89 replies to this topic

[rainycityastro]

I am not an optical expert. And I don't play one on the Internet. But I've been fascinated by it ever since I was a kid. 

 

Please note that this question has little practical application - except maybe to set boundary conditions. Or to sniff out marketing BS.  Since this is the forum with the largest concentration of what are genuine experts in the field, I wanted to pose the following question. So please go gentle on me.

 

What is the practical limit to refractor performance? 

 

I see terms like strehl 0.98 and more recently 0.99+ being touted by several manufacturers of apochromats. At least in green. Is this really realistic to achieve?

 

My doubts stem from the following considerations.

 

1. Even if the optic is figured to this high level, Each of the surfaces - upto 6 undergoes a coating - usually a Broadband Anti Reflective. Usually it is MgF2/SiO2 and other oxides. It involves heating the lens element 100 -200C and putting a rather thick coating on it. It leaves upto 30-100 MPa of compressive stress. 

This stress effect on lenses can be greater than 100nm of deflection. That's about 1/5 wavelength of light. Even if it is uniform ( a big IF) you are now multiplying it by 6 surfaces (or 2) and assume some non uniformity,  This eats significantly into your accuracy budget.

 

2. I understand they coat and then do a test and tweak centration to optimize things but that is basically only minimizing the damage that is already done. 

 

 

As I understand it the budget for S=0.99 is an RMS wavefront error of 13nm.  That is over 2-6 polished surfaces, coatings, assembly and test errors. It seems absolutely impossible.  0.98 isn't much better.  0.95 is maybe the best one can do.

 

Thoughts?

 

I have similar questions on Reflector performance but it is also complicated by central obstruction so lets keep it simple for now. 

Edited by rainycityastro, 20 June 2025 - 12:30 PM.

[Starman1]

Glass, as it turns out, spalls (chips, aka concoidal fracturing) at about the 6-10nm level at minimum, though MRF can even that out some.

Fused silica (quartz) spalls at 2-4nm, so theoretically can have a smoother surface, though polishing agents that can polish a surface that smooth are few and far between.

There are some techniques that can polish a glass surface to <1nm (10Å).

 

So a surface smoothness of 1/100 wave at 550nm pretty much represents the theoretical limit for polishing glass.

You're very unlikely to meet up with a surface that smooth, but it can be done (and it is done in some eyepieces).

 

I'm not mentioning issues like light scatter from inclusions in the glass, gaps in the coatings, and differential refraction from the glass resulting in chromatic wavefront error.

 

Add to that the error in figure resulting from polishing techniques, plus any coating flaws or residual errors, and the best you can hope for is for some cancellation of errors to take place.

An astute lens manufacturer would rotate the lenses to get the best results, but I doubt this is typically done anywhere (maybe SV or AP?).

 

So you are right to be skeptical of a 0.99 Strehl claim.

 

I've been doing field testing of optics for over 40 years, and I can only count on one hand, out of hundreds of scopes, the ones where the wavefront was so good I couldn't tell how good it was.

Once it's better than 1/8 wave on the wavefront, I'm in Terra Incognita.  That is, of course, after passage through the entire stack of optics, including eyepiece and diagonal.

I believe that figures out to about a 0.95 Strehl.  I am convinced that once it gets to there, the differences between scopes may boil down to solely surface smoothness, and not RMS error.

After seeing many many scopes, I'll take a 1/8 wave optic with a 2nm surface smoothness over a 1/20 wave optic with a 10nm smoothness because once the optics reach a certain level,

it's all about contrast, and I agree with Carl Zambuto that contrast matters.

[Oregon-raybender]

I agree, but the key issue is still your eyes and atmosphere need to factored

in as well as part of the optical system. We can measure 

in great detail the quality of an optical system in a vacuum, but....

that is not how they will be used.

 

I viewed thorough some wonderful telescopes that were near perfect(?), but

the add the atmosphere and eye limits that perfection. I saw Saturn

so sharp under idea skies and at the age of 26 or 27. My young eyes

could handle it. Today, forget it, too many floaters and stuff inside

makes it very hard to enjoy great views now, even with FFNs under

dark skies. As trained observer, this hard to let go of, but the run

of great views are still remembered. 

 

This is age old question, what makes the perfect telescope.?

As a professional, I made some beautiful optics. 

 

My question is, Who is capable to handle and explain in detail

what they are seeing using the perfect telescope?

The next person in line may not due these factors. Due you trust

the value of what anyone can say, "This is a perfect telescope

based my visual observing ! " 

 

Starry Nights 

[IslandPink]

A couple of points - AR coatings are not very thick. A 4 or 5-layer coating is often only 0.5 micron thick. Also coatings are stress-balanced in design ; although this hardly matters with an AR coat.

100-200 deg C is nothing for optical glass, which is typically annealed in the 500°C region.

 

Limits to how good an Apo refractor can be, must include the characterisation of the glass data at the 5 or 6 wavelengths, typically this is usually given to 5 decimal places. 

[Pixeltim]

In a far less scientific thought, I talked to a guy at Tele Vue yesterday. When asking about eyepiece selection, he told me the optics are at a level that I’ll run out of atmosphere long before magnification.

If we were outside the atmosphere, it would matter far more. (Although breathing would take precedence.)

[TOMDEY]

Most of my experience was on the research and metrology side of the production of optics. (B&L, Kodak, ITT, GE, Uncle Sam, etc.) Decades ago Daniel Malacara and I did a brief causal talk on "Telescope Quality - How Good is Good Enough?" I did the traditional wavefront part and Daniel addressed the higher spatial frequencies. His message is that you (should) want an incoming wavefront (as it approaches the image) that is both good traditional PV and RMS and also ~Smooth~. The first entry (lower spatial frequencies) is what we guys here typically obsess over when we demand near-perfect Strehl; the second entry (higher spatial frequencies) relates to polish and glass homogeneity. Coatings and stresses also contribute to both imperfection species. There's a lot of overlap: low, medium, high freq...

 

Coronagraphs and planet finders especially require near perfection of both.

 

"Almost Thankfully", aperture (expressed in wavelengths) itself becomes the biggest remaining limiter to both resolution and contrast. This also explains whether a Strehl is 95% or 99% hardly matters. Performance wise, 99% is just a wee bit better than 95%, not five times as good.

 

We concluded that you should perform two different performance tests: 1) traditional ~wavefront-sensing~  interferometry e.g. Fizeau double-pass autocollimation over all fields in the telescope's as-used configuration. 2) ~slope-sensing~ e.g. quantitative Foucault, same conditionals of set-up. I was working R&D on the "Quantitative Knife Edge" (QKE) at the time.

 

Best I've Ever Seen >>> A 1+ meter imager that was indeed single-pass "twentieth wave" PV over all fields and colors. A batch of smallish (2-inch) optical flat mirrors that were 1/100 wave (reflected wavefront) PV HeNe over the central 90% diameter ~clear aperture~. At those quality levels... the metrology itself becomes about half the effort. You don't just stick it on an interferometer and measure it --- most of the metrology effort is calibrating the interferometer itself, doing rotations and translations, backouts, fiducilizations, etc, etc, etc.

 

On the countably rare occasions that we confirmed a near-perfect wavefront in the metrology labs, we would excitedly invite in the other techs, engineers, and scientists to look at the screen, kick tires... and admire the optic.

 

PS: It's always struck me as kind of ironic that a great telescope and a crummy one can look superficially identical. Isaac Newton and other early telescope makers were painfully aware of this... and took much theory, research, and development --- to sort it all out. All because visible light has a pretty short wavelength!    Tom

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[rainycityastro]

A couple of points - AR coatings are not very thick. A 4 or 5-layer coating is often only 0.5 micron thick. Also coatings are stress-balanced in design ; although this hardly matters with an AR coat.

100-200 deg C is nothing for optical glass, which is typically annealed in the 500°C region.

 

Limits to how good an Apo refractor can be, must include the characterisation of the glass data at the 5 or 6 wavelengths, typically this is usually given to 5 decimal places. 

