A study on the evaluations of the active optics system performance for the primary mirror of the GEMINI Telescopes Project was conducted. Finite element analysis was employed to analyze the optical surface figures of the primary mirror. Four distinct influence matrices (generic 3-point kinematic system, combined unit case, 3-zonal multiple constraint system, and high frequency localized force set) were established based on the unit lc?,d cases at each of 120 active support locations and the restraint boundary conditions in the mirror model. A least square algorithm was developed. This scheme is able to accommodate the design constraints in the active optics systems. The active optics performances were evaluated by analyzing their capabilities in compensating the optical surface figures. For each active system, the level of the calculated active forces and the surface residual errors were examined. The results indicated that their performances are excellent and are in good agreement for most sampling surface figures. The results from the active optics performances based on the generic, the combined, and the 3-zone cases were practically identical for all the object surfaces. The active optics system based on the high frequency localized force set tends to predict a higher surface RMS error and requires a bigger force set. This effect became apparent when this system was applied to correct the surfaces from the natural mode analyses.
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