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CO vs. All That "Other Stuff"!

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#26 Asbytec

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Posted 09 January 2013 - 06:20 AM

Jon, that was my impression, as well, the visible spurious disc being smaller due to evacuated energy. Turns out, the actual Airy disc, itself, is a bit brighter than it would otherwise be. This is because it, indeed, is smaller in an obstructed scope, as I read it (link below.)

There is more energy in the rings, but the added diffraction changes the radius of the first minimum a tiny bit from 1.22 to 1.11 for CO = 0.3D. The resulting Airy disc is both smaller and a bit brighter that it would be at 1.22 Lambda/D. This is what gives that kick to the MTF curve beyond the performance of the unobstructed aperture at very high frequencies: a smaller Airy disc.

"The reason is the effect unique to CO (at least in its extent), namely, the reduction in size of the Airy disc caused by it."

http://www.telescope...obstruction.htm

#27 DesertRat

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Posted 09 January 2013 - 07:27 AM

Here is an animation of a PSF with obstructions of 0, 0.33 and 0.5. It hints at what you are referring to. Its difficult to display the visual appearance well, I just used a gamma of 2.0 to display the rings a little better. The visual or eyeball response is actually quite complicated being nonlinear as well as color dependent (and several other issues).

Glenn

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#28 Asbytec

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Posted 09 January 2013 - 09:19 AM

Thanks, Glenn.

Frank, I reduced the size of my obstruction by 10mm (from 52/140 - effective aperture to 42/150 at full aperture.) The most immediate improvement seen was on the visible rings and reduced diffraction effects on the moon. It took weeks or more to begin to realize Jupiter might actually be better, as well. Planetary improvement was just not instantly obvious.

As you make clear, observing is complicated. I do not know how to bias focus for mid range contrast - maybe smallest blur? If that happens, it does so by accident because it looks like best focus. I just focus at whatever power so the image is crisp or stars show best focus patterns.

Of course, you are correct. Models like MTF, while valid on a scientific level, are never complete. They are meant to illustrate concepts and it is up to us to explore them in all their complexity. They allow us to explore or compare one or two variable against two samples and make general statements. Generally we can say things like, all things held constant or negligible, this should do that. Throw in some seeing and it all goes to pot because we've changed the initial conditions.

#29 maknewtnut

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Posted 09 January 2013 - 11:00 AM

I believe many who frequently calculate area (often in comparison of obstructed vs unobstructed systems) are often incorrect as well. It's often seen that CO area is subtracted from apeture, and then resolution determined based on the result.

It seems to be a common mistake when attempting to do the same with a Maksutov. For example...since the radius of curvature on a Mak corrector is rather 'steep', we must remember that such a lens diverges incoming light. As a result, even axial rays might not be blocked even when a secondary baffle is larger than the secondary mirror (incuding those that are tapered just for that reason).

#30 Darren Drake

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Posted 09 January 2013 - 01:29 PM

Wow there certainly is a lot of info here in this thread. I would like to see a real world comparison to see if reality matches theory. Is someone out there with a premium apo and an identical aperture mak or good sct able to place an artificial obstruction of the same % in front of the apo lens and do a detailed comparison? This would be an apples to apples comparison and reveal if the cass is optically on par with the apo in every way except obstruction. I may try this myself sometime. I have a good buddy who just had first light last night with a newly acquired 6 inch AP superplanetary and I was there and may go back again tonight.

#31 Joe Cepleur

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Posted 09 January 2013 - 01:58 PM

I love reading about this sort of thing, and I try to learn what I can. The subject is so complicated and my budget so limited, that I'm glad Ed's theory is an ultimate truth for me:

Practically speaking, from my experience as a casual observer with MCT, SCT and achromatic refractor, I wish an instrument's intrinsic limitations were the only obstacle to a good view. Usually seeing (high level and local) is the most significant barrier to obtaining a detailed view. I've been careful to accumulate each of my scopes on a modest budget. If one keeps that factor in mind, the views through a sub $300 Maksutov or circa $400 C8 are astounding value, and show me far more than the 6" APO that I don't and won't own. They are also easy to mount for visual use. That these instruments are often considered as a "runner up" is a shame - a well tuned catadioptric scope with good optics can be a powerful tool. Rather like my MGB providing an excellent and fun drive, despite it not being an E Type Jaguar...


