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Equipment Discussions >> Refractors

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Eddgie
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Re: Reflector/Refractor equivalence formula new [Re: Fomalhaut]
      #5773696 - 04/02/13 07:00 PM

well, it has pretty good optics I would say. Star test shows very smooth optics. There is a zone about half way out which used to be very typical in Celestron SCTs bigger than 8".

The star test shows very little spherical aberration.

So yes, I would say that as large SCTs go, it is one of the best I have owned, thought the optical quality is not as good as my EdgeHD 8" which is stunningly good.

But as my post above indicates, the contrast transfer of the C14 is quite a bit better than a 6" APO, so with patience, it is easy to see more detail.

My seeing is rarely perfect, but unless seeing is less than about 2 arc seconds, I prefer to look at other things besides planets anyway.

When seeing is below about 2 arc seconds, usually is all it takes is patience for moments of sub arc second seeing, and when that happens, subtle details come into view.

About a year ago, I posted on resolving the Ray system from the feature Osiris on Ganymede and also the curve and flat rim of Reggio Galilee on Ganymede on the same night using the C14.

That didn't just happen. Seeing was maybe 2 arc seconds, so not that good.

I was using about 340x in mono-vision when I made the sighting (11mm plossl).

At the time, Ganymede was I think only 1.7 arc seconds, so this represents detail that was on the order of one arc second and less in size.

Anyway, I did not just put in the eyepiece and suddenly see these features. I probably spent 30 minutes looking at Ganymede before I got maybe 20 Seconds where the seeing steadied out.

Over maybe another 45 minutes, I saw both features two more times.

So, out of perhaps an hour and a half of viewing, I noted these features for a grand total of maybe 90 seconds.

But I saw them. I went in to validate my sighting using my astronomy program and sure enough, they were in the position and presented the shapes I saw.

So, there you have it. Maybe 90 minutes of viewing time.

I have seen shading on Ganymede using the 6" APO, but I have never really resolved specific shapes in that scope. It just doesn't have the contrast of the much bigger C14.

Planetary observing with larger apertures will show you more but only if you have excellent seeing or a lot of patience.


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GlennLeDrew
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Re: Reflector/Refractor equivalence formula new [Re: Eddgie]
      #5773706 - 04/02/13 07:04 PM

Eddie,
I in no way dispute all you've stated regarding resolving power, both linear and angular.

My argument, which could have more pointedly stated, is that resolving power and contrast transfer are not equivalent. To merely say that the larger aperture delivers higher contrast in untrue. All optical instruments of *perfect* quality deliver the same contrast as that of the eye alone. At the same exit pupil, all deliver the same quality of image.

For example, if when you place a series of aperture stops in front of your eye you find that the diffraction pattern on a point source just becomes apparent at 1.5mm, then with any excellent scope you will see the same degree of diffraction at the same 1.5mm exit pupil.

Another example, an expansion upon one supplied earlier. One makes up a series of test charts, all identical, but placed at a *distance appropriate to the magnification* of each instrument. One is for the unaided eye, another for a small scope, and a third for a big scope. All are to be viewed at the same 1mm pupil. In all cases, with the target subtending the same angular size on the retina, the visual appearance as regards 'softening' due to diffraction effects is identical.

This is why I say that the *appearance* of contrast scales with the exit pupil. Other things being equal, diffraction is purely exit pupil dependent. After all, the exit pupil is merely the shrunk-down entrance pupil. And to the eye, it's the aperture of its own pupil, or the exit pupil, whichever is the smaller, which ultimately controls diffraction.

So again, to the observer's retina, aperture alone has no role to play in contrast. That's controlled by the exit pupil.

It's only when restricting to the limited situation of directing attention on just one target of fixed angular size do we get the impression that a larger aperture improves contrast. But that's a 'red herring', really, for then the argument is merely stating what is fundamentally obvious. Namely, that a larger aperture reveals finer detail. But it does not improve contrast.

And this is perhaps where our wires are crossing. You're working in terms of *absolute resolving power*, while I'm reducing to the relative resolving power *as detected by the retina*.


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GlennLeDrew
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Re: Reflector/Refractor equivalence formula new [Re: GlennLeDrew]
      #5773767 - 04/02/13 07:22 PM

To say that a C14 has better contrast transfer than a 6" APO implies a poorer-than-expected quality in the refractor. The Cat's central obstruction introduces additional diffraction which impacts resolving power at certain scales, thus reducing contrast transfer. If the refractor were to be optically perfect, or good enough in that respect which matters, it would offer better contrast transfer, in spite of its much smaller aperture.

