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#1 JKoelman

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Posted 20 April 2013 - 08:24 AM

Contemplating all the posts here on contrast transfer, reflectors vs refractors, and obstructed vs unobstructed apertures, I decided to revisit chapter 18 in Rutten and Van Venrooij's "Telescope Optics, Evaluation and Design". This chapter is entitled "Resolution, Contrast, and Optimum Magnification". It dives into many interesting issues discussed here time and again - such as the effects of central obstructions on optical performance (Did you know that introducing a central obstruction in a diffraction limited optical system reduces its Airy disk?) and the combined effects of eye limitations, object contrast, and contrast transfer on visual performance.

One thing struck my attention: at the very end of the chapter Rutten and Van Venrooij discuss optimum magnification as function of aperture and introduce into this discussion the effects of object contrast and seeing conditions. They show a diagram on optimum magnification as function of aperture for various seeing conditions. For each seeing condition there is an optimum aperture that delivers the largest useful magnification. For instance, at bad seeing (scintillation or seeing disk width of 5 arc seconds) a 6" aperture delivers an optimum magnification of 100x. In contrast, apertures of about 3" max out at 70x, and the same applies to apertures of 12".

This surprises me. I always thought that despite limited seeing larger apertures never harm. At worst a larger aperture would deliver no better views than a smaller aperture. Yet, here it is stated that in terms of resolution a 6" can outperform a 12".

Any views?

#2 Cotts

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Posted 20 April 2013 - 09:58 AM

Johannes. I cannot envisage a situation where a 6" will out-resolve a 12", assuming equal optical quality. The smaller scope is less affected by seeing and will give views that seem more stable or pleasing*.

If the seeing is scintillating to 5" size (I have never seen seeing this bad in 50 years of observing, btw) both scopes will give terrible views on high-resolution targets like planets, the moon and double stars. As the seeing improves down towards 1" scintillation the 6-inch scope's image will appear to tighten up and be more stable while the 12-inch will still clearly show the fuzziness. If the seeing is smaller than the resolving power of the smaller scope then the 6-incher will operate at its resolution limit and give a very nice image while the 12-inch will still show the fuzz. If the seeing continues to improve below 1" the 12-inch will begin to show detail that the 6-inch cannot resolve.

The above paragraph relies on a mostly fictitious scenario - that seeing is constant when, in fact seeing varies from second to second, minute to minute and on longer timescales too. There are moments of excellent <0.5" seeing on many nights which are the moments that the 12-nch scope pounces on to the delight of its owner and which the owner of a 6-inch right beside won't even notice. It is these times that an experienced observer will wait for - often for hours - to get that glimpse with the finest details. If one observes Jupiter, e.g., for 10 minutes there is a significant chance the best moments will be missed by an observer so hasty.

* I have begun to despair about the use of this word which is often used by those with smaller scopes to imply that their scopes are somehow showing 'more' or 'better' views than the person with a larger scope right beside them. Many times my 3.1-inch refractor shows perfectly steady, motionless diffraction patterns while my 6-inch, at the same time, struggles with a wiggly, squirmy mess. But if we are looking at a 1.1" double star the 3.1-incher won't resolve it while the 6-inch shows a nice split during those moments of better seeing. There is no type or category of seeing where my 3.1 will resolve what my 6 will. But the view in the 3.1 is steady, stable motionless and textbook. Of an unresolved double star. (And, by extension to details on Jupiter, etc.) It is this that some call "pleasing".

Dave

#3 Jon Isaacs

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Posted 20 April 2013 - 12:31 PM

Any views?



Johannes:

Vlad (telescope-optics.net) has done some simulations that show similar results.

Dave's point that seeing is not a constant but rather variable is a good one, those moments when it all clears up, the larger scope can do it's stuff.

But also, look at the magnitude of the bad seeing.. Reading the curves on Page 218... 5 arc-seconds. That's horrible seeing. And yet, a 150mm scope still might be optimal.. For moderate seeing which they classify as a 2 arc-second, I see the peak at about 12.5 inches.

In any event, I am just glad I am not in a situation where I ever feel the need to try viewing the planets or split a double star under such poor conditions. If the seeing doesn't support the good high power views, which it generally does, I go fishing for something else. When the planets and double stars aren't biting, hopefully the DSO's are.

