This page is meant to provide a list of references that are directly relevant (marked with a *) or in some cases marginally relevant to the topic of resolution loss in roof prisms and the so-called phase coatings used to mitigate the problem. If you know of any additional literature, please email me at hurbenm at gmail.com and I will be happy to add it. I’m not particularly interested in sales brochures that optics manufacturers might supply, or “physics for dummies” attempts at explanations, or anything touting trademarked names which shed no light on the technical details, however.
For my treatment, please see The Physics of Roof Prisms and Phase Coatings or download here:
Bloss, F.D. (1961) “An Introduction to the Methods of Optical Crystallography,” Saunders College Publishing. Old, but includes a good reference for the effects of birefringence on interference colors as revealed by the use of polarizers. Available for free online.
Fox, M. (2010) “Optical Properties of Solids,” 2nd edition. Oxford: Oxford University Press. Provides a good connection between standard optics / E&M treatments and condensed matter physics.
Hecht, E. “Optics,” Fifth Edition, Pearson (2016). Standard, comprehensive undergraduate-level textbook; no mention of the roof prism interference issue or its solution.
* Ito T. & Noguchi, M. (2001) “Viewing optical instrument having roof prism and a roof prism,” US Patent US6304395B1. The most detail yet found for a “modern” (if 20 years old can be considered modern) phase coating design. Specific recipes for 9-layer structures are given, along with phase and reflectivity data. Effectively, this approach uses three consecutive Herpin equivalents, extending the ideas proposed by Mauer. I’ve extended the Mauer analysis to include these layers and it indeed indicates a much broader spectral region over which the phase offset can be minimized.
Jen, Y.J., Lakhtakia, A., Yu, C.W. et al. (2011) “Biologically inspired achromatic waveplates for visible light,” Nat Commun 2, 363. Shows how birefringent materials can be utilized in coatings that provide constant phase shift across a wide spectral range, making them achromatic. This would seem like a useful method to tune out the TIR phase shifts, in principle.
* Jinjun, L., Xueping, S. and Weibing, Z. (2013) “The splitting mechanism of
zero order diffraction pattern by roof prisms,” J. Opt. 42, 367-375. Reformulates the treatment from Mahan explicitly using Jones matrices. Unfortunately it is a translated paper and full of typographical problems. A very hard read.
* Jinjun L, Qiao, Y., Xueping, S. et al. (2011) “Research of the polarization aberration on Smith [sic] prism,” Physics Procedia, 19: 447-455. Generally a bad sign when even the paper title has a typo. Useful as another example of the Jones matrix treatment of a roof (Schmidt) prism, but a hard slog due to a poor translation effort.
* Macleod, H.A. (2021) “Thin-Film Optical Filters: Fifth Edition (Series in Optics and Optoelectronics),” 5th Edition, CRC Press. The only text found as yet which mentions the roof prism problem and the strategy of phase coatings; it cites the work of Rabinovitch and Toker and Ito and Noguchi.
* Mahan, A.I and Price, E.E. (1950) “Diffraction Pattern Deterioration by
Roof Prisms,” J. Opt. Soc. Am. 40, 664-686. Classic, comprehensive description of the resolution loss endemic to roof prisms. Covers both polarized and unpolarized light, as well as novel roof prisms with angles other than 90 degrees. Can be read at JSTOR online using a free account.
* Mahan, A.I. (1954)”Some newly solved and some unsolved problems in
optics,” J. Wash. Acad. Sci. 44, No. 6, pp. 165-194. Companion to the Mahan and Price article above, written for a more general audience. Also available on JSTOR.
* Mauer, P. (1966) “Phase Compensation of Total Internal Reflection,” J. Opt.
Soc. Am. 56, 1219-1221. First (and only) paper to discuss the use of a Herpin equivalent trilayer as a potential solution for the phase offset upon total internal reflection. The solution has a limited wavelength range, however.
* Mauer, P.B. (1968) “Two-Layer Phase Compensation of Total Internal Reflection,” J. Opt. Soc. Am. 58, 1160-1160. A follow-up the length of a paragraph showing that the prism glass can effectively act as the proximal layer, thereby enabling a two-coating approach. The spectral range is still too limited for wideband use.
