We have been asked to phase encode two point objects offset in y. Let us first turn to an example in which we have two point samples in the imaging plane that both have the x coordinate x = x₀, but they have different y coordinates. In this case, the signal is the sum of the individual signals from each object; therefore, we cannot determine their individual y coordinates from a single measurement such as that shown in Figure 13.15 and described by (13.42). Show that we can obtain two measurements, each measurement having a different value of the phaseencoding gradient amplitude G_y, to solve for y the position of the two point objects.

Figure P13.7 See Problem 13.13