Abstract

Very large space-borne telescopes have primary mirrors made of several independent segments that must be aligned to a fraction of a wavelength for optimum performance. All proposed solutions for such phase alignment appear to have some limitations. For example, gradient (tilt) sensors may control the figure of each individual segment but are insensitive to piston error between segments, whereas complementary segment-to-segment edge capacitance gauges can eliminate piston error but require absolute calibration. We show that absolute calibration of the mirror segments may be achieved by optimizing the intensity of the focused light, if the initial errors are less than about one wavelength. Implementation requires computer processing of a time series of focal-plane, single-detector intensity measurements as the various segments are dithered. The key issue addressed in this paper is that all numerical optimization techniques yield local optima rather than global optima, and numerical methods for distinguishing one from the other do not exist. We find that a comparison of the optimized focal-plane intensity or Strehl ratio for wide and narrow light spectra may be used to distinguish local and global optima and may provide a means to scan through local optima to reach the global solution.

© 1990 Optical Society of America