Let me push on this a little bit. First, we are talking S > 0.98, a far way off from 'merely' diffraction limited. The thickness is about a wavelength. And there are likely 6 surfaces unless oiled or cemented which bring other issues.  Even 10s of nm of non uniformity per surface will result in non smoothness of the final wavefront, no?

[IslandPink]

1. Glass, as it turns out, spalls (chips, aka concoidal fracturing) at about the 6-10nm level at minimum, though MRF can even that out some.

Fused silica (quartz) spalls at 2-4nm, so theoretically can have a smoother surface, though polishing agents that can polish a surface that smooth are few and far between.

There are some techniques that can polish a glass surface to <1nm (10Å).

 

2. So a surface smoothness of 1/100 wave at 550nm pretty much represents the theoretical limit for polishing glass.

You're very unlikely to meet up with a surface that smooth, but it can be done (and it is done in some eyepieces).

 

While I agree with the general thrust of this thread, that getting > 0.95 strehl is very hard, in practice, there is a lot of inaccurate information in this discussion.

 

1. Any polishing cuts through that 6-10nm level, that is just not a normal polished roughness level. Most optical glass is routinely polished to 2nm to 2.5nm even with modern high-speed polishing machines, and certainly with pitch.

Experiments at our factory 25 years ago for 405nm and UV optics showed that you could get down to 0.5nm rms with dilute ceria compound and extended runs.

 

2. I'm not sure there's a theoretical limit at lambda/100 with glass , but it's very hard to test that sort of level, certainly for overall figure error. 

On Zerodur, in recent years Zeiss have been able to demonstrate roughness in the 10's of pico-m on their mirrors for 13nm lithography. I have idea how they manage it, but the current linewidths would not be achieved if it wasn't happening.

[Alan A.]

"What is the practical limit to refractor performance?"

 

I would say if you can get greater than 95% strehl in red, green and blue in a refractor - I would say that's the practical limit.  Of note these figures typically represent on axis numbers, and various lens designs will do better or worse in off-axis performance - so that also needs to be kept in mind.

 

"I have similar questions on Reflector performance"

 

For a reflector, with an obstruction of 20% or less, good control of thermals, and I would say a smooth mirror that's 1/10-1/20th wave of at the wavefront would be a good practical limit.  And again - depending on the design of the reflector and the FOV you need, off axis performance will vary and is important to evaluate.

 

 

Best,

 

Alan

Edited by Alan A., 20 June 2025 - 03:41 PM.

[Starman1]

While I agree with the general thrust of this thread, that getting > 0.95 strehl is very hard, in practice, there is a lot of inaccurate information in this discussion.

 

1. Any polishing cuts through that 6-10nm level, that is just not a normal polished roughness level. Most optical glass is routinely polished to 2nm to 2.5nm even with modern high-speed polishing machines, and certainly with pitch.

Experiments at our factory 25 years ago for 405nm and UV optics showed that you could get down to 0.5nm rms with dilute ceria compound and extended runs.

 

2. I'm not sure there's a theoretical limit at lambda/100 with glass , but it's very hard to test that sort of level, certainly for overall figure error. 

On Zerodur, in recent years Zeiss have been able to demonstrate roughness in the 10's of pico-m on their mirrors for 13nm lithography. I have idea how they manage it, but the current linewidths would not be achieved if it wasn't happening.

Carl Zambuto claims to have smoothness below the 1nm level also, but Lyot tests, though not quantitative, show obvious surface structure on every mirror I've seen tested, and I didn't think Lyot could resolve structures smaller than 1nm.

Perhaps I'm remembering wrong and it was below 1Å that Lyot couldn't see any detail.

https://zambutomirro...oopticalcd.html

https://www.cloudyni...93-lyot-tester/

https://www.astroref...-wolfgang-rohr/

 

As for what is a "normal polished roughness level", I can see surface roughness in most commercial mirrors with a Ronchi eyepiece, which puts that roughness at a fairly large level.