(By the way, it did not that a CO reduces the size of the Airy disk slightly, the energy transferred into the rings has to come from somewhere. The disk is dimmer, therefore slightly smaller, that energy is transferred into the rings which smears the image thus reducing fine scale contrast. Of course that's a small effect, the way to decrease the size of the Airy Disk and increase the contrast is to increase the aperture, CO or no CO. )

Jon

#4 jrbarnett

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Posted 20 April 2013 - 07:41 PM

Under seeing limited conditions it is a fairly routine occurrence that a larger scope cannot resolve severely unequal magnitudes multiple stars (Sirius A and B, Trapezium A through F, etc.) when a much smaller unobstructed scope can. It doesn't take a book or a graph to prove it. It takes a night in the field with both scopes. Seeing is believing. Aperture under some circumstances can be a LIABILITY. :grin:

- Jim

#5 chaoscosmos

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Posted 20 April 2013 - 08:20 PM

:gotpopcorn:

#6 amicus sidera

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Posted 20 April 2013 - 08:45 PM

* I have begun to despair about the use of this word which is often used by those with smaller scopes to imply that their scopes are somehow showing 'more' or 'better' views than the person with a larger scope right beside them. Many times my 3.1-inch refractor shows perfectly steady, motionless diffraction patterns while my 6-inch, at the same time, struggles with a wiggly, squirmy mess. But if we are looking at a 1.1" double star the 3.1-incher won't resolve it while the 6-inch shows a nice split during those moments of better seeing. There is no type or category of seeing where my 3.1 will resolve what my 6 will. But the view in the 3.1 is steady, stable motionless and textbook. Of an unresolved double star. (And, by extension to details on Jupiter, etc.) It is this that some call "pleasing".

Dave



I completely agree; whether the view is "pleasing" or not is a function of aesthetics, not formulae. Well-stated! :applause:

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#7 johnnyha

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Posted 20 April 2013 - 09:01 PM

Who can forget the glorious Questar ads?

"A second reason is the turbulent Earth atmosphere all telescopes must look through. In essence, when observing, you are usually looking through bubbles of disturbed air – microcells typically 4” in diameter in the layer of the atmosphere nearest the surface of the Earth. The image-blurring effect of these microcells is largely invisible as long as the column of light entering the telescope is smaller than the 4” diameter of the cells.

It was for just this reason that an aperture of 3.5” was chosen for the Questar. In average to mediocre seeing conditions, a 3.5” Questar will see through individual 4” microcells undisturbed, showing more detail than a larger scope that has to put up with the blurring of multiple turbulent cells."

It's so wonderful that the Questar is able to shoot perfectly through the center of an individual "microcell" - and astonishing that the microcell could track so perfectly along with the Questar! :lol:

#8 Jon Isaacs

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Posted 20 April 2013 - 09:08 PM

Under seeing limited conditions it is a fairly routine occurrence that a larger scope cannot resolve severely unequal magnitudes multiple stars (Sirius A and B, Trapezium A through F, etc.) when a much smaller unobstructed scope can.


I asked you this before, when was the last time you split Sirius B with an 80mm?

My experience is that when seeing poor, a large scope often out performs a small scope on widely unequal doubles. Rigel is a good example. When it first rises in fall and is low on the horizon, I am often unable to split it with my 80mm's. My old 12.5 inch picks out it ever time.

Jon

#9 BillP

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Posted 20 April 2013 - 09:09 PM

Seeing is believing. Aperture under some circumstances can be a LIABILITY. :grin:

- Jim


Agreed. More is not always better Not with telescope, or with anything else. Imagine thinking this and going rabbit hunting with a 30-06 :lol: With the vast range of targets, the tools that work the best will always vary...that is for both eyepiece and telescope.

#10 JKoelman

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Posted 21 April 2013 - 12:42 AM

Thanks all. My key question boils down to: can seeing render "aperture be a liability" (as Jim states) or is the effect of seeing limited to "aperture can be unhelpful"? I take away from this discussion that depending on the seeing conditions there indeed is an optimal aperture beyond which aperture becomes a liability, but that two effects conspire to render this hardly relevant in practice:

1) unless seeing is exceptionally poor, the optimum aperture is rather large (and certainly larger than typical refractor apertures)

2) the theory considers a time-averaged seeing disc. In practice the visual observer can wait for those glorious moments when the fluctuating seeing renders a great view. In other words, for the patient observer the relevant seeing disc is not the time-averaged disc, but the minimum disc that occurs during the observation period. This minimum disc corresponds to an even larger optimum aperture.

If all of this is correct, the interesting fact remains that under typical seeing conditions and in the absence of adaptive optics, resolution-wise a top-quality 20-30" would blow away a 1,200" telescope.

