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 source 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-facile and comprehensive way, but using only prose, diagrams and animations. Such an approach is in fact more difficult than cranking through the equations, so I’m not sure when it will be done… but it is coming!