Updated technical material on roof prisms and phase coatings (2 Viewers)

[Lerxst]

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.

Thanks for catching that, I will add a definition. I didn't want to reference it at all, but it is common in the literature, and the Mauer paper uses it. I always wanted phase offset vs. wavelength, plain and simple. When I first started working through the phase coating part of this work, all I really had to go from was that old paper from Mauer, and my first task was to make sure that my model and my code reproduced his results to a T. So I was forced to use his approach initially to make sure I had not made one of many possible errors. And it is very easy to screw this up.

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?

You are getting at one of the most difficult ideas here and I am not happy with the write-up as it stands. I will need to expand upon it. Until then, here is my short attempt: (a) TIR only happens at that last interface between the final layer and the air, and we want that angle shallow. (b) all the others, the non-TIR reflections, cause additional, weaker reflections, but we need these to all add up with as little phase shift as possible over a broad wavelength range. Otherwise we’ll lose amplitude due to vanilla destructive interference that will occur with any multilayer - and this depends on the thicknesses, indices, and if the reflection gets inverted or not at each boundary. (c) It does seem like all these layers should confound each other, but they don’t if they are carefully constructed, in the same way and for the same reason that multilayer coatings can be tuned to provide very high, and "flat" transmittance across the entire visible band.

In any multilayer, one might think that more layers can only make for more headaches and a kind of unwinnable game of whack-a-mole, but what these many phase shifts between the layers allow you to do is something very much like Fourier composition of a square wave from many sine waves. If you look at my post on TMM and antireflection coatings, I go through an approximation showing how this is done. Specifically, in Anti-Reflection Coatings Part II: The Transfer Matrix Method - Physics, Birding and Blindness look at Figures 6 and 7, where I look at the simplest, two-reflection paths in a multilayer, and what each spectral response is, and how they look when added up.

Basically I think of transmittance vs wavelength as a periodic function which you want to look like a square wave with the top of the square extending over the visible range. Each of the possible reflection pairs within a multilayer has some transmittance vs wavelength that is too “wavy” but if you make their profiles stack up so one zigs where another zags, you can shape the result any way you want, within reason. It is just like a Fourier series. And just like a Fourier series, the more terms, the more freedom you have to sculpt the final waveform. For the phase coating it is the same idea. I did not include this explanation in the phase coating write up because I only managed to find a way to express it, graphically, while writing more recently on anti-reflection coatings. So I will eventually try to write something more coherent.

I don't know if that helps. This is tough to describe. My write ups on antireflection coatings are still chock full of math but I want to also make a "more intuitive" version of them also.

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

By residual degradation, do you mean to say, whatever is "left over" from the native roof prism degradation, that the coating could not correct for? (I think that is what you mean.) Good question and I have not thought about that, but I would venture to say either a point or line source (actually I like the cross shape used in the Mahan papers, because one arm of the cross will be affected by the roof line while the other will not, giving a control, if you will) looked at vs. wavelength over the visible range. I would imagine some multilayers are used which tail off at one end, while another vendor favors a different recipe that is worse at the other end, etc. No way to know without a full exploration of it spectrally, I would think.

Thanks again, this is well done and very helpful.

Thanks, I appreciate you giving it a hard look. It will mean a better rev2.

 

[tenex]

Thanks for catching that, I will add a definition...

Well, you do (below) say it's "proportional to the physical coating thickness and inversely proportional to the wavelength", but using it seems to make the graphs harder to understand. And I'm not approaching your presentation having read the Mauer paper.

You are getting at one of the most difficult ideas here and I am not happy with the write-up as it stands. I will need to expand upon it. Until then, here is my short attempt: (a) TIR only happens at that last interface between the final layer and the air, and we want that angle shallow. (b) all the others, the non-TIR reflections, cause additional, weaker reflections, but we need these to all add up with as little phase shift as possible over a broad wavelength range. Otherwise we’ll lose amplitude due to vanilla destructive interference that will occur with any multilayer - and this depends on the thicknesses, indices, and if the reflection gets inverted or not at each boundary. (c) It does seem like all these layers should confound each other, but they don’t if they are carefully constructed, in the same way and for the same reason that multilayer coatings can be tuned to provide very high, and "flat" transmittance across the entire visible band.

I quickly realized that the way I put my question didn't really make sense; the original version I discarded was actually about those different little reflections, how significant they are and how they add up, so that would have been the better one to ask. It's just very difficult to see what multiple coatings are doing here without the math that tracks it all.

In any multilayer, one might think that more layers can only make for more headaches and a kind of unwinnable game of whack-a-mole, but what these many phase shifts between the layers allow you to do is something very much like Fourier composition of a square wave from many sine waves.

Now that does make sense given my modest background in physics (though it might not without), and I had thought along similar lines looking at all those reflections, analysis and re-synthesis, but that didn't seem to be what you were saying. The hardest part is seeing the role wavelength plays (I haven't looked at the AR Coatings piece yet). So finally, the multilayer P-coating is really doing two things at once: this, plus the original goal of flattening the TIR angle.

Yes, you understood what I meant by "residual degradation". Is the further difficulty of the dual-function surface of Schmidt-Pechan prisms just a matter of transmission, or can it affect resolution also?

 

[Holger Merlitz]

Well, you do (below) say it's "proportional to the physical coating thickness and inversely proportional to the wavelength", but using it seems to make the graphs harder to understand. And I'm not approaching your presentation having read the Mauer paper.

I quickly realized that the way I put my question didn't really make sense; the original version I discarded was actually about those different little reflections, how significant they are and how they add up, so that would have been the better one to ask. It's just very difficult to see what multiple coatings are doing here without the math that tracks it all.

Now that does make sense given my modest background in physics (though it might not without), and I had thought along similar lines looking at all those reflections, analysis and re-synthesis, but that didn't seem to be what you were saying. The hardest part is seeing the role wavelength plays (I haven't looked at the AR Coatings piece yet). So finally, the multilayer P-coating is really doing two things at once: this, plus the original goal of flattening the TIR angle.

Yes, you understood what I meant by "residual degradation". Is the further difficulty of the dual-function surface of Schmidt-Pechan prisms just a matter of transmission, or can it affect resolution also?

As measured by Konrad Seil, the AR-coating on the dual-function surface affects the MTF and reduces the resolution of the final image.

Cheers,
Holger

 

[Holger Merlitz]

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.

There exists software to measure the MTF by analyzing images of 'edges' - you take a high resolution image of a chessboard pattern and the software scans the intensities along the transition from white to black and vice versa. From that it can somehow deduce the underlying MTF of the imaging system. In case of the prism-related phase shift, this MTF would depend on the orientation of the edge with respect to the roof edge.

Cheers,
Holger

 

[tenex]

As measured by Konrad Seil, the AR-coating on the dual-function surface affects the MTF and reduces the resolution of the final image.

Thanks Holger, I thought this might have been said before but wasn't sure. Yet this degradation can be reduced to the point that not only roof but S-P prisms in particular dominate the market today.

I suppose if you avoid romantic notions of what all this must be doing to the light that reaches your eyes, resolution loss from these effects is really no different from that caused by ordinary aberrations, and as long as the total is low enough you have a good binocular.

It's interesting that two rather different things seem to be going on with P-coatings. Instead of seeing exactly what needs to be done from first principles, as with flattening the TIR angle to reduce phase shift in the first place, you're deliberately complicating the situation further with multicoatings to introduce new variables (thicknesses and densities) which can then just be tweaked in a mathematical model to optimize the final result. With enough computing power you don't even need to follow all the details yourself. This isn't going to seem quite as elegant or intuitive to explain.

 

[Lerxst]

It's interesting that two rather different things seem to be going on with P-coatings. Instead of seeing exactly what needs to be done from first principles, as with flattening the TIR angle to reduce phase shift in the first place, you're deliberately complicating the situation further with multicoatings to introduce new variables (thicknesses and densities)

It isn't deliberate, not in the sense of us simply choosing to make it more complicated. As soon as you added that one TIR layer, your hand was effectively forced to add more layers. Imagine you only add that one layer and get close to mitigating the s- vs p-polarization offset at the coating/air interface. Okay, fine, but you now have created a reflection at the glass/coating interface, and this will result in a wavelength dependent interference effect when it superpositions with the TIR light. If you only need phase correction at a single wavelength, you'd tune to get constructive interference by setting the appropriate thickness, and call it a day. But if you want broad-band phase correction, you've got a problem now. You are going to get destructive interference at other wavelengths. And you'll only solve that by adding more layers which compensate for the problem that TIR layer created. The final layer fixes the TIR problem while the remaining layers function as a visible-light band-pass filter.

which can then just be tweaked in a mathematical model to optimize the final result. With enough computing power you don't even need to follow all the details yourself. This isn't going to seem quite as elegant or intuitive to explain.

