Cyber-Physical Systems (CPS) refer to the embedding of widespread sensing, networking, computation and control into physical spaces with the goal of making them safer, more efficient and reliable. This article proposes a control theoretic method, called physical watermarking, to authenticate the correct operation of a control system. Authentication in cyber-physical systems requires that the system operator verify both the identity of a component in not only, the information theoretic sense, but also within the framework of its physical dynamics.This article investigates the problem of designing the optimal watermark signal in the class of stationary Gaussian processes, which maximizes its visibility in the sensor responses while maintaining minimal impact to the system.