That said, another thread describes Orion61's refurbishing of my formerly salt-encrusted C8. We know the optics are not perfect, because we mixed one scope's good mirrors with another scope's good corrector. Still, I'm betting that because the parts were made with good precision to begin with and, more importantly, Larry will align all the parts as perfectly as is humanly possible, the scope should work pretty well, at least at lower powers. That's a good deal if one enjoys saving classic scopes, and a clear illustration of the importance of assembling everything precisely. He's not finished yet. Stay tuned! Low budget, 30% obstructed, classic C8 coming back to life!

My sense of obstructions is that, in exchange for a complicated set of problems, one buys also the offsetting larger aperture and smaller tube. Tremendous resolution there. Not quite the same brightness as an unobstructed scope, but it's easy to make that up in increased aperture. Whatever problems with contrast similarly vanish into the larger aperture (if one's taste says they do!), and all this requires a smaller mount to keep it steady. This makes astronomy affordable and portable. A 6" refractor is a wonder, if one can afford one, but is it really radically better than a much larger obstructed scope? I'm not trying to start flame wars. I'm only commenting that I can't afford to answer that question, and am happy with an old C8!

#32 DesertRat

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Posted 09 January 2013 - 03:12 PM

Norme wrote:

I do not know how to bias focus for mid range contrast - maybe smallest blur?



For a good scope, either sign of defocus drops contrast all along the MTF but especially at the mid range.

For a scope with spherical aberration however, you can defocus a small amount to tease details at the high end. But when that is done the mid level details suffer badly. An example: for a scope with spherical undercorrection a small amount of defocus (a fraction of a wave) inside will enhance details at the limit of resolution. See attached MTF.

Glenn

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#33 GlennLeDrew

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Posted 09 January 2013 - 08:41 PM

Frank,
Your noting the difference between looking at a picture of Jupiter on a wall as you vary your viewing distance vs its telescopic appearance while varying the magnification is not surprising. In the first case, your eye's pupil is (more or less) constant, and so both diffractive effects and surface brightness do not vary. But at the eyepiece, changing magnification profoundly affects the visible extent/impact of diffraction/aberrations, as well as the image surface brightness (not to mention atmospheric seeing.)

A better comparison would result if:

- The picture was printed at low resolution so that at the distance from which it subtends an angle of several degrees it reveals the degradation, and,
- At each halving of viewing distance the illumination source intensity is reduced to 1/4.

#34 Asbytec

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Posted 09 January 2013 - 10:52 PM

Glenn, that's interesting. So, -defocus is toward marginal focus? So, your finding best focus. Then +defocus is away from marginal focus toward paraxial focus finding the smallest blur? (or do I have the sign reversed?)

Gotta pay attention to that, I wonder if one does so automatically depending on the magnification or the target.

#35 DesertRat

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Posted 10 January 2013 - 12:52 AM

Norme, thanks!

The signs you have are correct for spherical undercorrection. They would swap places (as do the paraxial and marginal points) in the case of overcorrection.

In a scope with very good correction any defocus is going to degrade contrast transfer all across the board. So if you have a good scope as it seems from your reports, I'd be surprised if you could see this effect. In really good seeing while imaging I can see defocus errors of as little as 1/10 wave. Either way the image starts blurring similarly. Imaging with a ccd does not forgive defocus as it has no accomadation properties as our eyes do.

Glenn

#36 freestar8n

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Posted 10 January 2013 - 04:33 AM

Hi GlennLeDrew-

Yes, I'm aware the brightness has an effect, but I don't think it explains everything since I see such differences even between eyepieces at the same mag. And even if it is related to brightness, it means MTF alone doesn't describe the impact of CO - and it gets to my point about optimally setting defocus to match the current mag. and intentionally alter the MTF.