Yes, it is easy, if time-consuming, to get a good design by sweeping a large parameter space, and doing so explains nothing. The similarity to a Fourier compositions is as close to intuitive as I have gotten on this.

 

[tenex]

Proprietary coating secrets have been mentioned, and perhaps Zeiss or Leica once had an edge, but with today's computers, isn't anyone able to grind through such code as you provide here and get a similar high-performance result? Or is the secret sauce their actual methods of depositing coatings?

 

[Lerxst]

Proprietary coating secrets have been mentioned, and perhaps Zeiss or Leica once had an edge, but with today's computers, isn't anyone able to grind through such code as you provide here and get a similar high-performance result? Or is the secret sauce their actual methods of depositing coatings?

The code is straightforward and optimization methods are easy to implement, so I think that is the easy part now. Not being a process guy, I cannot answer your last question with any certainty. I can guess, based on my hard drive experience, where the deposition processes are even more cutting edge... and my guess is that most all optics manufacturers probably use very similar deposition tools and employ similar recipes. They all must know from completive analyses what the others are doing anyway. Within weeks after another hard drive company released a new product, we knew their designs as well as they did because we took it apart down to the nanometer scale. And the recording heads are very complex, photolithographically defined, 3-d transducers made on wafers with many kinds of deposition and plating processes.... way more complex than the 2-d films that make up optical coatings.

It would seem that the design and process has gotten pretty routine. I ordered, after much searching, the cheapest Schmidt prism I could find, because I wanted an uncoated roof prism to play with, and even though it was just a $7, it still had phase coatings.

 

[binolover]

Does phase coating matters for all roof binoculars? I heard that for the smallest aperture roofs some manufacturers don’t bother to phase coat them because it doesn’t make a lot of difference in the small ones. They said that for aperture of 25mm or lower phase coating doesn’t add as much improvement as it adds for larger binoculars.
Is it true?

 

[Hermann]

Does phase coating matters for all roof binoculars? I heard that for the smallest aperture roofs some manufacturers don’t bother to phase coat them because it doesn’t make a lot of difference in the small ones. They said that for aperture of 25mm or lower phase coating doesn’t add as much improvement as it adds for larger binoculars.
Is it true?

No, that's nonsense.

Hermann

 

[binolover]

No, that's nonsense.

My question was: is that disease of roofs named phase shifting which the image quality more prevalent to larger aperture binoculars than to the small ones?
I don’t deny that phase shifting affects all roofs binoculars and phase coating will help all of them.
What they said was that it helps the most the larger ones and in a smaller amount the smallest aperture ones.

 

[Hermann]

My question was: is that disease of roofs named phase shifting which the image quality more prevalent to larger aperture binoculars than to the small ones?
I don’t deny that phase shifting affects all roofs binoculars and phase coating will help all of them.
What they said was that it helps the most the larger ones and in a smaller amount the smallest aperture ones.

Can we keep this discussion out of this thread? This is a highly technical thread and should remain so.

To answer your question: What these manufacturers said is nonsense. In fact, binoculars with smaller apertures suffer AFAIK more from the detrimental effects of phase shifts than binoculars with larger apertures.

Hermann

 

[binolover]

In fact, binoculars with smaller apertures suffer AFAIK more from the detrimental effects of phase shifts than binoculars with larger apertures

I asked because for example for porro binoculars, ED glass becomes almost mandatory for apertures larger than 50mm, bellow is just a small improvement.

And I had a personal experience when I compared my small Pentax phase coated with a similar Minox 8x25 BD (or BV) but not phase coated. Can’t explain why, I believed mine was way superior but I ended up liking the Minox’s image more. And Minox omitted only their smallest roofs from phase coating. Can anybody explain why?

 

[tenex]

Michael, I've gone through your AR Coatings pages now too. I do like the way you develop the material, and smile in particular every time you say "You might think... but..." because it's exactly right.

So it seems here too that a simple single-layer coating would work well for just one wavelength, but it takes many layers to build a broader curve. One sees how a company like Zeiss would have had an early advantage with the best in-house experts to find approximate solutions to this messy problem before the advent of greater computing power.

