Fig. 1. (a) Optical system based on error separation technique, (b) error analysis of improved calibration optical system, and (c) error analysis of optical system based on error separation technique. FSM, fast steering mirror; HRM, hollow retroreflector mirror; BS, beam splitter; L, lens.

Fig. 2. (a) Schematic of the spatial alignment and stability of multi-beam optical system: M, mirror; TS, translation stage; PSD, position sensitive detector. (b) Experimental setup of the optical system.

Fig. 3. Single-direction decoupled control results along (a) x, (b) y, (c) α, and (d) β directions of the first laser beam and (e) x, (f) y, (g) α, and (h) β directions of the second laser beam.

Fig. 4. (a) Photography of the test setup and (b) positional deviations of emitted laser beams detected by external detection. AVG, average.

Fig. 5. Under-active disturbance: the results of the external detector (a) without and (b) with feedback for the first laser beam.

Fig. 6. Display of positional and angular deviations of the first laser beam (780 nm) over 1 h with feedback control. (a) Translational deviations, (b) and (c) deviations along the x and y directions over time, respectively, (d) angular deviations, and (e) and (f) deviations along the α and β directions over time, respectively.

Fig. 7. Display of positional and angular deviations of the second laser beam (532 nm) over 1 h with feedback control. (a) Translational deviations, (b) and (c) deviations along the x and y directions over time, respectively, (d) angular deviations, and (e) and (f) deviations along the α and β directions over time, respectively.

Fig. 8. Deviations of incident laser beams: (a) the first laser beam, (b) the second laser beam, and (c) positional and (d) angular (f = 0.3 m) deviations of exit beams under control with an optical beam profiler.