Matthew: You're absolutely right about a single slit. My concern is with double slits. The bottom two plots show the diffraction patterns, including zeros, from each slit independently. These look entirely plausible to me.

What's odd about this pattern is what's shown when the light from both slits interferes. The claim is that opening both slits at once leads to fringes within these single slit fringes that go completely dark. The problem, I think, is that when you interfere two light fields at a point, they produce fringes, but the maximal intensity of the bright fringes will be the sum of the intensities of each field, while the minimal intensity of the fringes will be the difference in intensity of the two fields. What's shown in the drawing is that the rapid fringes (which are associated with interference between the two slits) go to zero. This isn't possible, since one slit's intensity is much smaller than the other's in most of those regions, so the minimum intensity isn't zero.

Put mathematically, if the intensity of the field from slit 1 at point P is I_{1}(P). The intensity from slit 2 at point P is I_{2}(P). The total amplitude at point P can vary from I_{1}(P)+I_{2}(P) if the fields interfere constructively to |I_{1}(P)-I_{2}(P)| if the fields interfere destructively. The variation between these values cause the fringes, but they only go to zero if I_{1}(P)-I_{2}(P)=0. Clearly, the single slit patterns aren't equal in intensity, except right near the center of the plots, so you shouldn't get completely dark fringes out on the wings of each pattern, unless I'm missing something obvious here...

By the way, I did the calculation (Fresnel diffraction) out of curiosity--this case isn't that hard to do. You get rapid oscillating fringes within your larger patterns, but these fringes have low contrast that gets lower as you go further out along each pattern.