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Strehl Ratio

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#1 Steve Allison

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Posted 19 January 2019 - 09:03 PM

Dumb question time. I am asking it in this forum because Strehl ratios come up a lot in the various discussions posted here.

 

Does the Strehl ratio say anything about the smoothness (roughness?) of the optical figure, or the level of polish of the optical glass of the objective lens being tested?

 

I ask because there seem to be differences in the performance of telescopes with similar Strehl ratings. For instance, why do telescopes like Takahashi, Zeiss and AP appear to produce better images than some other telescopes with similarly high Strehls?

 

I know baffling and the precision of the centering of the lens elements certainly have an effect on performance, but what else is going on here to explain the performance differences among high Strehl ratio telescopes?

 

Thank you.

 

Steve


Edited by Steve Allison, 19 January 2019 - 09:05 PM.

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#2 agmoonsolns

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Posted 19 January 2019 - 09:19 PM

Great post! I really look forward to learning about the relationship between high Strehl ratios and performance.



#3 Darren Drake

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Posted 19 January 2019 - 09:24 PM

It depends on how the strehl was determined.   If it was with a simple foucault test and program like figure XP then a strehl ratio may not consider surface roughness and hence may be misleading if roughness is present.   An interferometer which measures many more points across the entire surface may do much better but still not get it totally right.  This is why I like to see a null test image with any optical report.

Here is some great info on this from Zambuto's websie.

https://zambutomirro...oopticalce.html


Edited by Darren Drake, 19 January 2019 - 09:28 PM.

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#4 JamesMStephens

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Posted 19 January 2019 - 09:53 PM

Background discussion on Strehl ratio https://www.telescop....net/Strehl.htm


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#5 Asbytec

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Posted 19 January 2019 - 11:06 PM

Here is some great info on this from Zambuto's websie.

https://zambutomirro...oopticalce.html

Here's what I see as the telling comments in the link above. 

 

"So what's the issue with primary ripple? It creates severe slopes that are not accounted for in surface measurement. These slopes scatter light and have the ability to severely reduce contrast. The result? Dick Suiter says it like this, "The net effect of mild primary ripple is to blow the scattered light into a knobby glow surrounding the image, which has its greatest brightness within a radius less than 5 times the airy disk. Such scattered light can be a bad problem because it is condensed enough to easily see" (Star Testing Astronomical Telescopes p. 237)."

 

"The Strehl ratio is a measurement of the large scale (geometric) surface. Regardless of the method of test being used, including the most advanced optical devices in existence, criteria such as medium scale surface roughness and turned edge are not taken into account." 


Edited by Asbytec, 19 January 2019 - 11:07 PM.

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#6 Steve Allison

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Posted 19 January 2019 - 11:09 PM

Thanks, guys!

 

Any other thoughts?


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#7 agmoonsolns

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Posted 19 January 2019 - 11:16 PM

Surface smoothness is every bit as important as the Strehl ratio. I have compared many different telescopes and those with the smoothest surfaces just seem to have that slight edge. This goes for eyepieces too.


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#8 Asbytec

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Posted 20 January 2019 - 01:21 AM

Reading more of what Suiter has to say, at least about ripple...

 

"We might expect the diffraction image from the roughness facets characteristic of primary ripple to be 5 to 20 times larger than the unaberrated image, but that simplified logic does not take into account the accidental correlations that occur when nearby scattering facets act in phase with one another. Antinodal bright areas and nodal dark regions will form. The net effect of mild primary ripple is to blow the scattered light into a knobby glow surrounding the image, which has its greatest brightness within a radius less than 5 times the Airy disk. Such scattered light can be a bad problem because it is condensed enough to easily see."

 

When roughness is small, as it is for optics, it only affects the diffraction shape of the image in a minor way. It removes light from the focused image and shoves it out into a blotchy halo of small diameter for primary ripple and large diameter for microripple. The missing energy is calculated by seeing how much the central intensity is lessened...For example, a 1/14.05-wavelength RMS deviation yields a Strehl ratio of 0.8 (the Maréchal tolerance). A 1/20-wavelength error typical of noticeable primary ripple gives a ratio of 0.9. A severe case of microripple might have a deviation as large as 1/100 wavelength, so the intensity is reduced only to 0.996. Clearly, microripple has a very different character than primary ripple.

