With the results of Problem 10.25 in mind, discuss the symmetries that would be evident in the Fraunhofer diffraction pattern of an aperture that is itself symmetrical about a line (assuming normally incident quasimonochromatic plane waves).

Data from Prob. 10.25

Show that Fraunhofer diffraction patterns have a center of symmetry [i.e., I(Y, Z) = I(-Y, -Z)], regardless of the configuration of the aperture, as long as there are no phase variations in the field over the region of the hole. Begin with Eq. (10.41). We’ll see later (Chapter 11) that this restriction is equivalent to saying that the aperture function is real.