On-sky Reconstruction of Keck Primary Mirror Piston Offsets Using a Zernike Wavefront Sensor

The next generation of large ground- and space-based optical telescopes will have segmented primary mirrors. Co-phasing the segments requires a sensitive wavefront sensor capable of measuring phase discontinuities. The Zernike wavefront sensor (ZWFS) is a passive wavefront sensor that has been demonstrated to sense segmented-mirror piston, tip, and tilt with picometer precision in laboratory settings. We present the first on-sky results of an adaptive optics fed ZWFS on a segmented aperture telescope, W.M. Keck Observatory's Keck II. Within the Keck Planet Imager and Characterizer light path, the ZWFS mask operates in the H band using an InGaAs detector (CRED2). We piston segments of the primary mirror by a known amount and measure the mirror's shape using both the ZWFS and a phase retrieval method on data acquired with the facility infrared imager, NIRC2. In the latter case, we employ slightly defocused NIRC2 images and a modified Gerchberg-Saxton phase retrieval algorithm to estimate the applied wavefront error. We find good agreement when comparing the phase retrieval and ZWFS reconstructions, with average measurements of 408 +/- 23 and 394 +/- 46 nm, respectively, for three segments pistoned by 400 nm of optical path difference (OPD). Applying various OPDs, we find that we are limited to similar to 100 nm OPD of applied piston, due to insufficient averaging of the adaptive optics residuals of our observations. We also present simulations of the ZWFS that help to explain the systematic offset observed in the ZWFS reconstructed data.