 

This 1/20-wavelength RMS aperture is acceptable in the MTF chart, yet it seriously distorts out-of-focus images. Fortunately, it seems to tuck away the messiness visible out-of-focus to yield a fairly crisp pattern while in focus."

 

Ref: Chapter 13.   Roughness

 

The link to telescope optics.net goes further into other aberrations and their effect on Strehl. 


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#9 Fomalhaut

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Posted 20 January 2019 - 04:47 AM

Caution: Strehl (measured over one specific wavelength only) should not be mixed up with Polystrehl (PS), the latter of which is (better measured than) calculated over different wavelengths.

So, while Strehl just informs on accuracy of optics in one wavelength, PS also does on overall chromatic correction.


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#10 starman876

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Posted 20 January 2019 - 11:26 AM

You got to love these educational threadswaytogo.gif



#11 Vla

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Posted 20 January 2019 - 11:29 AM

What comes first is, obviously, the question is how accurate is the Strehl given. It may not be, for various reasons. It can be given as the design Strehl, as opposed to one obtained from actual measurement, etc. As for the effect of roughness, microripple are negligible for general observing, but larger scale roughness can be significant. Illustration is on these graphs (bottom), which show that it potentially can degrade Strehl down to 0.6. The choice of scale is somewhat arbitrary, and the applied equation is for "statistical" roughness, assumed to cover the entire surface uniformly, which is the worst case scenario. Although the graph gives impression that the contrast drop is the largest at low frequencies, considering the inherent slope of the MTF plot it is more like near uniform loss of contrast across the entire range.


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#12 John Huntley

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Posted 20 January 2019 - 06:17 PM

The concept of system strehl is interesting and seems to me more relevent to how a scope will actually perform:

 

https://astromart.co...em-strehl-ratio


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#13 CounterWeight

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Posted 21 January 2019 - 01:51 AM

To me the main point of any Strehl measurement, is to have insight into how it was performed.  This requires a significant knowledge of not only optics but metrology.

 

Critical to me is that 'Strehl' does not equal a 'standard'.  You cannot equate company A figured Strehl to Company B figured Strehl even if using poly Strehl. 

 

I am not saying it is useless or meaningless, it's a meaningful metric (among several possible) just that you cannot say Strehl and assume that it means the same thing everywhere.  That is a gross concept error. For me, unscientific. For it to have a verifiable scientific meaning I should be able to measure it anywhere in the world and come up with same or reasonably close result.

 

 

I'd want to know at what point do certain issues show up and how, there you need to know how many samples were taken to compute the Strehl and their specific location.  So all lenses would have to have a TDC marker!, as well as the lens cell!  What is the difference between 100 samples and 1000 samples for an area?  Are there critical points where issues appear or just inflections in a gauss distribution?  What differentiates A from B or C?  What body of research validates the method?

 

The science is sound, and I'd love to see a NIST standard as to how it is measured and what I could reasonably expect it show in terms of optical production flaws.

 

Right now, it to me is sort of the Strehl 'wild west'.  This is not to throw shade on anyone doing it!  I applaud them as they are trying to provide the end user with a diagnostic report (plot or matrix or both)  that represents a certain optical quality relating to those specific measured parameters.



#14 Asbytec

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Posted 21 January 2019 - 06:52 AM

"One of the most frequently used optical terms in both, professional and amateur circles is the Strehl ratio. It is the simplest meaningful way of expressing the effect of wavefront aberrations on image quality. By definition, Strehl ratio - introduced by the German physicist, mathematician and astronomer Dr. Karl Strehl at the end of 19th century - is the ratio of peak diffraction intensities of an aberrated vs. perfect wavefront. The ratio indicates the level of image quality in the presence of wavefront aberrations..."

 

"...expressing vital property of the single most important optical indicator, the PSF, building stone of nearly all intensity distribution forms..."