#11 JKoelman

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Posted 21 April 2013 - 01:01 AM

(By the way, it did not that a CO reduces the size of the Airy disk slightly, the energy transferred into the rings has to come from somewhere. The disk is dimmer, therefore slightly smaller, that energy is transferred into the rings which smears the image thus reducing fine scale contrast. Of course that's a small effect, the way to decrease the size of the Airy Disk and increase the contrast is to increase the aperture, CO or no CO. )

I think the effect is more fundamental. By introducing a central obstruction the average distance between points within the area of light gathering increases, thereby decreasing the angular size at which zero crossings of the light amplitude occur. In other words: the central disc plus all outer rings diminish in size.

Unfortunately, and as you state, one does not benefit from the reduced size of the diffraction pattern, as the spill over of light into the outer diffraction rings more than compensates for the reduced sizes.

Note however, that in contrast transfer diagrams central obstructions do lead to better contrast at very high resolutions (and very low contrast transfer values). This is thanks to the smaller Airy disk.

#12 Jon Isaacs

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Posted 21 April 2013 - 06:25 AM

I think the effect is more fundamental. By introducing a central obstruction the average distance between points within the area of light gathering increases, thereby decreasing the angular size at which zero crossings of the light amplitude occur. In other words: the central disc plus all outer rings diminish in size.



Interesting.. Do you have a reference for this. I thought the diameter of the minimums and maximums was determined by the aperture. Looking Rutten and Venrooij's section on COs, I see no mention of it.

Jon

#13 JKoelman

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Posted 21 April 2013 - 06:47 AM

See this page (most notably the computation with 99.9% obstruction compared to that for unobstructed optics). The math behind this is explained here.

#14 Jon Isaacs

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Posted 21 April 2013 - 07:10 AM

See this page (most notably the computation with 99.9% obstruction compared to that for unobstructed optics). The math behind this is explained here.


The math on the wiki page is not something I am going to do. I did not see anything in David's work that directly addressed the issue of the spacing of the diffraction rings as a function of CO so one could say that an 8 inch scope with a 30% CO would have a smaller first ring diameter than an 8 inch scope without a CO...

Jon

Jon

#15 JKoelman

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Posted 21 April 2013 - 07:25 AM

I did not see anything in David's work that directly addressed the issue of the spacing of the diffraction rings as a function of CO so one could say that an 8 inch scope with a 30% CO would have a smaller first ring diameter than an 8 inch scope without a CO...

Have a look at his graphs:

The 3rd graph shows the diffraction pattern for an unobstructed 8" aperture with a first zero at 3 micro radians.

The next graph shows this pattern for the same 8" aperture but now with a CO of 34%. The first zero is at 2.65 micro radians.

The last graph shows the same aperture with 99.9% obstruction. The first zero is at 1.8 micro radians.

In the accompanying text he summarizes this with: "You gain some resolution with the huge obstruction, but not a tremendous amount."

#16 Mark Harry

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Posted 21 April 2013 - 07:33 AM

Around here, a scope particularly over about 10" -IS- a liability; Often being where 3 different air masses are colliding. East ocean, Canadian, or south temperate. (more often than not, viewing doesn't allow powers with a 6 past about 125x.) Considering that, the Rutten reference applies well here. And I much prefer to gradually glean info with a smaller ap's pleasing image, rather than look at a pile of mush out of a larger instrument wasting half the night waiting for a split second of superiority. (hi rez planet stuff, or doubles, etc) At least; that's what works for me, and what I find more enjoyable.
M.

#17 Cotts

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Posted 21 April 2013 - 08:09 AM

I did not see anything in David's work that directly addressed the issue of the spacing of the diffraction rings as a function of CO so one could say that an 8 inch scope with a 30% CO would have a smaller first ring diameter than an 8 inch scope without a CO...

Have a look at his graphs:

The 3rd graph shows the diffraction pattern for an unobstructed 8" aperture with a first zero at 3 micro radians.

The next graph shows this pattern for the same 8" aperture but now with a CO of 34%. The first zero is at 2.65 micro radians.

The last graph shows the same aperture with 99.9% obstruction. The first zero is at 1.8 micro radians.

In the accompanying text he summarizes this with: "You gain some resolution with the huge obstruction, but not a tremendous amount."


Here are the graphs of the 0% and 30% obstructions on a 203mm scope. (Screen grabbed from the article you quote.) My eyes show the same first minimum and the same first maximum. I'm not sure where you got your numbers.

I left out the 99% obstruction because no one has a scope over 40% obstruction that is used for anything but wide field photography where the Diffraction pattern is not resolved at the plate scales in effect.

