electric field. Next, we relate the characteristic time scale of speckle intensity fluctuations in the PDV signal to the rate of lateral surface translation and to parameters characterizing the optical probe. Analytical results are compared with a numerical simulation and found to be in close agreement.