Pan-Tilt Servo Mechanism

In order to allow some head motion, it is required to keep the pupil centered in the image. The magnitude of the rotation angle of the camera which brings the pupil to the center of the image (assuming the rotation is around its principal point), will only depend of the image size and the field of view (FOV) of the camera. If the center of the pupil is at the pixel (x,y) (assume the pixel (0,0) to be the center of the image), and given the FOV $=(\phi_x,\phi_y)$, and image size $W \times H$, the pan and tilt are given by: