How to calculate a straight edge diffraction pattern?

The trick is that because the "slit" is infinitely wide, you shouldn't work in the far-field approximation (Fraunhofer diffraction integral which leads to Fourier optics), but with distances computed to the square order (Fresnel diffraction integral). The results are appropriately named Fresnel integrals (this time this is a name of a special analytical function that is well documented). So, to get the maxima and minima, you need to find zeroes of the derivatives of these functions (which is fortunately much easier than actually computing the function). What you get is, that the squares of maximum positions are equally spaced.

The principle behind the diffraction integrals is simply adding contributions with phase delays proportional to the distance from that point. Google will tell you everything you need to know about the Huygens principle and the derivation of the result for straight edge diffraction (example - warning, they use imaginary units).

Maybe a paper referring to measurements (follow the references to learn more).

And a formula for max/min:

$$x_{max/min}(m)=sqrt{frac{lambda L (L-y)}{y}(m+tfrac{3}{4})}$$ where even $m$ are maxima and odd $m$ are minima. $y$ is the distance of the light source to the edge and $L$ is the distance of light source to the screen. For infinite $y$ and $L$ (sunlight, for instance), only the $L-y=D$ distance from the edge to the screen matters, and you are left with $$x_{max/min}(m)=sqrt{lambda D (m+tfrac{3}{4})}$$ Now take $lambda=500,rm{nm}$ and $D=1,rm m$. You get the max/min pattern: 0.61mm, 0.9mm, 1.17mm, 1.37mm,...