  Context: The detection and characterization of Earth-like exoplanets
(exoEarths) from space requires exquisite wavefront stability at contrast
levels of $10^{-10}$. On segmented telescopes in particular, aberrations
induced by cophasing errors lead to a light leakage through the coronagraph,
deteriorating the imaging performance. These need to be limited in order to
facilitate the direct imaging of exoEarths. Aims: We perform a laboratory
validation of an analytical tolerancing model that allows us to determine
wavefront error requirements in the $10^{-6} - 10^{-8}$ contrast regime, for a
segmented pupil with a classical Lyot coronagraph. We intend to compare the
results to simulations, and we aim to establish an error budget for the
segmented mirror on the High-contrast imager for Complex Aperture Telescopes
(HiCAT) testbed. Methods: We use the Pair-based Analytical model for Segmented
Telescope Imaging from Space (PASTIS) to measure a contrast influence matrix of
a real high contrast instrument, and use an analytical model inversion to
calculate per-segment wavefront error tolerances. We validate these tolerances
on the HiCAT testbed by measuring the contrast response of segmented mirror
states that follow these requirements. Results: The experimentally measured
optical influence matrix is successfully measured on the HiCAT testbed, and we
derive individual segment tolerances from it that correctly yield the targeted
contrast levels. Further, the analytical expressions that predict a contrast
mean and variance from a given segment covariance matrix are confirmed
experimentally.
