Analysis of edge jumps in multi-wavelength phasing of segmented-mirror telescopes

Interferometric methods for phasing the primary mirrors of segmented-mirror telescopes generally need to make measurements at multiple wavelengths in order to achieve suitably large edge height capture ranges. In the presence of measurement errors, such methods have the potential for grossly wrong measurements, so-called edge jumps. In this paper, we investigate the causes of edge jumps using the example of Thirty Meter Telescope (TMT) phasing. We explain the reasons for their occurrence and develop a mathematical understanding of the conditions under which they arise. We describe how stability analyses of the vast parameter space relevant to TMT phasing can be accomplished in an efficient way and present examples of results. These concepts are also applicable to other multi-wavelength interferometric phase measurement techniques.