I don't think commercial scopes have smooth or premium-figured mirror surfaces on average.  I don't disagree at all with your point 1, I just don't think commercial optics reach that level.

MRF is capable of surfaces accurate to Angstroms, but commercial mirrors aren't made that way.

[rainycityastro]

"What is the practical limit to refractor performance?"

 

 

For a reflector, with an obstruction of 20% or less, good control of thermals, and I would say a smooth mirror that's 1/10-1/20th wave of at the wavefront would be a good practical limit.  And again - depending on the design of the reflector and the FOV you need, off axis performance will vary and is important to evaluate.

 

 

Best,

 

Alan

In my non-expert opinion, I think the number is closer to 1/10 wave than 1/20 wave. To get to 1/20 wave, I believe MRF is needed. Ion beam figuring will make the figure very smooth and bring the RMS value lower - perhaps as low as lambda/80. It has negligible effect on PV.

 

In my research, the finest mirrors - ultra flats from Zygo - meant to be used as reference flats at government labs like LLNL have a certified accuracy of lambda/40.  These aren't even coated. Coating will change the figure and that is not acceptable at the highest levels.

Edited by rainycityastro, 20 June 2025 - 04:35 PM.

[IslandPink]

Thanks for the info on Zambuto. I hope I can get nice results on my next mirror. I have some special 0.3µm ceria that I got many years ago from Pilkington.

 

I think a Lyot test probably goes to 1 Å rather than 1nm, thanks for reminding me of Lyot , I read about it many years ago. It's a very sensitive test for roughness.

 

I agree that commercial scopes won't have particularly special polishing, but a lot of what we do at work on glass ( Avionics displays like Head Up Displays ) only has normal polishing with polyurethane laps, and that gets us 2 to 2.5nm . This is pretty standard stuff which would be similar in the Asian suppliers' workshops. We have white-light interferometers with microscope heads for checking small-scale roughness, we can get very accurate measures when we need to.

Roughness at a level of 5nm would be unacceptable on a HUD, and most visual optics, it would give too much integrated scatter.

 

I think from the OP's point of view, I am very sceptical of high Strehl numbers myself. Firstly I think they are quoting the Strehl for the on-paper design without any fabrication effects.

Secondly I know that if you use Zemax to get an MTF on the default settings, you get a very optimistic result ( you need to increase the pupil mesh density quite a lot ) ; and I wouldn't be surprised that the same is true of Strehl predictions.

[IslandPink]

 

In my research, the finest mirrors - ultra flats from Zygo - meant to be used as reference flats at government labs like LLNL have a certified accuracy of lambda/40.  These aren't even coated. Coating will change the figure and that is not acceptable at the highest levels.

This was true about 40 years ago.

 

This was the state of the art 5 years ago :

https://www.euvlitho.com/2018/P22.pdf

 

All of the mirrors used in the ASML machines are coated with dozens of layers of carbides, in order to reflect at 13nm in the deep UV.

 

Apologies if I seem overbearing - I had psychometric tests at work in the last couple of weeks that showed I was definitely the sort of person who is not happy if something is wrong on the internet  

Edited by IslandPink, 20 June 2025 - 04:53 PM.

[rainycityastro]

This was true about 40 years ago.

 

This was the state of the art 5 years ago :

https://www.euvlitho.com/2018/P22.pdf

 

All of the mirrors used in the ASML machines are coated with dozens of layers of carbides, in order to reflect at 13nm in the deep UV.

 

Apologies if I seem overbearing - I had psychometric tests at work in the last couple of weeks that showed I was definitely the sort of person who is not happy if something is wrong on the internet  

Wow, that's crazy impressive.  We've moved way past ion milling at this stage. however this is not optics as astronomers know it anymore.

Edited by rainycityastro, 20 June 2025 - 05:19 PM.

[Spinwiz]

I agree, but the key issue is still your eyes and atmosphere need to factored

in as well as part of the optical system. We can measure 

in great detail the quality of an optical system in a vacuum, but....

that is not how they will be used.

