  Kernel-phase is a data analysis method based on a generalization of the
notion of closure-phase invented in the context of interferometry, but that
applies to well corrected diffraction dominated images produced by an arbitrary
aperture. The linear model upon which it relies theoretically leads to the
formation of observable quantities robust against residual aberrations. In
practice, detection limits reported thus far seem to be dominated by systematic
errors induced by calibration biases not sufficiently filtered out by the
kernel projection operator. This paper focuses on the impact the initial
modeling of the aperture has on these errors and introduces a strategy to
mitigate them, using a more accurate aperture transmission model. The paper
first uses idealized monochromatic simulations of a non trivial aperture to
illustrate the impact modeling choices have on calibration errors. It then
applies the outlined prescription to two distinct data-sets of images whose
analysis has previously been published. The use of a transmission model to
describe the aperture results in a significant improvement over the previous
type of analysis. The thus reprocessed data-sets generally lead to more
accurate results, less affected by systematic errors. As kernel-phase observing
programs are becoming more ambitious, accuracy in the aperture description is
becoming paramount to avoid situations where contrast detection limits are
dominated by systematic errors. Prescriptions outlined in this paper will
benefit any attempt at exploiting kernel-phase for high-contrast detection.
