Illustration of modeled lens shapes and the phase delay ΔΦ. Very different shapes of the lens models (upper panel) are chosen to represent distinct astrophysical origins. The total phase delay of the Gaussian lens (lower panel) includes a parabolic-shaped geometrical delay (gray line) apart from the dispersive delay caused by the lens. The images (stars) were generated on the phase delay; the image at the zero-point of the x-axis is the source itself, and the extra images are created by the lens. The dashed green lines are caustics for the Gaussian lens (green curve). Only when the lens is between inner and outer caustics, two new extremes will be created on the phase delay, which means two new images will be created.