Efficient method for the reduction of large piston errors in segmented-mirror telescopes

Phase Discontinuity Sensing (PDS) is one of two successful approaches to segment phasing currently in use at the Keck telescopes, but it has only very limited capture range. In this work, we describe and present numerical simulations of a broadband version of the current (narrowband) PDS algorithm which can extend the capture range from 0.4 mum to 40 mum. Like the original algorithm, the new broadband PDS algorithm (BPDS) does not require any special-purpose hardware, only a high-resolution area detector operating in the 2 - 3 mum range. The potential application of this algorithm to Extremely Large Telescopes is also discussed.