Large-aperture deformable mirror correction of tiled-grating wavefront error

When tiling three gratings, with each individually exhibiting astigmatism and power due to holographic errors and coating stress, the resulting wavefront aberrations contain high-frequency components as well as the fundamental frequency, which is nearly three cycles across the aperture in the tiling direction. A deformable mirror (DM) that was designed to compensate for much slower errors (e.g., those arising from distortion in amplifier disks) is being used to compensate for this tiling-induced error. This investigation studies the effectiveness of compensating only the fundamental frequency of the tiled aberration, and shows that this provides a significant improvement that is adequate for a range of expected aberrations. Limitations of the DM correction technique are also studied.