  Future space telescopes with coronagraph instruments will use a wavefront
sensor (WFS) to measure and correct for phase errors and stabilize the stellar
intensity in high-contrast images. The HabEx and LUVOIR mission concepts
baseline a Zernike wavefront sensor (ZWFS), which uses Zernike's phase contrast
method to convert phase in the pupil into intensity at the WFS detector. In
preparation for these potential future missions, we experimentally demonstrate
a ZWFS in a coronagraph instrument on the Decadal Survey Testbed in the High
Contrast Imaging Testbed facility at NASA's Jet Propulsion Laboratory. We
validate that the ZWFS can measure low- and mid-spatial frequency aberrations
up to the control limit of the deformable mirror, with surface height
sensitivity as small as 1 pm, using a configuration similar to the HabEx and
LUVOIR concepts. Furthermore, we demonstrate closed-loop control, resolving an
individual DM actuator, with residuals consistent with theoretical models. In
addition, we predict the expected performance of a ZWFS on future space
telescopes using natural starlight from a variety of spectral types. The most
challenging scenarios require ~1 hr of integration time to achieve picometer
sensitivity. This timescale may be drastically reduced by using internal or
external laser sources for sensing purposes. The experimental results and
theoretical predictions presented here advance the WFS technology in the
context of the next generation of space telescopes with coronagraph
instruments.
