Adaptive Optics Calculations Using the Connection Machine

Abstract

The performance of reflecting optical telescopes located on the surface of the earth are subject to distortions due to the force of gravity on the mirror and the turbulence of the atmosphere on the light path. Reflective optics are also planned for use in high-powered laser systems, where the intensity of the light itself is capable of producing distortions in the air within the instrument, thereby affecting the shape of the focused wavefront. A solution proposed by optical designers is the use of adaptive optics: an optical system in which the figure of the mirror is deformable to the extent necessary to correct for the distortions mentioned. An adaptive optical system uses a feedback loop concept, in which the distortions of the optical wavefront are measured, the necessary corrections are computed, and a set of actuators is moved to provide those corrections. The calculation of the corrections is computationally intense. Specifically, the measurement of the distortions provides a collection of phase differences between measuring points corresponding to the actuator positions. This set of phase differences is larger than the number of actuators, leading to an overdetermined problem. As physical systems have some amount of noise present, the technique of least-squares solution serves both to provide the best choice of actuator positions for this overdetermined problem and to suppress the noise in the measurements. The necessary algorithms for solving the computation portion of the adaptive optics problem consist of a matrix generator to derive the computational representation of the physical system, a matrix inversion routine, and a high-speed least-squares solver. In the optical astronomy paradigm, the computational requirement is for a small number of adjustments per second, due to the rate of atmospheric turbulence. For the laser system, with more stringent requirements, we demonstrate an improvement of 11 2 orders of magnitude, made possible only through the use of supercomputer methods. Extrapolation of these results indicates that even greater acceleration is possible if the interprocessor communication is minimized; in other words, supercomputer designers have not yet solved the problem of making interprocessor communication as efficient as that within processors (or, in the present case, between processors on a single chip).