Continuous image distortion by astrophysical thick lenses
  Image distortion due to weak gravitational lensing is examined using a
non-perturbative method of integrating the geodesic deviation and optical
scalar equations along the null geodesics connecting the observer to a distant
source. The method we develop continuously changes the shape of the pencil of
rays from the source to the observer with no reference to lens planes in
astrophysically relevant scenarios. We compare the projected area and the ratio
of semi-major to semi-minor axes of the observed elliptical image shape for
circular sources from the continuous, thick-lens method with the commonly
assumed thin-lens approximation. We find that for truncated singular isothermal
sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens
approximation is accurate to better than 1 part in 10^4 in predicting the image
area and axes ratios. For asymmetric thick lenses consisting of two massive
clusters separated along the line of sight in redshift up to \Delta z = 0.2, we
find that modeling the image distortion as two clusters in a single lens plane
does not produce relative errors in image area or axes ratio more than 0.5%