Overall I'm saying it's a complex system and not easily explained or described - so it's hard to predict the role of CO, and it's hard to explain a preference of refractor over SCT, for example, strictly as resulting from CO. And MTF of the OTA by itself is not a complete description of the experience at the eyepiece.

Frank

#37 freestar8n

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Posted 10 January 2013 - 04:41 AM

Hi Glenn/DesertRat-

I notice in your plot legend that you describe one line as being 1/4 wave SA, and the others being SA plus defocus. How would you label those other lines in terms of the amount of SA they contain? Normally I would say they all have about 1 wave of SA, and varying amounts of defocus. This conveys the point that there is an inherent defect in the OTA that results in 1 wave of SA - always - and you can play with defocus to alter the P-V and RMS - and MTF - to partially correct for it.

If you had 1 wave of coma, you would get no similar benefit from defocus, in terms of reducing the RMS wavefront error. But spherical and astigmatism can be partly cancelled by defocus.

Also - what software did you use to make that plot? I'm interested in what convention is uses.

Thanks,
Frank

#38 Eddgie

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Posted 10 January 2013 - 09:43 AM

I'm saying it's a complex system and not easily explained or described.



I agree 100%. It is very complex.

MTF plotting gives an exact result for one specific case, which is sinosodial 100% contrast lines varying in frequency from 1 line pair per millimeter at the focal plane to the maximum linear resolution at the focal plane.

For example, any two f/10 scopes have linear resolution of about 182 line pair per millimeter at the focal plane. It does not matter about the aperture, though while both a 4" f/10 telescope and an 8" f/10 telescope both have 182 line pair resolving power, an extended target will appear twice as large (half the frequency) in the 8" scope.

But the point here is that almost none of the detail we view consists of alternating black and white sinosodial lines.

While a line extends to either side/end of the focal plane, a lot of extended object detail consists of splotchs, curves, and other non-geometric shapes.

While a black line on a white background is narrowed only form the sides by diffraction. Suppose you had a dark "Peanut" shaped feature on Jupiter.

A bigger scope with better contrast transfer might show this "Peanut" to be exactly what it appears to be. But the smaller scope might show only the ends as small ovals because the contrast loss might cause the "Waist" of the peanut to disappear, severing the ends. Two observers using two different scopes with different contrast transfer... one reports seeing a "Peanut" shaped feature, the other reports seeing two teardrop shaped features with the tails pointing to one another!

A recent thread in the Solar System forum dealt with how some observers saw Io as distinctly oval, while I (using at larger scope with better contrast transfer) saw it as distintly round.

It is an excellent thread that is a textbook case for how MTF works. Different observers using scopes with different levels of contrast transfer, all seeing something different.
. And MTF theory explained it exactly. There are even some CAD drawings in the tread that show this. It is a great story with some historical figures playing an interesting role, as some great observers of the past also saw the same thing and reported seeing Io as being oval!

In general, I think that MTF though does a pretty good job of desribing how contrast is transferred, but as you say, it is extremly complex.

And while I think that the 1/4th wave = 30% obsstruction slightly overstates the damage (especially at the high frequencies), I do not at all dispute that a big obstruction lowers contrast.

But a bigger aperture puts it back.. LOL.

And this has been my own message for a long time. From my own experience, given reasonable optical quality, the biggest differentiator on extended object performance has been clear aperture. In just about every scope I have owned or used, the more clear aperture, the better view extened targets I have had.

I pretty much simplify it to that level because as a general rule, it matched my own experience. If two scopes plot similarly in MTF in the low and mid-frequency part of the spectrum, for visual use, the amount of detail visible has been similar.

This does though ignore the brightness/scale advantage that the larger aperture always has, which can offset a little contast loss simply becuase the image for a given magnificaiton is much brighter. I personally find that brightness makes the lowest contrast detail easier to see, especially as the magnification gets higher and the exit pupil in the smaller aperture gets below about 1mm.

