Approach based on χ² to phasing segmented-mirror telescopes using multiple wavelengths: data reduction, wavelength...

The design of extremely large segmented-mirror telescopes (ELTs) calls for their segments to be phased, and a number of different interferometric techniques have been proposed in the literature for this purpose. To achieve the required large capture ranges for ELTs (typically a few microns), most of these techniques use measurements at multiple wavelengths, similar to what is done in standard distance-measuring laser interferometry. In this paper, we present a χ²-based framework not tied to a specific phasing technique to obtain intersegment edge heights from multiwavelength data. We show how this scheme can be used to select an optimal set of wavelengths that maximizes the capture range while achieving the very low error rates required for ELT phasing. We take into account the wavelength uncertainty associated with the finite-width interference filters used in on-sky phasing. Finally, we present data from the Keck 2 telescope that illustrate the method for three-wavelength phasing.