Segmented Mirror Phasing Algorithm Evaluation for the Hobby-Eberly Telescope

The Hobby-Eberly Telescope’s (HET) primary mirror is the most important subsystem that dictates image quality of the HET. There are 91 hexagonal mirror segments forming a single 11-meter-wide spherical surface; each segment is aligned with each other in tip/tilt, but piston is only manually controlled. Though HET operates under Seeing-limited conditions, large piston error can still significantly degrade HET’s image quality. This motivated us to explore ways to sense piston error for eventual closed loop control. Here, we investigated BroadBand Phasing (BBP) method, as used at Keck, as it appears suitable for HET. We evaluated the BBP algorithms and procedures developed by Chanan et. al.. We modeled the diffraction patterns of a point spread function (PSF) for both monochromatic and broadband light through a split aperture centered at the edge between two adjacent segments. An arbitrary piston step between two halves of the aperture was included. Our goal was to assess the accuracy this method in recovering an input piston error in various photon noise conditions. The piston recovery process involved cross-correlating a set of “template” PSFs against a set of “measured” PSFs with some unknown piston error. This resulted in a Gaussian-like “coherence” curve which peaks at the input piston error. First, we simulated 4 sets of PSFs at 21 piston steps: a Template, a no-noise Measurement, and two Measurement sets with differing signal-to-noise ratios. All PSF sets were created over the same piston step-through range from -500 μm to 500 μm (50 μm step) and the “unknown” input piston error in the three Measurements was -100 μm. Next, we determined the cross-correlation of the Template image to each Measurement image using Pearson’s r (𝑟) and located the largest and smallest 𝑟 values. Finally, we subtracted the minimum 𝑟’s from the largest for each three Measurement cases, fitted a Gaussian curve, and located its peak value. In our simulation, the peak location was within ±5 μm from the input piston error for all cases thereby showing that the BBP method can be adequate for measuring piston errors down to ±25 μm level across HET’s primary mirror. We acknowledge support from the NSF REU grant AST-1757983 (PI: Jogee).