#39 Joe Cepleur

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Posted 10 January 2013 - 10:25 AM

This does though ignore the brightness/scale advantage that the larger aperture always has, which can offset a little contrast loss simply because the image for a given magnification is much brighter. I personally find that brightness makes the lowest contrast detail easier to see, especially as the magnification gets higher and the exit pupil in the smaller aperture gets below about 1mm.


I thought that "contrast" was simply the difference between the brightest and darkest parts of an image. Lower the contrast on a zebra, and he eventually looks solid gray. If contrast were indeed tied to brightness, then clear aperture would be its most important determinant. A large aperture with a large obstruction might have the same clear aperture as a smaller instrument with a smaller or no obstruction, for equal brightness. I know that, with an obstruction, diffraction effects also blur the image a bit, further reducing contrast as details become too fuzzy to see. Reading all the complexities described in this thread, I have to wonder, is my understanding of the basic relationship between contrast and brightness correct?

I know I'm in over my head here, but that's how I learn. I research topics I don't know. I'm currently working on "Modulation Transfer Function," but fear it may be time to revisit the seemingly basic notion of "contrast!"

#40 DesertRat

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Posted 10 January 2013 - 02:47 PM

Joe,

Contrast is not just the difference between the brightest and darkest part of an image.

I think what people are referring to above has to do with the properties of the human visual system. It is not a linear system, so the mean level of brightness, the size of the exit pupil, magnification and many other things come into the picture.

It is a complicated problem. In your reading get hold of the definition of intensity, contrast (there are several) and gamma, and explore the visual system. That is if you want to.

You might start here:
http://en.wikipedia....ntrast_(vision)

Glenn

#41 DesertRat

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Posted 10 January 2013 - 02:52 PM

Frank,

The graph depicts 0.075wv rms low order spherical in each case. Not exactly 1/4wv PTV but close enough for depicting what happens. I could provide a graph with exactly 1/4wv PTV levels, but it would not show anything new. In my code I always input aberration levels as rms figures, but can force them to be the classic breakpoints.

The software is homebrewed with elements begged and borrowed, and under a constant state of development. I use it for example in creating aberrated PSF's used in deconvolution and for work I'm currently doing in digital microscopy. It has created high fidelity fresnel zone plates, as well as propagated wavefronts in the near and far fields. I've verified its accuracy with respect to almost exact solutions and on an optical bench. In my code I can focus on a speciman at different depths from a digitally captured hologram. For the PSF animation above I used a 2dfft size 4096x4096, you'll note how smooth the PSF appears there, it was not resampled. It shows a scope of 14" aperture operating at an efl of 10m in red light, and presents the PSF at approx 43 pixels per arcsecond. The code is working well at a number of levels, and I have a high confidence level in its power.

The conventions it uses are classical. Sorry. When I say an optic has 1/4wv PTV I'm using the classical idea of an optical path differenced from a gaussian sphere (albeit shifted) that would focus to a point. At this level the strehl is approximately 0.8. I do have Zernike code in development, mostly for depicting color coded wavefronts and interferograms in a graphical manner similar to some commercial programs.

In this forum I think it best to keep to conventional and classic descriptions of wavefront error. For a test scenario, call up an optician and say you want a mirror better than 1 wave.

Finally, it is true in the world of coherent imaging the MTF is never even calculated. It would'nt make sense. There you can have a complex multidimensional PSF and the transfer function is a full bodied OTF. Obviously in those circumstances phase plays a big part, in backyard astronomy not so much.

If you have a better way to graphically depict the effect of a CO please show us. A picture in this case really is better than a thousand words.


Everybody,

Astigmatism is different in how its responds to defocus in a practical sense. Since a real object like a planetary surface has structures with both horizontal and vertical components you might enhance one over the other. For imaging however, unless you use a non circularly symmetric kernel in a wavelet or for decon the results will dissapoint.

The basic point is that for a good telescope defocus is not a useful technique to tease out detail. You will be focussing anyway as you chase seeing and temperature effects. So in that case if you are seeing something better you have achieved best focus for that moment. A scope with significant aberrations is another story. CO is not an aberration, it only defines the entrance pupil, which could be any shape really.