But: weren't the early MgF2 AR-coatings in fact just single-layer, and still performed well enough across the visible spectrum to be used for years? Yet you summarily dismiss them as inadequate, and move right on to the need for multicoating. And similarly for P-coating, leading me to wonder whether the original ones weren't also single-layer after all, and already a significant improvement, only subsequently refined? So much here depends on factors that aren't immediately obvious; one just has to find out how far an approach will actually fall short. Twice in reading this I got the impression that single-layer coatings were just a simplistic starting point that would never work, but in at least one case they did, until multicoating was able to do better still.

 

[Lerxst]

Michael, I've gone through your AR Coatings pages now too. I do like the way you develop the material, and smile in particular every time you say "You might think... but..." because it's exactly right.

Thank you. Appreciate the kind words.

So it seems here too that a simple single-layer coating would work well for just one wavelength, but it takes many layers to build a broader curve. One sees how a company like Zeiss would have had an early advantage with the best in-house experts to find approximate solutions to this messy problem before the advent of greater computing power.

But: weren't the early MgF2 AR-coatings in fact just single-layer, and still performed well enough across the visible spectrum to be used for years? Yet you summarily dismiss them as inadequate, and move right on to the need for multicoating.

It is pretty impressive what a single layer coating can do. And I wish I had a complete timeline of the history of coatings; when did company X go from single to 3, or to 6, or 9 layers, etc. I'm not sure such explicit information is available unless you are a long-time engineer within one of these companies. It is an ongoing effort I make when I have to time, to try to get some historical sense for this, but it is hot or miss.

So I would say two things in response about my 'dismissal' -- the first is that, of course, in a competitive market, you'll take any performance gain, be it <0.1%, because they'll accumulate and eventually bino aficionados such as yourself or a number of others on this board will be able to discriminate the difference. (Or people will be swayed by the idea that they can and buy the bin just based on a stat sheet or a numerical claim....) Plus, even though the company won't divulge their proprietary recipes, they can still file related patents and they can make claims about their exclusive "special coating" and they won't be misleading anyone. Second, with that single layer is that you cannot just "match it" to the glass, because you cannot tune the index to be the square root of the glass' index. But there is an advantage of even a simple multilayer here, and it is something I don't really discuss, is the "Herpin equivalent" concept: you can make a three layer system out of two materials as a sandwich, such as A-B-A, and regardless of index of A and index of B, there will be certain set of thicknesses that will make the ABA trilayer behave exactly like a single layer of whatever index you want. It is a way to go engineer or tailor any index you want, but you need at least 3 layers. My guess is that with there being so many uses for films, besides AR coatings, uses that are more difficult to engineer with a single layer (such as narrow pass-band filters, say) that the multilayer technology was getting so easy, why NOT hunt down a 0.01% gain if it is no harder than standing pat?

And similarly for P-coating, leading me to wonder whether the original ones weren't also single-layer after all, and already a significant improvement, only subsequently refined? So much here depends on factors that aren't immediately obvious; one just has to find out how far an approach will actually fall short. Twice in reading this I got the impression that single-layer coatings were just a simplistic starting point that would never work, but in at least one case they did, until multicoating was able to do better still.

The first proposed p-coating goes back to the 50s and the author was named Kard and the journal was a Soviet one, I believe. If you look at the Mauer paper, also from the 50s, you'll see he talks about it and the drawbacks of a single layer and why a Herpin trilayer was a big improvement: with p-coatings you stand in danger of falling off a performance cliff if the angle of incidence at TIR changes too much, and of course it does because FOV is not zero. Mauer also shows in his paper that even for three layers, his phase coating does not have a very impressive spectral response, certainly not one that a modern bino enthusiast would care to see. The Mauer paper is in my reference post and is worth a look for anyone that has wading through all the stuff I wrote.

 

[Holger Merlitz]

And I wish I had a complete timeline of the history of coatings; when did company X go from single to 3, or to 6, or 9 layers, etc. I'm not sure such explicit information is available unless you are a long-time engineer within one of these companies. It is an ongoing effort I make when I have to time, to try to get some historical sense for this, but it is hot or miss.

Years ago I wrote a short chapter about AR coatings and their history for Hans Seeger's book (Zeiss Handferngläser 1919-1946), all in German. Here a few bits and pieces which I could find, and which are obviously incomplete.

