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

TLDR

The broadband algorithm previously achieved 30 nm phasing accuracy for Keck’s primary mirror segments. This study introduces a complementary narrow‑band phasing algorithm. The narrow‑band algorithm, though limited in dynamic range, is faster than the broadband method and attains about 6 nm phasing precision. Cross‑checks confirm both algorithms, which converge to an edge‑minimizing configuration that aligns with the wave‑front‑error‑minimizing configuration when segment aberrations are eliminated, demonstrating high confidence in their performance.

Abstract

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 nm. 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.