The MTF is one of the best ways to depict what happens with a CO. I don't know of a better way to demonstrate the CO effect in a graphical presentation. One could show an idealized planetary surface with varying amounts of CO, its easy to do the calculations but its not easy to capture the real visual effect.

Glenn

#42 Alph

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Posted 10 January 2013 - 03:48 PM

The MTF is one of the best ways to depict what happens with a CO. I don't know of a better way to demonstrate the CO effect in a graphical presentation

I would say that the MTF depicts some aspects of diffraction quite well. How does the MTF relate to what we can really see/resolve is a different story. Unfortunately the MTF requires extensive knowledge of complex complex math. I am not sure how many folks who discuss so passionately MTF on this forum have that knowledge. The most telling statement on the effects of central obstruction is the Meade's decision to discontinue the f/10 SCTs.

#43 DesertRat

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Posted 10 January 2013 - 04:25 PM

Alph,
Good point. As said earlier CO effects are often grossly overstated or the reverse in some cases.

How to understand and interpret the MTF is described in Suiter as well as countless sites dealing with photography. But anyone with a high school educaton can derive value from it, which is the level of the Suiter book.

Glenn

#44 Alph

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Posted 10 January 2013 - 04:37 PM

How to understand and interpret the MTF is described in Suiter as well as countless sites dealing with photography.


To fully understand the MTF, you need to know a lot, otherwise you are taking it at face value as many folks on this forum do. The required math skills are well above high school level. The rigorous treatment is well above Engineer's math level. It is not a simple arithmetic or basic calculus.

#45 DesertRat

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Posted 10 January 2013 - 05:16 PM

To fully understand the MTF ...



I never said fully!

Agreed the MTF should not be taken at face value. The sum total of what has been written about it here and other threads helps some. It is advisable to read Suiter or another source to understand it better. Its not perfect, but few things are. I don't believe I have seen a MTF here or in those other threads which convey invalid information.

To generate a MTF is not difficult, it involves creating an optical transfer function and calculating its effect on an idealized sequence. These operations involve transforms, but the whole thing can be done in a single page of script. Most engineers I've worked with do understand that level of math. But you don't need to know the details of how it is generated to derive some value from it.

If you or someone has a better way to relate this information let us know.

Or perform an experiment. Add an obstruction to a refractor or increase an existing obstruction and see its effect.

Glenn

#46 cn register 5

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Posted 10 January 2013 - 05:41 PM

I'd like to see some "blind" experiments done where the person evaluating the image does not know if the scope has an obstruction, or how big it is.

I think that may be difficult to manage because as soon as you defocus the obstruction - or lack - is obvious. Maybe someone else has to focus and the evaluator only sees in focus images.

Chris

#47 DesertRat

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Posted 10 January 2013 - 05:52 PM

Its not easy to evaluate CO experimentally, visually anyway.

The biggest problem with a largish obstruction for novices is placement of the eye at low powers.

We'll keep this thread going until we're sick of it. And come back later and the same issue will be under review!

Glenn

#48 Joe Cepleur

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Posted 11 January 2013 - 05:37 PM

Joe,

Contrast is not just the difference between the brightest and darkest part of an image.

I think what people are referring to above has to do with the properties of the human visual system. It is not a linear system, so the mean level of brightness, the size of the exit pupil, magnification and many other things come into the picture.

It is a complicated problem. In your reading get hold of the definition of intensity, contrast (there are several) and gamma, and explore the visual system. That is if you want to.

You might start here:
http://en.wikipedia....ntrast_(vision)

Glenn


Thanks, Glenn;

I've begun. Looks as though I have my work cut out. It's astonishing how complex this all is, if one studies it in detail. I'm intrigued with the notion that different images, even sections of images with different frequencies of light or differently sized details, all can respond differently.

I suppose we study this sort of topic partly for the pleasure of understanding, and partly for its predictive powers? Presumably, if one understands these details well, one could imagine what kind of scope might be well suited to viewing a particular object, or might be a wise modification or purchase when upgrading.

