I'm looking for a webpage or a book or reference that might give me a better (and hopefully more scientific) understanding of how the Bahtinov mask works (which I understand to be the same as diffraction around the mirror arms, but I don't fully grasp how that occurs). Can anyone think of any good links here?
The answer is simple once you know these basic facts:
A) The spikes due to any edge in the cone of light (including spider vanes, etc.) go through the center of the star only when the scope is in perfect focus. If you move the ocular out of focus, the spikes are actually sweeping left and right to the star's center. This is not characteristic solely to the Bahtinov mask, it happens with any spike. Go ahead and try it on a very bright star with your straight vane spider. The effect is weak, but not zero. The Bahtinov mask is just a clever device that amplifies the effect a lot. E.g., look at this regular 3-vane spider going in and out of focus:
B) Multiple parallel edges don't make multiple spikes, but just one spike, thick and bright. The more edges you have, the brighter the spike.
So that's how Pavel Bahtinov came up with the idea. Let's have lots and lots of edges in the FoV, so as to make very bright, very visible spikes. Make two spikes that intersect at an acute angle - those are the oblique edges on one side of the mask. Then have another spike bisecting the acute angle - those are the parallel edges on the other side.
Why acute angle? Well, it's easier to tell when the 3rd spike is going straight through the intersection of the other two when the angle is acute - the eye can detect smaller errors that way. If the angle was wider, it would be harder to tell when the 3rd spike is slightly out of center.
It's hard to tell because the difference is small, but it's not just the 3rd spike that moves relative to the X formed by the other two. In fact, all three spikes are shifting sideways as you move in and out of focus. But because of the angle you only see the central spike (the 3rd spike) moving clearly.
Here's a site that explains everything very well:
I'm not sure about any particularly great scientific articles that will help you understand. Wikipedia has a basic article on Bhatinov masks. However, I hope the following diagrams demonstrate the concept well enough. The general idea of a Bahtinov mask is that it creates a specific layered diffraction pattern. The three patterns overlay each other in a specific manner such that when they line up, it is obvious. The patterns form a central "pole" and an "X". When the pole runs through the center of the X, you're properly focused. If the pole is shifted to one side or the other, you're not in proper focus. The examples below are a bit basic and exaggerated, but hopefully they demonstrate well enough.
Out of Focus Left
Out of Focus Right