Control laws for a three-element Risley prism optical beam pointer

In traditional Risley prism beam pointers, two wedge prisms are used to steer the optical path. This type of beam director is attractive for free space laser communication and beam scanning systems because the beam director is compact and conformal. Furthermore, moderately large apertures can be accommodated without significant weight or power consumption. However, this approach is not well suited to tracking systems, since while tracing a continuous, constant velocity path, control singularities can occur that require infinite rotational speeds of the prisms. This phenomenon is particularly evident at pointing angles near the system boresight. A third prism can be used to eliminate these singularities, but the system is then under-constrained and infinite solutions exist for the prism orientations. In this paper, a method of uniquely determining the proper orientations of three prisms in an optical beam pointer is presented. It is shown how the method can be used to optimize a system for optical tracking by minimizing the angular velocities required of the prisms. Also, a specific implementation of the method has been demonstrated in the laboratory. Smooth tracking of arbitrary target trajectories is demonstrated across the field of view of the system.