Phase discontinuity sensing: a method for phasing segmented mirrors in the infrared.

We describe a novel method for phasing segmented optics in which the signal is the difference between inside-of-focus and outside-of-focus long-exposure infrared images. A detailed algorithm based on a correlation of this difference image with theoretical images or templates is presented. In a series of tests of this phase discontinuity sensing (PDS) algorithm at the Keck 1 telescope, at a wavelength of 3.3 microm, the rms piston error (averaged over the 36 primary mirror segments) was repeatedly reduced from approximately 240 to 40 nm or less. Furthermore, the PDS phasing solution was consistent with our previous phasing camera results (to within 66-nm rms), providing strong independent confirmation of this earlier approach.