If contrast transfer is merely tied to resolving power in the larger sense, as when changing the aperture of the entrance pupil, then the term 'contrast transfer' is largely superfluous.

As I understand it, 'contrast transfer' describes the actual contrast as compared to that of a perfect, unobstructed system of the same aperture, as is usually illustrated in the MTF chart. If so, we must be careful to not conflate the better resolving of a larger aperture with better contrast transfer.


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JimP
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Reged: 04/22/03

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Re: Reflector/Refractor equivalence formula new [Re: GlennLeDrew]
      #5773782 - 04/02/13 07:31 PM

Ziggy, if I did not believe that you are completely and absolutely sold on Celestron telescopes I would find your posts to be more objective. As it is, you, me and most others on these forums have a bias toward one type scope or another and find ways to show how the telescope we chose, the one we spent big money on, is the best. The old saying "there are lies and there are statistics" is true.

If mathematical equations were all that was needed we could just read a book and never observe to see for ourselves how our scopes actually perform.. For example, I suspect all your equations "assume" perfect collimation, scope at thermal equilibrium, etc.

I own a 20" F/3.3 Mike Lockwood Quartz mirror Starmaster, a 10" F/9 TMB LZOS triplet apochromatic refractor and an AP 10" F/14.6 Maksutov. Aperture is not the do all end end all to observing. I have to collimate my 20" Every time I use it. I have never had to collimate either 10" scopes. A friend of mine, Bob, contacted me about how I should get an auto collimator to tweek the collimation of the 20". Go to the Catseye website and read all about using an auto collimator. When your headache goes away finish reading my post.
I love all my scopes. They are all very special and I would not give up Any of them. My advice is Quit worrying about Aperture and which scope is Better than the one you have. It's not!

JimP


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Eddgie
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Re: Reflector/Refractor equivalence formula new [Re: GlennLeDrew]
      #5773860 - 04/02/13 07:58 PM Attachment (15 downloads)

Not so. You need to read my post.

A 6" aperture transfers far less contrast to the focal plane than a 14" aperture.

Please read my post above, or ask anyone that has read Suiter's book.

There are examples that show this clearly.

A larger aperture (all other things being equal) preserves more contrast from the target than a smaller aperture.

The S' max for a 6" scope is only 1.32 lines per arc second (apparent size of the detail on the target).

The S' max for a 14" aperture is almost 2.5 times that figure.

This means that a C14 preserves far more contrast than a 6" aperture.

Here is the MTF plot for each scope.

Notice that the S' Max for the 6" is only .43 of the S' max of the 14" (about 1.32 lines per arc second at the target for the 6" vs almost 2.8 lines per arc second in the C14).

Even with the big central obstruction and 1/8 wave of spherical aberration, the C14 is still transferring much more contrast than the 6" APO.

You should read Suiter's Book.


The book "Telescope Optics" will also confirm this data.


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timps
sage


Reged: 02/24/13

Re: Reflector/Refractor equivalence formula new [Re: Eddgie]
      #5774024 - 04/02/13 08:59 PM

And that is why I will buy a 14" SCT.

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timps
sage


Reged: 02/24/13

Re: Reflector/Refractor equivalence formula new [Re: timps]
      #5774091 - 04/02/13 09:14 PM

It is good to read peoples opinions. Sometimes they assist and sometimes they confuse but really, it all comes down to what one sees through the eyepiece. If Eddgie has both scopes and obviously has the oportunity to compare them through the eyepiece then I will tend to agree with what he is saying.

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Eddgie
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Re: Reflector/Refractor equivalence formula new [Re: GlennLeDrew]
      #5774296 - 04/02/13 10:14 PM

Glen, I really encourage you to get Suiter's Second Edition of Star Testing.

Suiter addresses this topic in detail.

In Chapter 3, Suiter goes to great lengths to explain how a larger aperture (design and quality being equal) will have better contrast for all size details.

In Appendix B, he presents alternate was of calculating contrast transfer.

In all models, the larger aperture (again, quality and design being equal) always has better contrast for every size detail.

The book "Telescope Optics" also has a lengthy explanation of contrast transfer, though in this book, they don't directly present diagrams showing the contrast transfer for different apertures. Instead, they only show the formulas for calculating S' Max.