 

"Wavefront deviations from perfect spherical are directly related to the size of phase errors at all points of wave interference that form diffraction pattern. In other words, it is a nominal wavefront deviation from spherical that determines the change in pattern's intensity distribution."

 

"It is the root-mean-square, or RMS wavefront error, which expresses the deviation averaged over the entire wavefront. This average wavefront deviation determines the peak intensity of diffraction pattern and, hence, numerical value of the Strehl ratio (note that the RMS error itself is accurately representing the magnitude of wavefront deviation only when it is affecting relatively large wavefront area, which is generally the case with the conic surface aberrations)..."

 

"For relatively small errors - roughly 0.15 wave RMS, and smaller - the RMS wavefront error, and the resulting Strehl ratio, accurately reflect the effect of overall change in energy distribution, regardless of the type of aberration. With larger errors, the correlation between the RMS error and the Strehl vanishes..."

 

"As a general rule for aberrations below 0.15 wave RMS, the relative drop in peak diffraction intensity indicates how much of the energy is lost, relatively, from the Airy disc."

 

https://www.telescop....net/Strehl.htm

 

My simplified take on Strehl is derived from the above. 

 

There may be no actual standard and different ways to measure Strehl, both mono and ploy chromatic, there are many factors that give us cause. However, every telescope will have a Strehl of some measure even if we do not know what it is. It is related to the peak diffraction intensity of an actual aberrant wavefront Airy disc to that of a perfect aperture (which we do know). Diffraction at the aperture is unavoidable and known, and therefore can be factored out. Diffraction effects can be increased with an obstruction. To my understanding, the Strehl ratio is not affected by added obstruction diffraction or shading other than blocking the central zone from measurement of any wavefront deviation.

 

Whatever the Strehl, what seems to be implied is an intensity distribution from the central disc to the diffraction rings due to aberration. The central peak intensity is reduced, and the surrounding ring intensity is increased. This causes a loss of contrast on small scales near the first diffraction ring and slightly beyond, and quickly normalizing at larger scales. The intensity distribution to the diffraction rings is increasingly detrimental to contrast performance on small scale planetary detail (and tight double stars) as aberration increases. Thus, small scale planetary resolution is reduced but not the Rayleigh and Dawes resolution limits. 

 

An obstruction also compounds matters by further redistributing light from the Airy disc to the rings through added diffraction changing the way the waves interact in phase. Obstruction shading has no affect on the intensity distribution, however. Theoretically, the obstruction changes the pattern of diffraction, and it /may/ cause an increase in performance at high spatial frequencies near the angular diameter of the Airy disc. (In practice, I find this tiny realm very difficult to observe even in excellent lab-like seeing. I have tried to see this theory in action and failed. smile.gif )

 

I understand Strehl to be a measure of peak diffraction intensity of an aberrant system, and it already factors in the necessary and unavoidable loss of intensity due to diffraction at the aperture. Some argue the same should apply to the peak diffraction intensity including the obstructed (negative) aperture, which is less than the maximum 83.8% light in the central disc. This offers a way to compare relative performance between obstructed and unobstructed types, which is nice to know if this is what we want to do, but it looses it's beauty of speaking to performance due to aberration alone. 


Edited by Asbytec, 21 January 2019 - 06:57 AM.

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#15 Vla

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Posted 21 January 2019 - 09:53 AM

The concept of system strehl is interesting and seems to me more relevent to how a scope will actually perform:

 

https://astromart.co...em-strehl-ratio

It may be tempting to have a telescope optical quality expressed in a single all-inclusive number, but it cannot be called "Strehl". Strehl is defined as the relative normalized peak diffraction intensity of aberrated vs. aberration-free aperture, and as such strictly relates to wavefront deformation. Its purpose is to indicate the effect of wavefront deformation on image contrast. Light transmission does not affect image contrast, and central obstruction does it in a different way than wavefront deformations (it significantly shrinks the central maxima, which actually improves contrast at high frequencies, as well as the resolution limit). System Strehl is a very valid concept, as long as it limits to all aberration sources. Obstructions - and certainly light transmission - should be kept out of it.

