Algorithm Evaluation on Segmented Mirror Phasing for the Hobby–Eberly Telescope

The Hobby–Eberly Telescope’s (HET) primary mirror is composed of 91 hexagonal mirror segments aligned in tip/tilt, while piston is manually controlled. BroadBand Phasing (BBP), as used at Keck, may be suitable for HET to sense piston error. Using the procedures laid out in Chanan et al., we modeled diffraction pattern point-spread functions (PSFs) of monochromatic and broadband light through split apertures centered at the edge between two adjacent segments. We simulated 4 sets of PSFs at 21 piston steps, 1 Template group and 3 differing Measurement groups. We determined the cross-correlation of the Template images to each Measurement image using Pearson’s r ( r ) and located the two extremes. We subtracted the minimum r ’s from the largest, fitted a Gaussian curve, and located the peak values. The peak’s location was within ±5  μ m from the input piston error for all cases, thereby showing that BBP may adequately measure piston errors down to ±25  μ m.