<title>Phasing the primary mirror segments of the Keck telescopes: a comparison of different techniques</title>

We have developed and tested extensively three different methods for phasing the primary mirror segments of the Keck telescopes. Two of these, referred to as the broadband and narrowband algorithms respectively, are physical optics generalizations of the Shack-Hartmann technique. The third, Phase Discontinuity Sensing, is a physical optics generalization of curvature sensing. We evaluate and compare experimental results with these techniques with regard to capture range (as large as 30 micrometers ), run-to-run variation (as small as 6 nm), execution time (as short as twenty minutes), systematic errors, ease of implementation, and other factors, in the context of the Keck telescopes and also of future very large ground-based telescopes.