Single slit diffraction pattern in 2D

I was looking at previous exams and I saw a question with single slit diffraction. Please look at picture on the website: http://www.physicsforums.com/showthread.php?p=4807732#post4807732

So, this made me think: "Wow, I never thought single slit diffraction could be applied in 2D with one pattern horizontal and the other vertical."

Then, I thought why is there no diffraction patterns along all the surface of the viewing screen. Can anyone explain why? The textbook I am using emphasizes how when a wave enters a boundary place, each point sends out its own spherical wavelet in 3D. So, why don't we see that on the viewing screen?

• Could you specify your question? Do you want to know why you cannot see "3D interference" on a two dimensional screen? Would your question be answered by moving the screen back and forth and thus capturing the depth of the interference pattern? – M.Herzkamp Jul 28 '14 at 10:36

$$I = 16C^2a^2b^2\left(\frac{\sin(\theta_xka)}{\theta_xka}\right)^2\left(\frac{\sin(\theta_yka)}{\theta_yka}\right)^2$$
where the width of the slit is $2a$ and the height $2b$.
The first maximum in $\text{sinc}^2(x)$ has an amplitude of about $0.047$, so the relative intensity of the first order spots in the $x$ and $y$ directions, $I_{10}$ and $I_{01}$, will be $4.7$% of the central spot. However the intensity of the first off axis spot, $I_{11}$, will be $0.047^2$ or about $0.2$% of the central spot, which is so faint it's hard to see. Higher order off-axis spots are even fainter.