Fig. 1. Prototype laser-pointing system. S is the laser source; L is the thin lens; M is the spot image on the CCD; T is the beam tilt of the waist center on the source plane; a₀, θ_x are the position offset and inclination angle of the beam relative to the optical axis in the x direction, respectively, and b₀, θ_y are those in the y direction; u is the distance between the source plane and the lens; f is the focal length; δ_z is the defocus distance of the CCD. The optical axis of the system is along the z direction.

Fig. 2. Prediction errors E_j for all epochs, spot image M₂ and image difference for beam tilts in the x direction. (a) and (b) show the prediction errors, the spot image and image difference on the vertical CCD, respectively. (c) and (d) show those on the tilted CCD with a rotation of 60° around the y-axis. (e) and (f) show those on the tilted CCD with a rotation of 60° around the x-axis.

Fig. 3. Prediction performances E_mean with different focal lengths f, tilting angles θ and defocus distances δ_z. (a) and (b) show spot samples and the prediction performance with typical focal lengths f = 40 and 100 mm, respectively. The partially enlarged plot in the dotted rectangle represents the prediction results for θ = 60°. (c) and (d) show the prediction performance when the tilting angles are 45° and 60°, respectively.