Gravitational lensing in a concordance LCDM universe: The importance of   secondary matter along the line of sight
  To date, in almost all strong gravitational lensing analyses for modeling giant arc systems and multiple quasar images, it has been assumed that all the deflecting matter is concentrated in one lens plane at a certain distance - the thin lens approximation. However, in a few observed cases, lenses at more than one redshift have been identified as contributing to the image splitting.   Here we report on a quantitative investigation of the importance and frequency of significant multiple lensing agents. We use multi-lens plane simulations to evaluate how frequently two or more lens planes combined are essential for multiple imaging, as compared with the cases where a single lens plane alone provides enough focusing to be supercritical.   We find that the fraction of cases for which more than one lens plane contributes significantly to a multi-image lensing situation is a strong function of source redshift. For sources at redshift unity, 95% of lenses involve only a single mass concentration, but for a more typical scenario with, e.g., a source at a redshift of z_s = 3.8, as many as 38% of the strongly lensed quasars/arcs occur because of a significant matter contribution from one or more ADDITIONAL lens planes. In the 30% to 40% of cases when additional planes make a significant contribution, the surface mass density of the primary lens will be overestimated by about 15% to 20%, if the additional contributions are not recognized. 
Joachim Wambsganss, Paul Bode, Jeremiah P.Ostriker