Originally Posted by

**bill alsept**
Guys, I'm not trying to be lazy here. I really can't figure the equation out YET. I had a train of thought going and needed to compare it to the actual predictions of the edge diffraction pattern. All I ever see are images like these without details of the fringe spacing's:

Well, yes, you're going to have to get up to speed on the relevant maths if you want to do the calculation. As you can see from Born and Wolf, one prerequisite is the ability to evaluate Fresnel integrals. There's no closed-form, simple equation to do so, but there are simple algorithms. There are also online calculators of Fresnel integrators that will take care of the heavy lifting of those intermediate calculations. It's also straightforward to get Matlab to spit out the answers. There's a free Matlab-compatible package called Octave that I would enthusiastically recommend.

That said, as I understand your goal, you seem to be interested mainly in what the pattern looks like in the very, very far field (e.g, a million wavelengths away). Look at the pictures above -- you should note two general trends. One is the convergence to an asymptote. The other is a decrease in the spacing between successive fringes. By the time you get to a million wavelengths away, you will be so absurdly close to the asymptote that calculating it will require a ludicrous number of significant digits, and you will similarly find that the spacing will have reduced to zero for all practical purposes. So, if I understand you correctly, there's really no need to bother learning about the mathematical details. However, if you want to understand the near- or intermediate-field behavior, then yes, you'll need to come up to speed on a bit of maths.

ETA: I went back and reread some of your earlier posts. I see that you are most interested in the first dozen or so fringes, not ones a factor of a million out. In that case, you will have to evaluate the Fresnel integrals on the way to getting your final answer. Not hard, but a bit tedious.

Also, I came across an online Fresnel integral evaluator, so there's always that option to help reduce the tedium a little bit.