Mock observed lens that includes substructure in the lens model (far left), the reconstructed lensed image (second from left), the normalized imaging residuals (center), the residual time delay surface (second from right), and the residual convergence (far right). The residual time delay surface is the true time delay surface from the mock lens minus the model-predicted time delay surface from the lens model fit to the data. Similarly, the residual convergence is the full multi plane convergence (Eq. (10)) minus the convergence from the model fit to the mock data. The lensed quasar image positions are marked as points (crosses) in the center (right) panels. Each row corresponds to one substructure-perturbed dataset for the lens systems based on RXJ1131−1231, PG1115+080, and HE0435−1223.