Updated technical material on roof prisms and phase coatings (1 Viewer)

[Lerxst]

I have updated a series of posts related to the topics of resolution degradation inherent to uncoated roof prisms and the use of multilayer phase coatings to mitigate the problem. These may be of interest to a few people here. I welcome feedback on any of this material.

Some of this is still a work in progress, as I have an additional model that I have yet to complete, which aims to account in detail for the specific color versus orientation results readily observed when coated prisms are placed between polarizers. I was hoping to finish that before presenting all this material together, but I need to put this project into abeyance for a while. Meanwhile, there is a considerable amount of new animations and code that I have added to the following posts, not to mention some interesting new references that I have only recently uncovered. I've added entirely new material exploring how the polarizer-based test of Weyrauch and Dörband works, and include an English version of their oft-mentioned German-language reference.

Specific pages and their contents:

The Physics of Roof Prisms and Phase Coatings, Simplified: Part I - Michael Hurben, PhD
Added new animations for ray tracing through various prisms. Otherwise dedicated to developing an intuitive model for the origin of the phase offsets.

The Physics of Roof Prisms and Phase Coatings, Simplified: Part II - Michael Hurben, PhD
Added some new elliptical polarization animations. Otherwise mostly concerned with tracing the change in polarization states along the two roof prism paths.

The Physics of Roof Prisms and Phase Coatings, Simplified: Part III - Michael Hurben, PhD
Updated to include an analysis of a nine-layer phase coating, extending the approach used in Mauer’s classic three-layer paper. A short Python program for simulating up to 9 layers using transfer matrices is included.

The Physics of Roof Prism and Phase Coatings, Simplified: Polarization Effects - Michael Hurben, PhD
Includes a discussion of the polarizer test for coated/uncoated prisms (see next entry as well) and some ruminations on the color effects in coated prisms. I’m working on extending this into a useful model but it is not finished.

On the Passage of Linearly Polarized Light through an Uncoated Roof Prism - Michael Hurben, PhD
An exploration of the light transmitted through an uncoated Schmidt-Pechan prism as a function of polarization angle. Includes Python code for calculating output polarization for coated and uncoated prisms, including both S-P and A-K designs.

Technical References for Roof Prism Resolution Loss, Phase Coatings, and Related Topics - Michael Hurben, PhD
A list of references, many of which are included as PDF files. I’ve unearthed a few new ones recently, which is wonderful, given the paucity of literature on this subject.

The Physics of Roof Prisms and Phase Coatings - Michael Hurben, PhD
My initial technical treatment that derives an expression for the single slit interference pattern degraded by an Amici roof prism, based on a Jones calculus approach to the polarization states. Also includes a treatment of the phase coating strategy using the transfer matrix method. Recently updated the paper to fix several minor typos.

 

[Tringa45]

This post has received little attention and is rather hard to digest.
It is nevertheless one of the most technically competent ever to have been posted on BF, so I thought it worthy of a bump.

John

 

[[email protected]]

I think it is a little too technical for the general Bird Forum member. It is for me. It is like Steven Hawkins book the 'Brief History of Time' which was a bestseller but very few people finished reading it because they couldn't understand it. I couldn't.

 

[Lerxst]

This post has received little attention and is rather hard to digest.
It is nevertheless one of the most technically competent ever to have been posted on BF, so I thought it worthy of a bump.

John

Thank you for the kind words. I began developing that material a few years ago after looking for details on this fascinating problem, and finding very little that had any explanatory depth. As for the technical difficulty (which is inherent to the topic), I am happy to get feedback on which specific sections are hard to follow. With the exception of one of the above links, I’ve tried to not include any math.

More recently, I followed up with a series of posts on anti-reflection coatings. This is a topic that is less obscure than phase coatings, but which can still be a little mysterious. These posts, however, do not shy away from the mathematics, although I have tried to go for intuitive explanations as well. They are located here:

Anti-Reflection Coatings, Part I: Single Layer - Physics, Birding and Blindness

Anti-Reflection Coatings Part II: The Transfer Matrix Method - Physics, Birding and Blindness

Anti-Reflection Coatings Part III: Oblique Incidence - Physics, Birding and Blindness

 

[Ignatius]

Being neither a mathematician nor a physicist, this latest batch as well as the OP is going to take a while to read and comprehend. Thank you for sharing your work.

 

[james holdsworth]

Thanks for your extremely thorough contributions.

 

[tenex]

At least we may understand why it took so long to develop phase coatings.

 

[Holger Merlitz]

Thank you for the kind words. I began developing that material a few years ago after looking for details on this fascinating problem, and finding very little that had any explanatory depth. As for the technical difficulty (which is inherent to the topic), I am happy to get feedback on which specific sections are hard to follow. With the exception of one of the above links, I’ve tried to not include any math.

