Line-of-Sight Kinematics for a Two-Axis Head Mirror Equations for predicting and controlling mirrored LOS pointing

摘要

Gimbaled planar mirrors are used to point and stabilize a camera's or laser's line-of-sight (LOS). The mirror with its reflection property adds another degree of complexity to the already complex area of LOS pointing and stabilization modeling and control. For example, when the optics and detector are located off gimbal and utilizing a 2-axis gimbaled mirror to point the LOS, the image at the detector rolls one for one with the outer gimbal rotation. This is difficult to understand unless the equations are developed to show this. The LOS pointing kinematic equations for a planar gimbaled mirror begin with the mirror reflectance equation [2,3]. This equation describes the reflected ray or vector in terms of the incoming ray and the mirror unit normal, and ultimately creates the mathematical relationship between the reflected ray, the base (or a user-defined reference frame), and the detector reference frame. This kinematic relationship is differentiated to form the LOS rate equations from which one can easily see what states are necessary, and how these states are combined, for inertially stabilizing the LOS about its roll, pitch, and yaw axes.