Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm

In a previous paper, we described a successful technique, the broadband algorithm, for phasing the primary mirror segments of the Keck telescopes to an accuracy of 30 nn. Here we describe a complementary narrow-band algorithm. Although it has a limited dynamic range, it is much faster than the broadband algorithm and can achieve an unprecedented phasing accuracy of approximately 6 nm. Cross checks between these two independent techniques validate both methods to a high degree of confidence. Both algorithms converge to the edge-minimizing configuration of the segmented primary mirror, which is not the same as the overall wave-front-error-minimizing configuration, but we demonstrate that this distinction disappears as the segment aberrations are reduced to zero. (C) 2000 Optical Society of America OCIS codes: 010.7350, 120.5050, 350.1260.