• 1817: Fraunhofer applied acids to etch glass surfaces in order to reduce reflections
• 1904: First patent for a similar method, Dennis Taylor
• 1935: First patent No. 685767 for a single-layer coating via vapor deposition, Alexander Smakula. This patent was then declared classified and remained unpublished until 1939
• 1936: First US patent for an identical method, John Strong
• 1939: Zeiss first applies its 'T-coating' to Flak-binoculars, range finders and submarine periscopes
• 1939: First report on double-layer coatings (C.H. Cartwright and A.F. Turner, Phys. Rev. 55, p. 675 (1935))
• 1941: Zeiss first applies the T-coating to civilian binoculars
• 1941: Leitz first offers the 'Leitz-Brilliant' camera lenses with single-layer coating
• 1942: German Patent No. 742463 for a triple-layer coating, Walter Geffcken
• After 1945: Zeiss uses double-layer coatings for some of its camera lenses
• 1971: First triple-layer "T3"-coating used by Zeiss Jena for its camera lenses, followed by other camera makers such as Optische Werke Rathenow and Pentacon
• 1976: Patent (DWP 123081) for coatings of 7 and 8 layers
• 1978: T3 coatings are introduced to binoculars, almost simultaneously around the world. The technology had previously been optimized by the camera makers

Most of the above cited data stem from the following two sources:

• Die blauen Linsen oder die Geschichte der Vergütung, von Hartmut Thiele, in Legenden und Geschichten der Photoindustrie, Privatdruck, München, 2006
• Physik und Technologie Optischer Schichten. Wichtige industrielle Innovationen und Entwicklungen aus Jena, von Erich Hacker, im Jenaer Jahrbuch zur Technik- und Industriegeschichte, Bd. 1, herausgegeben 1999 vom Verein Technikgeschichte in Jena

Cheers,
Holger

 

[Tringa45]

Belated thanks for the additions even though I was similarly overwhelmed.
While appreciating that you are not privy to manufacturing secrets, perhaps you could answer a few queries.

1) Asuming that "hard" protective coatings on eye lenses and objectives may have higher refractive indices than the glass substrate, would this degrade transmission at these surfaces , or could it be remedied?

2) Would you expect individual tailoring of multicoatings to specific optical glass sorts or rather to a span of refractive indices?

3) What is the point of 1/2 wavelength coating thicknesses and those considerably less than 1/4 wavelength?

4) Among amateur astronomers there seems to be a preference for enhanced aluminium or silver erecting mirrors over dielectric mirrors as they are allegedly less prone to scatter. This is perhaps understandable as a total of around 60 dielectric coatings may accumulate to degrade flatness. However, there is one manufacturer of simple but expesive 2 group, 4 element eyepieces, which are only single coated. It is claimed that they have less scatter and better contrast than if multicoated. Is this plausible or just BS?

Thanks in advance,

John

 

[Lerxst]

Belated thanks for the additions even though I was similarly overwhelmed.
While appreciating that you are not privy to manufacturing secrets, perhaps you could answer a few queries.

I will try. Many answers are variations on the same theme, as you will see.

1) Asuming that "hard" protective coatings on eye lenses and objectives may have higher refractive indices than the glass substrate, would this degrade transmission at these surfaces , or could it be remedied?

Remedied easily for a multilayer. Consider: suppose you designed a nine-layer coating to be anti-reflective over the visible range. Your design is:

Air/Layer1/Layer2/..../Layer9/Lens

Now, if you took that design and plopped a hard, anti-scratch layer between Air and Layer1, you'd certainly compromise the AR performance. But if you designed this as a ten layer system from the start, knowing you had the final layer for durability, your nine AR layers would be tweaked in thicknesses to make up for that "mechanical layer" no matter what its index was.

I should add a point for tenex: wanting to add a layer for anti-scratch etc. is another reason why a single layer AR coating is less than ideal. Harder to "tune away" the problems caused by the durability coating if the AR only has one layer to tweak. Get me many layers and I can accommodate anything.

2) Would you expect individual tailoring of multicoatings to specific optical glass sorts or rather to a span of refractive indices?

Not sure. Brushed under a huge rug that I am not looking under is the following: how well does coating material X adhere to glass type Y? Will the difference stress/strain profiles vs temperate lead to potential reliability problems? I guessing that in some cases, yes. I know from hard drive recording head fabrication done on wafer and various deposition methods that sometimes you have to be take extra steps because process # 18, say, might involve temperatures that adversely affect something you deposited in step #16. Seems feasible to me that optical multilayer depositions might bring up some scenarios like that. So my hunch is that both glass and material mechanical properties may require some extra considerations that simple optical calculation with the TMM cannot address.