More recently, I followed up with a series of posts on anti-reflection coatings. This is a topic that is less obscure than phase coatings, but which can still be a little mysterious. These posts, however, do not shy away from the mathematics, although I have tried to go for intuitive explanations as well. They are located here:

Anti-Reflection Coatings, Part I: Single Layer - Physics, Birding and Blindness

Anti-Reflection Coatings Part II: The Transfer Matrix Method - Physics, Birding and Blindness

Anti-Reflection Coatings Part III: Oblique Incidence - Physics, Birding and Blindness

These are again excellent articles, Michael, thanks so much that you are taking the trouble to work these things out in all their details! Would it be possible to apply the transfer matrix formalism to TIR in the presence of an anti-reflection coating, to try to rationalize what Konrad Seil might have measured on his prisms? If you could show what is going on here, and perhaps even figure out some ways to minimize the effects of the coating, then you surely were in a position to publish your results in journals such as SPIE or JOSA, because nothing of this kind seems to be known so far (at least in the available literature).

Cheers,
Holger

 

[Lerxst]

These are again excellent articles, Michael, thanks so much that you are taking the trouble to work these things out in all their details! Would it be possible to apply the transfer matrix formalism to TIR in the presence of an anti-reflection coating, to try to rationalize what Konrad Seil might have measured on his prisms? If you could show what is going on here, and perhaps even figure out some ways to minimize the effects of the coating, then you surely were in a position to publish your results in journals such as SPIE or JOSA, because nothing of this kind seems to be known so far (at least in the available literature).

Cheers,
Holger

Thanks Holger. I will take a look at this. Using the TMM to get reflectance vs wavelength for various AR designs for oblique, internal reflections will be straightforward to do, and I am glad you have again piqued my curiosity about this. The only thing I don't have details on are the specific AR coatings that are being used within a typical S-P prism, but I can try various multilayers that are in the literature just to see what they do. I imagine that by now, the AR coatings on the TIR surfaces have been as "tuned up" as they can be in order to mitigate any unwanted effects. But I wouldn't expect manufacturers to share any proprietary details on these any more than they do with phase coatings.

The Seil paper described measured MTF-curves for various AR coating scenarios and indicated that fewer layers were better. I've never looked into MTF curves but I think they should be straightforward to calculate. Famous last words.

 

[Holger Merlitz]

Thanks Holger. I will take a look at this. Using the TMM to get reflectance vs wavelength for various AR designs for oblique, internal reflections will be straightforward to do, and I am glad you have again piqued my curiosity about this. The only thing I don't have details on are the specific AR coatings that are being used within a typical S-P prism, but I can try various multilayers that are in the literature just to see what they do. I imagine that by now, the AR coatings on the TIR surfaces have been as "tuned up" as they can be in order to mitigate any unwanted effects. But I wouldn't expect manufacturers to share any proprietary details on these any more than they do with phase coatings.

The Seil paper described measured MTF-curves for various AR coating scenarios and indicated that fewer layers were better. I've never looked into MTF curves but I think they should be straightforward to calculate. Famous last words.

The MTF curves would be wonderful, but they are not even needed at this stage of the research project. As soon as you can show that there are additional phases generated by a single layer coating, which would distort the wavefront, and you further show that these effects turn worse with a selected multi-layer coating, you are essentially done. You will have demonstrated the origins of the problems as reported by Seil. The precise consequences - how all this affects the image of a point source or a pattern of bars, and how this translates into the MTF curve - could as well be worked out in subsequent projects, either by yourself or by other fellows who got the corresponding software.

Cheers,
Holger

 

[Patudo]

It would be really interesting to have your take on how possible/practical it might be to add multi-coatings to uncoated optics, or indeed to optics that already have single-coated prisms and lenses. Quite a few of us have speculated about how well older binoculars might perform with new coatings - we would be very grateful for insights from someone more knowledgeable about coatings than us!

 

[Lerxst]

It would be really interesting to have your take on how possible/practical it might be to add multi-coatings to uncoated optics, or indeed to optics that already have single-coated prisms and lenses. Quite a few of us have speculated about how well older binoculars might perform with new coatings - we would be very grateful for insights from someone more knowledgeable about coatings than us!

I wish I could offer something of value on that, but that is a process question. And I have no familiarity with the ins and outs of how optics manufacturers manage their deposition processes in practice. Has anyone posed that question to a company like Edmund? I'm not sure if they do any coatings in-house but they would certainly have some perspective on your question.

I do not have any optics industry experience. My career has been in magnetic materials and hard drive recording. Much of my doctoral work involved working with a special class of excitations (magnetostatic waves) in magnetic layers, so I've spent a lot of time working with wave solutions to Maxwell's equations in films, which overlaps with a lot of optical phenomenon, obviously. Now I find it recreational to dive deep into complicated problems like the roof prism / phase coating issue, which has intrigued me for years.

 

[Lerxst]

The MTF curves would be wonderful, but they are not even needed at this stage of the research project. As soon as you can show that there are additional phases generated by a single layer coating, which would distort the wavefront, and you further show that these effects turn worse with a selected multi-layer coating, you are essentially done. You will have demonstrated the origins of the problems as reported by Seil. The precise consequences - how all this affects the image of a point source or a pattern of bars, and how this translates into the MTF curve - could as well be worked out in subsequent projects, either by yourself or by other fellows who got the corresponding software.

Cheers,
Holger

I will have a look.

