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

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Abstract
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 μm and reduce these to 30 nm—a dynamic range of 3 orders of magnitude. Segment aberrations contribute substantially to the residual errors of ∼75 nm.

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