The radius to the first minimum (and to any other minimum or maximum in the diffraction pattern for that matter) is entirely a function of aperture. The intensity of the light within the pattern varies with central obstruction. To maintain otherwise requires the re-writing of all standard optics textbooks (non-peer reviewed internet 'texts' notwithstanding).


Dave

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#18 JKoelman

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Posted 21 April 2013 - 08:30 AM

My eyes show the same first minimum


If you've that bad eyes, it helps to consider a more extreme case (like 99.9% CO). Amplifies the effect, you know... :grin:


The radius to the first minimum (and to any other minimum or maximum in the diffraction pattern for that matter) is entirely a function of aperture.

That claim can only be classified as a misinterpretation of the textbooks. Diffraction patterns depend on the full geometry of the light gathering area. For non-cylindrical symmetrical apertures one can not even define a single first minimum.

#19 Jon Isaacs

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Posted 21 April 2013 - 10:45 AM

If you've that bad eyes, it helps to consider a more extreme case (like 99.9% CO). Amplifies the effect, you know...



The 99.9% is essentially an end point. One cannot predict behavior in the middle of the curve based on an unrealistic endpoint calculation, it may just be a mathematical artifact. Just for a bit of perspective, a 99.9% CO is a circular slit, 8 inches in diameter whose width is equal to to the thickness of a human hair.

My eyes saw the same thing Dave's did but they are pretty poor graphs. There is an answer to the question we are asking, I don't know the answer, I don't see you deriving the answer, I am sure there a people here who can provide the answer.

Jon

#20 JKoelman

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Posted 21 April 2013 - 12:21 PM

Yeah, there are folks here who have the software to simulate spot diagrams. They will be able to dispel the myth that "the Airy disk size is solely a function of aperture". I can spell out the math and prove that for a fixed aperture Airy disk size decreases monotonously with increasing CO, but I am sure that won't convince you.

#21 Jon Isaacs

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Posted 21 April 2013 - 01:09 PM

Yeah, there are folks here who have the software to simulate spot diagrams. They will be able to dispel the myth that "the Airy disk size is solely a function of aperture". I can spell out the math and prove that for a fixed aperture Airy disk size decreases monotonously with increasing CO, but I am sure that won't convince you.


The issue is the diameter of the diffraction rings, not the diameter of the Airy disk itself.

Jon

#22 gnowellsct

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Posted 21 April 2013 - 08:58 PM

I guess I don't understand the discussion. I've been observing for 6 or 7 years with a C14 and a 4" ED Vixen doublet. The Vixen is a very nice little scope and shows quite a bit on the planets. But it never ever shows more than the C14. One one or two occasions I've had the FS128 set up next to the C14 and it's the same thing. I have reasons why I like my smaller scopes but putative "better performance in bad seeing" is certainly not one of them: though to be fair the math mavens assure us that there is better wave front and seeing cells etc.

I'm just saying I'm out there with two scopes one bolted on to the other and I can use whichever I want and if the smaller aperture had such an advantage you'd think the night would come when I would say "whoa! I'm not wasting any more time with this ridiculous fourteen inch aperture!"

It is true that purveyors of small scopes tend to say that in areas of unstable skies you "might as well" have a small scope as a big one. But these days I'm not sure why the discussion comes up. You can get a small scope and for the price of a Pentax eyepiece at some point you can pick up a used eight inch dob on the 'mart and then you can see for yourself. GN

#23 Ziggy943

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Posted 21 April 2013 - 09:45 PM

This subject has been the headline of many threads and keeps coming up. Why? Because there is some truth to it and I suspect that most of us have experienced it at some point in time.

As recent as last night people were telling me that my view of Jupiter, in a TEC 160mm F/8 refractor was better than the other telescopes in the field. OK, it's not a technical comparison, and I didn't go up and down looking at the other scopes but those were the judgement calls of a fair number of people.

Personally, and I have related this on several threads, my 9" refractor routinely showed better images of Jupiter, Saturn, the Moon and other solar system objects than larger reflectors in the field. That was the general opinion of the larger reflector owners also. Side by side there are no graphs, no theory, you only have the image in the eyepiece in front of you.

#24 Mark Harry

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Posted 22 April 2013 - 05:53 AM

4" 'fractor against a 14" of any type???
Come on, that's no comparison. (no offense)
M.

#25 Jon Isaacs

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Posted 22 April 2013 - 05:25 PM

4" 'fractor against a 14" of any type???
Come on, that's no comparison. (no offense)
M.


It all depends on the target.

But I think the original question was whether there were seeing condition when a smaller scope could out resolve a larger scope. I think are.

Jon






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