  Bispectrum phase, closure phase and their generalisation to kernel-phase are
all independent of pupil-plane phase errors to first-order. This property, when
used with Sparse Aperture Masking (SAM) behind adaptive optics, has been used
recently in high-contrast observations at or inside the formal diffraction
limit of large telescopes. Finding the limitations to these techniques requires
an understanding of spatial and temporal third-order phase effects, as well as
effects such as time-variable dispersion when coupled with the non-zero
bandwidths in real observations. In this paper, formulae describing many of
these errors are developed, so that a comparison can be made to fundamental
noise processes of photon- and background-noise. I show that the current
generation of aperture-masking observations of young solar-type stars, taken
carefully in excellent observing conditions, are consistent with being limited
by temporal phase noise and photon noise. This has relevance for plans to
combine pupil-remapping with spatial filtering. Finally, I describe calibration
strategies for kernel-phase, including the optimised calibrator weighting as
used for LkCa 15, and the restricted kernel-phase POISE technique that avoids
explicit dependence on calibrators.
