The mathematical model of the velocity sensed by a laser beam incident in an arbitrary direction on a rotating target
undergoing arbitrary vibration is now well established. The model combines a three-dimensional description of the
velocity of the point of incidence on the target with knowledge of the orientation of the incident beam and any known
point along the line of incidence of that laser beam. For scanning LDV, where the beam is deflected through the use of
optical devices, recent work has introduced a general mathematical procedure for determination of the final beam
orientation following successive reflections and refractions through an optical system. This paper describes this work,
including how inevitable translational and angular misalignments can be incorporated and, for the first time, how
Doppler shifts on transmission through or reflection from rotating / oscillating optical components can be calculated.
Demonstration of the application of this procedure is seen in the proposal of a novel, scanning LDV arrangement in
which rotating wedge prisms are used to track a rotating component. Preliminary experimental results are shown for this
arrangement. The versatility of the mathematical procedure is shown by application to a tracking LDV arrangement
using a rotating Dove Prism. The predictions show how angular and translational misalignments distort the desired scan
path and how the whole body rotation of the target can result in measurement of small velocity components at integer
multiples of the prism rotation frequency.