Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm.

To achieve its full diffraction limit in the infrared, the primary mirror of the Keck telescope (now telescopes) must be properly phased: The steps or piston errors between the individual mirror segments must be reduced to less than 100 nm. We accomplish this with a wave optics variation of the Shack-Hartmann test, in which the signal is not the centroid but rather the degree of coherence of the individual subimages. Using filters with a variety of coherence lengths, we can capture segments with initial piston errors as large as +/-30 microm and reduce these to 30 nm--a dynamic range of 3 orders of magnitude. Segment aberrations contribute substantially to the residual errors of approximately 75 nm.