#49 Starman1

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Posted 11 January 2013 - 06:27 PM

When I first bought an SCT and left it outside in the shade on my roof for several hours, I started the night with a completely cooled scope at ambient temperature.
The scope had also just been collimated.
The seeing that night was exceptionally good.

The first image I had (at about 100X), the stars were all tiny little round points with a single diffraction ring. At 200X, the images were the same.
A few years later, after never having been able to duplicate that night, I finally got an SCT Cooler from Lymax. It made a profound difference in star image quality. I was back to the tiny stars on good nights.

I look through SCTs all the time where I observe (there are a lot of owners), and not 1 in 10 is collimated or even close to being cooled down.
I know from personal experience that the central obstruction isn't the biggest factor damaging good images. Nights with a properly cooled and collimated 8" SCT taught me that.

But if, in the field, only 1 in 10 users will ever think about cooling or collimation, is it any wonder this type of scope has a reputation for mushy optics? And refractors are considered superior, even in smaller sizes?

I have a Gregory-Maksutov Cassegrain, and I have learned a lot about cool-down from that instrument. Pretty much the ONLY way that instrument has good star images is if it's allowed to cool. I set it out, in the shade, 3-4 hours before I'm going to start observing. And when I do start observing, the images are excellent for the aperture. I think that 5" Mak takes as long as an 8" SCT to cool down.

So what's my point? SCT owners should worry less--a lot less--about the size of the secondary mirrors, and a lot MORE about cooling and collimation. Because, when everything is right, even the run of the mill scope does pretty darn well with image quality. If the larger secondary obstruction really damages the images (and I'm sure it does some)
it's a pittance compared to other factors.

#50 freestar8n

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Posted 12 January 2013 - 06:23 AM

OK - I asked about the software because I was looking for someone else who uses your convention - but if it's your own code then it makes sense to follow your convention. I don't think I can change your mind - but I will just say that my use of "1 wave of spherical aberration at minimum rms focus results in a Strehl of 0.8" is consistent both with classical aberration theory and every text on the subject I know - except for Suiter. I regard spherical aberration as an intrinsic flaw in the wavefront that has a well-defined quantity specified by the p^4 term, regardless of reference sphere, and when you combine it with varying amounts of defocus, you get different Strehl and MTF. But at this point I have no doubt you prefer Suiter's description.

If you buy a telescope that has a Strehl of 0.8, it probably has a combination of aberrations that includes both 3rd and 5th order spherical. But if the only aberration is 3rd order spherical, then it could be 1 wave and still work well - because a change in focus reduces its impact by a factor of four.

Regarding MTF and what is better - well my main point is that it is limited and misleading in a visual context. MTF is used in professional imaging and design, but that usually involves linear detectors rather than the eye. And there is virtually no professional astronomy done by staring into an eyepiece anymore, so visual performance wouldn't be published much.

I did look at Rutten/van Venrooij and was surprised that they do go into detail on the changing role of the visual system on the overall MTF. Just looking at a single MTF and leaving out the additional MTF of the detection process is an incomplete description - yet many of these threads imply MTF is rigorous and all-encompassing. It just isn't, but I would use it pedagogically to explain an actual observation at an eyepiece - i.e. I think it is ok to lead with an empirical result and use MTF to explain what's happening. But I would not use MTF in a predictive way to compare two systems - particularly if the object being studied is not specified.

I don't have strong feelings about the impact of CO, except I do adopt a more modern stance on optics/imaging that you need to specify the entire imaging system and what you are measuring before you can make a comparison. For certain double stars a CO may help - just as other apodizations with masks may help make the second star stand out.

Rutten/van Venrooij cite roughly 10-30% as historical values for how much can be tolerated in visual use. They also mention that based on contrast, 30% is approximately as bad as 1/4 wave wavefront error. But I view that as an amateur text, and it doesn't allude to the limitations and subtleties of MTF in a compound imaging system that a text on Fourier optics would.

Frank






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