Simplified model of pinhole imaging for quantifying systematic errors in image shape

We examine systematic errors in x-ray imaging by pinhole optics for quantifying uncertainties in the measurement of convergence and asymmetry in inertial confinement fusion implosions. We present a quantitative model for the total resolution of a pinhole optic with an imaging detector that more effectively describes the effect of diffraction than models that treat geometry and diffraction as independent. This model can be used to predict loss of shape detail due to imaging across the transition from geometric to diffractive optics. We find that fractional error in observable shapes is proportional to the total resolution element we present and inversely proportional to the length scale of the asymmetry being observed. We have experimentally validated our results by imaging a single object with differently sized pinholes and with different magnifications.