 

As an illustration, let's look at 1/4 wave of spherical aberration vs. 33% c.obstruction. According to their peak diffraction intensity they should be similar in effect. Their actual MTF look like this. The obstructed aperture has nearly 10% smaller central maxima, linearly, which by as much ups its limiting resolution, and also compensates for the energy lost, so its average brightness remains nearly unchanged, unlike the case with spherical aberration (hence the contrast increase). Other aberration will have different plots than SA, but none will improve neither contrast (over perfect aperture), nor resolution limit.

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#16 Asbytec

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Posted 21 January 2019 - 10:32 AM

I like to think of performance as the final intensity of the central peak on the focal plane of the system which includes aberration and diffraction effects, including added diffraction of an obstruction. Not Strehl alone, but both Strehl and added diffraction combined. To me, this is a very important single number to consider. It's hard to observe the boost of resolution near maximum spatial frequencies. 


Edited by Asbytec, 21 January 2019 - 10:34 AM.


#17 Vla

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Posted 21 January 2019 - 10:52 PM

Norme, I do the same for getting the idea of where it is in the ball park, but it is not the Strehl, and it is not really accurate - which should be even worse than inaccurate Strehl. For instance, if you have 1/4 wave p-v of SA and 33% obstruction, you'd multiply 0.80 and 0.79 which gives you 0.63. But the actual encircled energy - i.e. Strehl - is 0.69, and the difference is not negligible. That is because obstruction diminishes the aberrations, and that is another thing I didn't even mentioned in the previous post. Suiter gives an example of an aperture with 1/2 wave p-v of SA, which has more encircled energy (44%) with 50% obstruction (matter of fact, with any obstruction) than unobstructed (p198, 1st ed). Sure, the lower aberration level and c. obstruction, the less inaccurate it gets treating obstruction as aberration, but where do you draw the line? Simplicity is nice, but not so much when it comes at a price. For the accurate picture of optical quality, obstruction and aberrations should be looked at as something different, because it's what they are.


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#18 Asbytec

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Posted 22 January 2019 - 03:09 AM

I agree with simplicity in terms of measure and concept is nice. Accuracy and being easily knowable would be very nice. But...

Just when discussing Strehl as a performance measure, presumably of the primary objective, there is more to consider as you, et al, have shown. Especially with an obstruction. It's not really the Strehl that matters, it's the final imaging quality of the system.

When it boils down to it, seeing effects, etc, matter, too. But, the final Strehl-like peak intensity is a good baseline to speak about the quality of the image. Even if we don't know what its value is, at least we can speak to the concept between different types and varying quality.

Edited by Asbytec, 22 January 2019 - 03:12 AM.


#19 Vla

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Posted 22 January 2019 - 09:46 AM

Knowing what we know, it is better to use 1-c^2 as the c.o. PSF degradation factor instead of the formal (1-c^2)^2, where "c" is the linear obstruction diameter as a fraction of aperture. That is still approximation, but more realistic. In the same example, 1/4 wave and 33% obstruction, it would give a combined PSF peak 0.72, which is half as far from the actual encircled energy, and on the plus side, where it is generally supposed to be considering contrast increase at the high frequency end and increase in limiting resolution (which can't be directly compared, being qualitatively different, but do represent real gain). Fact that obstructed (mirror) telescopes have other problems, like four times higher sensitivity to surface errors, requiring higher fabrication standard, scatter from reflective coatings, more of thermal and seeing problems (being generally larger), and some others, which would often make the (1-c^2)^2 factor seem more realistic, even optimistic, shouldn't be the reason to use it. You want to know where the problems actually come from, instead of having them all disguised under "c. obstruction effect".


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#20 Jeff B

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Posted 22 January 2019 - 11:02 AM

Knowing what we know, it is better to use 1-c^2 as the c.o. PSF degradation factor instead of the formal (1-c^2)^2, where "c" is the linear obstruction diameter as a fraction of aperture. That is still approximation, but more realistic. In the same example, 1/4 wave and 33% obstruction, it would give a combined PSF peak 0.72, which is half as far from the actual encircled energy, and on the plus side, where it is generally supposed to be considering contrast increase at the high frequency end and increase in limiting resolution (which can't be directly compared, being qualitatively different, but do represent real gain). Fact that obstructed (mirror) telescopes have other problems, like four times higher sensitivity to surface errors, requiring higher fabrication standard, scatter from reflective coatings, more of thermal and seeing problems (being generally larger), and some others, which would often make the (1-c^2)^2 factor seem more realistic, even optimistic, shouldn't be the reason to use it. You want to know where the problems actually come from, instead of having them all disguised under "c. obstruction effect".