Merlitz, H. (2023) “The Binocular Handbook: Function, Performance and Evaluation of Binoculars,” Cham, Switzerland: Springer. The most comprehensive technical treatment of binoculars available.
Murphy Jr., T.W. and Goodrow, S.D. (2013) “Polarization and far-field
diffraction patterns of total internal reflection corner cubes,” Appl
Opt. 52(2):117-26. Corner cube reflectors present a closely related problem, because the same mechanism that causes roof prism resolution loss is at play, this time working on three consecutive reflections. For that reason, papers such as this are an enlightening and relevant read. But because such devices are often used in laser applications (distance ranging of lunar targets, for example), there is no need for broadband coating solutions, so this is a bit of dead-end if the end goal is to see phase coating solutions amenable for consumer optics.
Piegari, A. & Flory, F. (2018). “Optical Thin Films and Coatings: from Materials to Applications,” 2nd edition. Another good, recent text that does not include any discussion of phase coatings.
Rabinovitch, K. & Toker, G. (1994) “Genetic algorithm and thin-film design,” Proceedings of SPIE, 2262(1), 163-174. Discussion of an optimization technique for navigating the very large parametric space endemic to multilayer film design.
* Rabinovitch, K. and Toker, G. (1994) “Polarization effects in optical thin films,” Proceedings of SPIE, 2253(1), 89-102. The proposed coating solution here involves a dielectric layer in addition to a silver coating, which eliminates TIR. The claim is that the losses inherent to a metallic coating can be largely mitigated by the dielectric. Is anyone using this approach? I have no idea. Have not yet tried to model this yet.
Rabinovitch, K. (1989) “The Application Of Thin Films Technique To Compensate Polarization Effects On Total Internal Reflection,” Proceedings of SPIE, 1038, 337-349. Very short on details. Uses Dirac notation in the analyses, which is a nice touch, and introduces the Poincare sphere to account for polarization states. Proposes as solution without any specifics other than the performance being limit to a wavelength range much too small to be achromatic.
Rabinovitch, K. and Pagis, A. (1974). “Polarization Effects in Multilayer Dielectric Thin Films,” Optica Acta: International Journal of Optics, 21(12), 963–980. Gets tantalizingly close to addressing an open question, namely, the polarization-dependent interference colors observed for phase coatings. Unfortunately they only consider other coating scenarios.
Sarangan, A. (2020) “Optical thin film design,” 1st edition, CRC Press (2020). A fine overall reference, but contains no mention of phase coatings.
* Seil, K. (1991) “Progress in binocular design,” Proc. of SPIE Vol. 1533, Optomechanics and Dimensional Stability. The only reference I have seen that points out the potential problems of anti-reflective coatings on several non-roof TIR surfaces in Schmidt-Pechan prisms. It is expected that such coatings have been modified to reduce the losses discussed here, but I have yet to find anything in the literature or patents (not surprising).
Sørensen, B.E. (2013). “A revised Michel-Lévy interference colour chart based on first-principles calculations,” European Journal of Mineralogy, 25, 5-10. Valuable read for instructions on constructing a version of the Michel-Lévy interference chart, which displays how interference colors depend on thickness and birefringence. Note that Equation 1 is incorrect. It should read:
* Weyrauch A. and Dörband, B. (1988) “P-Coating: Improved Imaging in Binoculars through Phase-Corrected Roof Prisms,” Special reprint from Deutsche Optikerzeitung, Heidelberg, No. 4. German text from Zeiss (translated to English here) announcing their development of phase coating; it features no technical details. The polarizer test is described briefly but not explained. See here and here.
* Xueping, S., Liu, W. and Lu, J. (2017) “Analysis and correction of far-field
diffraction pattern for corner-cube reflector,” J. Opt. 46. Includes a treatment of the same interference problem in the context of a corner-cube reflector, and addresses the solution with a phase coating. Close, but no cigar for what we want: the film details are not provided, and the coating is intended to correct only for monochromatic light.