Method of analysis for determining and correcting mirror deformation due to gravity

The Navy Precision Optical Interferometer, located near Flagstaff, Arizona, is a ground-based interferometer that collects, transports, and modulates stellar radiation from up to six primary flat collectors, known as siderostats, through a common vacuum relay system to a combiner. In the combiner, the modulated beams are superimposed, fringes obtained, and data recorded for further analysis to produce precise star positions or stellar details. The current number of observable stellar objects for the astrometric interferometer can increase from 6000 to at least 47,000 with the addition of full-aperture 20-deg down-tilting beam compressors in each optical train. Such an aperture increase, from the current 12.5 to 35 cm, opens the sky to many additional and fainter stars. Engineering analysis of our beam compressor primary mirror shows that the maximum allowable sag, 21 nm, occurs prematurely at 2.8-deg down-tilt angle. Furthermore, at the operational down-tilt angle of 20 deg, the wavefront deformation increases to 155 nm. We present a finite element analysis technique and design modification concept to reduce tilt-induced deformation on the mirror surface. This work is a first pass to determine the feasibility for a mechanical solution path forward. From this analysis, we found that four outwardly applied 17.8-N forces on the rear surface of the mirror could reduce sag from 155 to 32 nm at 20-deg down-tilt angle.