Control Matrix Design for ReducedWavefront Error

Astronomical telescopes have allowed humans to view the deep reaches of space. These systems can show galaxies and stars that are farther away from the Earth than many humans can imagine. However, the light that is emitted by the objects in space has to pass through the atmosphere to reach these telescopes. The atmosphere bends what would have otherwise been a flat wavefront of light when the light arrives at the Earth. This bending of the light blurs the image and limits a telescope's ability to resolve the objects found in space. Adaptive optics systems remove these atmospheric effects and improve telescope resolution. Adaptive optics systems use a wavefront sensor, a reconstructor, and a deformable mirror to return the aberrated wavefront to its original flat shape. The residual wavefront error of these systems can be minimized through the modification of the control matrix that creates the reconstructor. The minimized error translates directly to improved resolution in the telescope's images. Control matrix modifications are powerful tools for improving correction due to the matrix's central role in converting the sensed wavefront information into deformable mirror motion. Some control matrix modifications include partial illumination correction and mode passing. A simulated adaptive optics system is designed to evaluate control matrix modifications. In the simulated system, aberrated wavefronts are created using a series of phase screens, the wavefront is sampled using a Shack-Hartmann wavefront sensor in the Fried Geometry, a control matrix generator creates and implements the modifications on the control matrix, and a deformable mirror performs the correction. Five control matrix modifications are evaluated including fixed value, nearest neighbor, slope removal, no modification, and mode passing. The slope removal modification is found to most effectively minimize the residual error in the wavefront. The amount passed modes are attenuated after reflecting off the deformable mirror is also examined. Finally, situations of high and low performance are found for all methods and aberration mode dependencies discussed.