Well said Vla. 

 

The points in bold have been made very clear to me visually when comparing my TEC 200ED to my CZ 11" F7.2 newt system.  The CZ mirror is outstanding and smoooth with a 16% of the diameter central obstruction and a conventional spider.  However, despite the obvious differences between them in brightness, they are very close to each other in sharpness and that subjective "contrast" thing.  

 

I can also vouch about the point of surface smoothness.  A case in point is my CFF 160 F6.5.  In DPAC at focus, I can see the signs of the hand figuring of the aspheric applied as a uniform texture to the surface.  However, the spherical corrections in green, blue, and red, are very good and I can detect no differences in their focal positions either.  Importantly, the scope gives sharp, low scatter images at high power.  The strehl quoted on the test report is ~.98.  


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#21 Asbytec

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Posted 22 January 2019 - 08:59 PM

Knowing what we know, it is better to use 1-c^2 as the c.o. PSF degradation factor instead of the formal (1-c^2)^2, where "c" is the linear obstruction diameter as a fraction of aperture. That is still approximation, but more realistic. In the same example, 1/4 wave and 33% obstruction, it would give a combined PSF peak 0.72, which is half as far from the actual encircled energy, and on the plus side, where it is generally supposed to be considering contrast increase at the high frequency end and increase in limiting resolution (which can't be directly compared, being qualitatively different, but do represent real gain).

 

Fact that obstructed (mirror) telescopes have other problems, like four times higher sensitivity to surface errors, requiring higher fabrication standard, scatter from reflective coatings, more of thermal and seeing problems (being generally larger), and some others, which would often make the (1-c^2)^2 factor seem more realistic, even optimistic, shouldn't be the reason to use it. You want to know where the problems actually come from, instead of having them all disguised under "c. obstruction effect".

Yea, great point. It's impossible to know what the exact figures are without a trusted system IF, having a report on the primary alone, star testing, or by simply looking in the eyepiece. We want to dim (or maybe increase) the central peak a little more to compensate for things we do not really know including the narrowing of the peak and the resulting slight increase in height. 

 

You're right, we do not want to include shading effects of the obstruction in trying to estimate any Strehl-like performance. But, if it serves as an approximation, that's better than we can do with a single bit or no information. Folks like to compare our instruments and our views which often include variances of the observer as well as local seeing conditions and just about everything else. I believe we can do it in a relative way, holding all else equal, even if actual performance is different than the equation might express.

 

When you crunch the numbers, the result does /seem/ a bit optimistic. Sometimes it seems like a small miracle we can see anything at all as well as we do. 


Edited by Asbytec, 22 January 2019 - 09:01 PM.

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#22 John J. Hudak

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Posted 16 January 2021 - 04:39 PM

I like the notion of the Strehl ratio. From Wikipedia -"The Strehl ratio, S, is frequently defined as the ratio of the peak aberrated image intensity from a point source compared to the maximum attainable intensity using an ideal optical system limited only by diffraction over the system's aperture." From https://www.astronom...olvingpower.htm - A “perfect” telescope has 84% of the starlight in the said Airy disk and 16% in the rings - and it is impossible for more light [than this] to go into the disk.

 

We do need a meaningful figure of merit for the quality of images that can be produced by telescope optical systems. The discussions in this thread point out that a number of defects that are not at all related to aberrations can degrade the actual strehl ratio: surface roughness, surface ripples, turned down edges etc. I think I agree.

 

It seems like we could use a "bench top" method that could measure the ratio of how much light is in the central peak vs the rings for a telescope system, not just its primary. We would also need methods for measuring its resolving power in line pairs per millimeter as discussed in https://www.astronom...olvingpower.htm

 

Can someone point out how to perform these measurements?




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