3) What is the point of 1/2 wavelength coating thicknesses and those considerably less than 1/4 wavelength?

For AR, which is usually what we care about, the quarter wave naturally crops up because it allows for destructive interference in a simple way; but other applications (like a dielectric mirror) will suggest a half wave so that we can get constructive interference. More generally, I respond to this question with: which wavelength? Nobody on this forum wants to talk about monochromatic light. So my hand-wavey answer, which I try to flesh out in my blog post about the TMM, is that all those layer thicknesses make it possible to create a bunch of different reflection vs wavelength profiles that add together to give flat spectral response, just like making a square wave by adding a bunch of sine waves.

When I started digging into the phase coating issue years ago, I found that the inherent roof prism problem is shared by corner cube reflectors - a corner cube is like a three-way roof prism. They have it even worse! But nobody uses corner cubes to form quality visual images for humans to enjoy. The are used mostly for distance measurements. Plop some down on the moon and point a laser at them from earth and you've got a nice ruler to measure the distance. And if you want to reduce that nasty interference effect, you don't need some nine layer phase coating, because your laser is monochromatic. So the literature on corner cubes reveals a fascinating, harder problem than a roof prism but with a simpler solution for practical use.

4) Among amateur astronomers there seems to be a preference for enhanced aluminium or silver erecting mirrors over dielectric mirrors as they are allegedly less prone to scatter. This is perhaps understandable as a total of around 60 dielectric coatings may accumulate to degrade flatness. However, there is one manufacturer of simple but expesive 2 group, 4 element eyepieces, which are only single coated. It is claimed that they have less scatter and better contrast than if multicoated. Is this plausible or just BS?

Not sure, honestly. Partly an expense issue? Plopping down a metal is a helluva lot simpler than fabricating a state of the art dielectric mirror. I also think that with astronomy, especially if you are wielding some monster Newtonian reflector, you can afford to lose reflectivity in a silvered prism near the eyepiece because you've bought so much light-gathering capability via the objective mirror's gargantuan aperture (relative to eyes or bino objectives). Heck, that silvered mirror in a 16-inch reflector has already lost a bunch of light thanks to metal coating, but so what? The entire mirror is so big you'll get to ridiculous stellar magnitudes anyway. Obviously not a luxury that can be afforded to bino users in a dark forest, but then again chasing after faint deep sky objects is a totally different game anyway.

Been a long time since I have thought about optics in an astronomy context.

 

[Trinovid]

I will try. Many answers are variations on the same theme, as you will see...if you took that design and plopped a hard, anti-scratch layer between Air and Layer1, you'd certainly compromise the AR performance. But if you designed this as a ten layer system from the start, knowing you had the final layer for durability, your nine AR layers would be tweaked in thicknesses to make up for that "mechanical layer" no matter what its index was.

That was very well written and easy to follow. You really deserve a special trophy for this entire thread and willingness to answer all theories and questions in such patient and careful detail. Thanks so much for this thread!

 

[has530]

I just wanted to say this is awesome and I will definitely have more to add to this conversation once I have time to make it through the extensive material! For the time being I have a thought on primary mirror coatings.

Not sure, honestly. Partly an expense issue? Plopping down a metal is a helluva lot simpler than fabricating a state of the art dielectric mirror.

While that may be part of it I would also assume it has to do with the surface geometry. The spectral reflectivity depends not just on the dielectric layer thickness but also angle of incidence. For a flat mirror (like a star diagonal or prism) it can be pretty easy to lay down even layers but in a primary mirror if you manage to lay down perfectly spaced layers and then the incident light enters parallel to each other but strike the mirror at a variety of angles and thus the light path length in the dielectric medium is different depending on your distance from the optical axis and thus your spectral reflectance becomes a function of radius. Much simpler to just deposit a mirror of metal which is a pretty good reflector and much more forgiving in terms of deposition thickness. Then if you want to get fancy you can overlay a small number of dielectric layers to enhance reflectivity at wavelengths where your metal is a poor reflector (like violet where silver is rapidly falling off); I think manufacturers sometimes refer to this as “enhanced-<metal name>” mirrors. These are somewhat common now in telescopes and also in ultrafast laser systems thanks to other nice properties like low group delay dispersion.