 

 

Starry Nights

Which brings up a question what would it take to put an amateur telescope into orbit????    I say amateur in contrast to a government funded project.

 

What has me thinking in this manner is my trip to the Dayton Hamfest.   There is a rather active group of Hams that are involved in satellite communications including satellites put into orbit simply for Ham usage.   Would it be at all possible for the amateur astronomy world to put their own satellite into orbit and skip the nasty atmosphere?

 

Such a telescope would need to fit a cube satellite format which would limit aperture size.    Which then brings up the question of how much of an advantage would we get over say a 12" scope on the ground (if any).   Even a 3.5" aperture in space would be a massive win for my location which never has good seeing.   Just seeing the moon can be a challenge with the cloud cover.   By the way the 3.5" comes form the approximation of a 8cm aperture inside a 10cm cube Cubesat.

 

The big problem here of course would be the required aerospace engineering which would mostly need to be voluntary.   You would need a short optical system to keep the hardware costs down but there are plenty of options there.   Now I'd be the first to admit that a 3.5" aperture telescope in space isn't the greatest thing compared to Hubble or a spy sate but it is achievable and you would need to start someplace.     The next size up would be the 20cm standard which might enable a 7.5" class aperture.

[IslandPink]

Sorry I just realised that 2018 wasn't 5 years ago. This is my subconscious rebelling against ageing.

[Starman1]

Sorry I just realised that 2018 wasn't 5 years ago. This is my subconscious rebelling against aging.

Next month I celebrate turning 39 for the 36th time (counting the first time).

It seems months pass now like days passed when I first turned 39.

You can protest, hold up signs, wear the shirt, but "Old Man River, he just keeps rollin' along..."

[Alan A.]

"What is the practical limit to refractor performance?"

 

"I would say if you can get greater than 95% strehl in red, green and blue in a refractor - I would say that's the practical limit."

 

 

When I posted the above about 95% strehl in R G B I should have indicated that I meant measured performance, NOT design Strehl.  I believe this has been acheived for example in the  Takahashi TOA-130 - a fine instrument.

 

 

Best,

 

Alan

[Alan A.]

"In my research, the finest mirrors - ultra flats from Zygo - meant to be used as reference flats at government labs like LLNL have a certified accuracy of lambda/40.  These aren't even coated. Coating will change the figure and that is not acceptable at the highest levels."

 

 

 

This is very interesting.  I have been aware for some time that coatings can impact the surface figure and smoothness of an optic.  How much does the coating bring a lambda/40 flat down to - lambda/20?  And I presume since this is a flat we are talking about it's measured at the surface rather than the wavefront?

[rainycityastro]

I learned that a protected-aluminium coating routinely leaves a low-order convex hill on high-precision flats – typically 0.05–0.30 fringe PV – because of residual tensile stress and slight thickness non-uniformity. The effect is perfectly normal, elastic, and reversible. 

This can be easily characterized and compensated by a Zygo. But it is there. 
 

Maybe somebody can confirm or refute. 

Edited by rainycityastro, 20 June 2025 - 07:32 PM.

[IslandPink]

It should be possible to control these effects better, but I should talk to my friend Jon who knows all about this stuff. Various types of rotation in the plant should control uniformity at least, but it affects loading/yield.

Edited by IslandPink, 20 June 2025 - 07:44 PM.

[rainycityastro]

 

I believe that figures out to about a 0.95 Strehl.  I am convinced that once it gets to there, the differences between scopes may boil down to solely surface smoothness, and not RMS error.

After seeing many many scopes, I'll take a 1/8 wave optic with a 2nm surface smoothness over a 1/20 wave optic with a 10nm smoothness because once the optics reach a certain level,

it's all about contrast, and I agree with Carl Zambuto that contrast matters.

Yes, that is borne out mathematically as well.

Strehl is inherently tied to surface smoothness as in RMS error.  IOW you might be ¼ λ PV but it will be a crappy optic if it isnt smooth.

 

Here is the original experiment.

