Analytic Solution of Free Space Optical Beam Steering Using Risley Prisms

This paper provides some mathematical formulae for Risley beam steer control system that is used for free space optical interconnection system. Given the prisms´ orientations, the analytic formulae can be used to calculate the pointing position. For the inverse problem, i.e., given the desired pointing position, the required prisms´ orientations can be obtained efficiently by applying any numerical method for systems of nonlinear equations related to the formulae. Unlike some existing methods, these formulae are not first-order approximation but an accurate closed analytical form. It does not need a good initial guess on the motor positions required by some other methods. It also does not need a feedback loop to get the correct pointing position but it can be used in feedback implementation. This feature is especially imporutant for systems that need to slew the beam to the desired position quickly and accurately.