Isolating non-linearities of light propagation in inhomogeneous
  cosmologies
  A new formulation for light propagation in geometric optics by means of the
Bi-local Geodesic Operators is considered. We develop the BiGONLight
Mathematica package, uniquely designed to apply this framework to compute
optical observables in Numerical Relativity. Our package can be used for light
propagation on a wide range of scales and redshifts and accepts numerical as
well as analytical input for the spacetime metric. In this paper we focus on
two cosmological observables, the redshift and the angular diameter distance,
specializing our analysis to a wall universe modeled within the post-Newtonian
approximation. With this choice and the input metric in analytical form, we are
able to estimate non-linearities of light propagation by comparing and
isolating the contributions coming from Newtonian and post-Newtonian
approximations as opposed to linear perturbation theory. We also clarify the
role of the dominant post-Newtonian contribution represented by the linear
initial seed which, strictly speaking, is absent in the Newtonian treatment. We
found that post-Newtonian non-linear corrections are below $1\%$, in agreement
with previous results in the literature.
