Abstract

A deformable mirror was required to input controlled aberrations to a prototype wavefront sensor. Zernike polynomials were used in conjunction with NASTRAN to optimize the locations of actuators and to construct the necessary forces to approximate each aberration requiring correction. A correction matrix was constructed using the aberrational magnitudes created by the selected actuator configuration. This approach reduces the complexity of the correction matrix from a rectangular matrix sized by the number of actuators to a square matrix sized by the number of aberrations to be corrected. By inverting the correction matrix and solving for an identity matrix, participation factors were calculated to correct each off-diagonal term representing unwanted residual aberrations. This evaluation was extended and applied to test data where any deviation from the optimum design (fabrication, manufacturing, and alignment tolerances) resulted in unwanted residual aberrations. When the off-diagonal terms were eliminated, optimal tolerance correction was accomplished.

© 1988 Optical Society of America