I’ve written a technical article on the topic of why the roof prisms used in binoculars require specialized coatings in order to improve their performance. I was prompted to pull this together because I couldn’t find a single reference that traced through this interesting problem in a non-trivial way. The article includes a derivation of the phase shifts at the heart of the effect, the role of the roof prism geometry, a demonstration of how resolution is lost (based on changes to the diffraction pattern), and finally some details concerning how coatings can mitigate the problem.
I found this all highly recreational, but I realize that many people that are curious about this topic will not share my enthusiasm for the mathematics. If you are not comfortable with calculus-based physics, the attached pdf file isn’t going to be very edifying, I’m afraid. So I have also set myself the task of writing a parallel account that covers the same material in a non-trivial and comprehensive way, but using only prose, diagrams and animations. For that, please see:
The Physics of Roof Prisms and Phase Coatings, Simplified: Part I
The Physics of Roof Prisms and Phase Coatings, Simplified: Part II
The Physics of Roof Prisms and Phase Coatings, Simplified: Part III
The Physics of Roof Prism and Phase Coatings, Simplified: Polarization Effects
On the Passage of Linearly Polarized Light through an Uncoated Roof Prism
Technical References for Roof Prism Resolution Loss, Phase Coatings, and Related Topics