 

[kimsrk]

I have updated a series of posts related to the topics of resolution degradation inherent to uncoated roof prisms and the use of multilayer phase coatings to mitigate the problem. These may be of interest to a few people here. I welcome feedback on any of this material.

Some of this is still a work in progress, as I have an additional model that I have yet to complete, which aims to account in detail for the specific color versus orientation results readily observed when coated prisms are placed between polarizers. I was hoping to finish that before presenting all this material together, but I need to put this project into abeyance for a while. Meanwhile, there is a considerable amount of new animations and code that I have added to the following posts, not to mention some interesting new references that I have only recently uncovered. I've added entirely new material exploring how the polarizer-based test of Weyrauch and Dörband works, and include an English version of their oft-mentioned German-language reference.

Specific pages and their contents:

The Physics of Roof Prisms and Phase Coatings, Simplified: Part I - Michael Hurben, PhD
Added new animations for ray tracing through various prisms. Otherwise dedicated to developing an intuitive model for the origin of the phase offsets.

The Physics of Roof Prisms and Phase Coatings, Simplified: Part II - Michael Hurben, PhD
Added some new elliptical polarization animations. Otherwise mostly concerned with tracing the change in polarization states along the two roof prism paths.

The Physics of Roof Prisms and Phase Coatings, Simplified: Part III - Michael Hurben, PhD
Updated to include an analysis of a nine-layer phase coating, extending the approach used in Mauer’s classic three-layer paper. A short Python program for simulating up to 9 layers using transfer matrices is included.

The Physics of Roof Prism and Phase Coatings, Simplified: Polarization Effects - Michael Hurben, PhD
Includes a discussion of the polarizer test for coated/uncoated prisms (see next entry as well) and some ruminations on the color effects in coated prisms. I’m working on extending this into a useful model but it is not finished.

On the Passage of Linearly Polarized Light through an Uncoated Roof Prism - Michael Hurben, PhD
An exploration of the light transmitted through an uncoated Schmidt-Pechan prism as a function of polarization angle. Includes Python code for calculating output polarization for coated and uncoated prisms, including both S-P and A-K designs.

Technical References for Roof Prism Resolution Loss, Phase Coatings, and Related Topics - Michael Hurben, PhD
A list of references, many of which are included as PDF files. I’ve unearthed a few new ones recently, which is wonderful, given the paucity of literature on this subject.

The Physics of Roof Prisms and Phase Coatings - Michael Hurben, PhD
My initial technical treatment that derives an expression for the single slit interference pattern degraded by an Amici roof prism, based on a Jones calculus approach to the polarization states. Also includes a treatment of the phase coating strategy using the transfer matrix method. Recently updated the paper to fix several minor typos.

It might take months to digest this, but wow. I've been looking for something like this for sometime. Thanks for the incredible work.

 

[Lerxst]

It might take months to digest this, but wow. I've been looking for something like this for sometime. Thanks for the incredible work.

You are welcome and thank you for looking at it.

I hope to improve the presentation of this, and I solicit feedback on where the material is hardest to digest. I have gotten too close to it, as it were, and it is hard for me to appreciate which portions are less intuitive for others.

 

[tenex]

Very well written but somewhat ironically under the circumstances, you've chosen hard-to-read grey text.

Part I fig. 19 might be clearer if the arrows for the electric field were bidirectional <-->? I stumbled over this for some reason.

 

[Lerxst]

Very well written but somewhat ironically under the circumstances, you've chosen hard-to-read grey text.

Thank you. I think I fixed it and it is black now.

 

[tenex]

Hm, it's still grey here, but I have a bookmarklet that quickly makes it black. As for those arrows, they're not incorrect, but somehow got me thinking of a direction of propagation instead. An oscillating animation would be fun, but doesn't really seem necessary.

(Edit: two minutes later, yes it's black, thanks.)

 

[Lerxst]

Hm, it's still grey here, but I have a bookmarklet that quickly makes it black. As for those arrows, they're not incorrect, but somehow got me thinking of a direction of propagation instead. An oscillating animation would be fun, but doesn't really seem necessary.

As for the font, I installed a CSS plugin that allowed me to universally change the body text to black and hypertext to blue (except for a few that are red because I'd set them up that way long ago when trying to fight with this same Wordpress theme, ugh. Nice theme but the font colors are terrible). When I refresh the page I get black and blue and no gray.

As for the arrows, I looked at doing double arrows, but then that is not consistent with having the localized regions indicated polarized material with ellipses and +/- signs. It really does call out for an animation that reverses everything back and forth. I'll add that to my to-do list. I can add a k vector arrow too. Thanks for your comments.

 

[tenex]

Just a couple more thoughts. It's a bit awkward to encounter the odd term "phase thickness" in Fig 4c of Part III before it gets defined, but one gets over it.

When contemplating Part III Fig 5a or a nine-layer equivalent, what is the simplest possible takeaway: that the less dense coating is increasing the angle of TIR to reduce the problematic phase offset, and layers of greater density are then interspersed to take repeated advantage of the effect for different wavelengths?

Are there specific circumstances (point source, certain wavelengths, etc) in which one could most easily see the residual degradation?

Thanks again, this is well done and very helpful.