 

Lord Rayleigh examined how much uniform phase error could be tolerated before the central diffraction spot of a star image lost visible contrast.
His thought-experiment was extremely simple:

Split the pupil into two halves.

Let one half of the emerging wavefront lag the other by a fixed amount Δϕ.

Superpose the two halves in the focal plane and ask how bright the Airy core becomes.

When the peak-to-valley (PV) phase step reached ¼ λ (i.e. ½ π rad) the core intensity fell by about 20 %.
Rayleigh remarked that “under ordinary conditions such a reduction is not sensibly prejudicial.”

 

That single number – lambda ⁄ 4 PV – is what we still call the Rayleigh quarter-wave criterion.

Key point: Rayleigh’s model contained only one very smooth, low-order aberration – a single step (equivalent to mild defocus or coma).
He did not analyse roughness, ripple, polishing zones, or any mixture of aberrations. 

 

The moment you have roughness, ripple, zone etc, you might still be ¼ λ PV but you will definitely not be diffraction limited. 

[Starman1]

"In my research, the finest mirrors - ultra flats from Zygo - meant to be used as reference flats at government labs like LLNL have a certified accuracy of lambda/40.  These aren't even coated. Coating will change the figure and that is not acceptable at the highest levels."

 

 

 

This is very interesting.  I have been aware for some time that coatings can impact the surface figure and smoothness of an optic.  How much does the coating bring a lambda/40 flat down to - lambda/20?  And I presume since this is a flat we are talking about it's measured at the surface rather than the wavefront?

Obviously not my much, as eyepiece lenses are routinely multi-coated and some eyepieces with 8 or even 9 elements yield wavefronts after passage with < 1/100 wave deformation.

I would expect BBAR coatings to have unnoticeable effects.

 

Now, the issue lies with dielectric coatings on glass, which can be stacks of 40-75 different layers several wavelengths thick, a very different story than lenses.

Roland Christen made sure to use an oversized mirror in his star diagonal so the light from the objective doesn't even strike the outer surface of the mirror, where the coatings, and performance, roll off.

I had a 1/30 wave secondary mirror Zygo tested AFTER an enhanced coating was added, P-V about 1/33 lambda, and the RMS on the surface of 0.004 wave.  It seems that the few layers in enhanced coatings don't detract from the optical quality.

 

I suspect a lot of the issues with multi-layer coatings ended once IAD coating became commonplace.  A lot of old information is endlessly repeated on-line, though.

[MKV]

So you are right to be skeptical of a 0.99 Strehl claim.

 

I've been doing field testing of optics for over 40 years, and I can only count on one hand, out of hundreds of scopes, the ones where the wavefront was so good I couldn't tell how good it was.

Once it's better than 1/8 wave on the wavefront, I'm in Terra Incognita.  

  Even if a mirror tests at S of 0.99 on the bench it's irrelevant. What counts is the wavefront entering the eye or a recording device at the exist pupil of a complete optical assembly under actual working conditions (including eyepieces, Barlow, field flatteners, filters, etc.). On earth, one will never, ever, see or record a 0.99 Strehl wavefront no matter how good the mirror is..

 

On the other hand, a true true 1/8 wave PV telescope is a gem, and nothing to sneer at. A true 1/8 wave telescope would have an exit pupil Strehl of 0.95.

 

Any telescope better than 1/10 wave PV (Strehl 0.97) is as good as it gets on earth. Beyond that -- atmospheric errors exceed optical errors. In these examples, one assume a perfectly mirror figure and irrelevant surface roughness.

[MKV]

And I presume since this is a flat we are talking about it's measured at the surface rather than the wavefront?

Correct. A flat specified with a wavefront OPD and a Strehl score is an oxymoron. Strehl scores apply only to image-forming optics (optics capable of focusing light), and specifically operating at the Airy disc level (hence excluding ordinary photographic lenses). 

 

This Things that matter in a flat are (1) power, i.e. concavity or convexity, (2) regularity (of the figure, presumably spherical), and (3) degree of surface roughness.

Edited by MKV, 21 June 2025 - 12:30 AM.