I found that it was necessary to read both a few times to get the concept, but Suiter's book gave the key on page 59.
People that think that refractors always have better contrast than other designs are mistaken. This is only true when the quality is the same or better, and the clear aperture is more than in the case of the obstructed instrument.

In the same way that larger refractors have better contrast transfer than smaller refractors, a bigger reflector, even if not optically perfect and with a large central obstruction, can still have better contrast transfer than a smaller refractor.

And that is what the MTF chart exists for. I allows you to express in lines per arc second (at the target) how much contrast will be preserved from the starting contrast.

I really encourage you to read Suiter's book.

Anyone that has the book can confirm from the diagram at the bottom of page 59 that the graphs I presented above tell the store.

A 12" scope will have far better contrast transfer at the focal plane than a 6" scope, and a 32% obstructed 14" scope with 1/8th wave of spherical aberration will have better contrast transfer at the focal plane than the most perfect 6" APO ever made.

Anyone that looks at page 59 in Suiter's book and spends the time reading the chapter will concur with this.

Edited by Eddgie (04/02/13 11:10 PM)


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GlennLeDrew
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Re: Reflector/Refractor equivalence formula new [Re: Eddgie]
      #5774445 - 04/02/13 11:35 PM

Eddgie,
I was recently given Suiter's 1994 edition by a friend. In it, the MTF chart is always normalized to the *fraction* of the maximum spatial frequency. This is appropriate when considering a telescope in the afocal configuration, where diffraction effects scale as the exit pupil.

My emphasis in this discussion is on the appearance of the image at the eyepiece and at given exit pupil. The better quality instrument, irrespective of aperture, will deliver the better quality view.

The eye sees an image, and knows not what is the aperture delivering it. All it 'knows' is whether the image is good or not so good as regards such things as diffraction and aberrations. If at some particular exit pupil one rates the view less afflicted by diffraction and aberrations for a smaller aperture, then that smaller aperture, in some respect at least, delivers by definition better contrast transfer.

Any two telescopes, no matter how much they may differ in aperture but which have identical MTF charts, will deliver identical contrast at the same exit pupil.


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moynihan
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Reged: 07/22/03

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Re: Reflector/Refractor equivalence formula new [Re: Eddgie]
      #5774447 - 04/02/13 11:36 PM

I assume that the references to Suiter, and page 59, are to his book on star testing?
Anyway, i just grabbed my copy.
On page 163:
9.1 Central Obstruction
The most obvious and potentially most damaging kind of transmission change is caused by the centrally placed diagonal or secondary mirror. ... However, the negative consequences of central obstruction can be readily and precisely calculated. We will see that they worsen considerably beyond a linear obstruction of 20 to 26 percent of the aperture. As long as the obstruction is kept inside that fraction, the image closely approximates that of an unobstructed telescope."

The section continues, exploring various aspects of the central obstruction, equivalence formula, etc.
It appears that (from that section, and his formula on page 163), that all other things being equal (including the crucial element of seeing...) that the unobstructed equivalent of a 14" with a 32% would be 9.52", according to Suiter. On that score, the 34% CO equivalent of a 6" unobstructed aperture would be a tad more than 9 inches?


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maknewtnut
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Reged: 10/08/06

Re: Reflector/Refractor equivalence formula new [Re: Cotts]
      #5774496 - 04/03/13 12:09 AM

Quote:

The trouble with a rule of thumb is that people's thumbs vary greatly in length.....

Dave




Dave nailed it with his analogy. A vast majority of the arguments summarized by the thread title are pure bunk.


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timps
sage


Reged: 02/24/13

Re: Reflector/Refractor equivalence formula new [Re: moynihan]
      #5774519 - 04/03/13 12:22 AM

When they refer to the percentage of the central obstruction, Is that a percentage by area or diameter?
Celestron 14" for example: secondary mirror obstruction by area is 10.3% but by diameter is 32.1%.


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jrcrillyAdministrator
Refractor wienie no more
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Re: Reflector/Refractor equivalence formula new [Re: timps]
      #5774546 - 04/03/13 12:38 AM

Quote:

When they refer to the percentage of the central obstruction, Is that a percentage by area or diameter?




Could be either (percentage by area is figured by taking the square root of the percentage by diameter; nobody actually measures the area). You can tell which has been stated by the figure. It will only make sense as one or the other (10%-15% range would be area while 30%-45% would be diameter). Which is chosen generally depends on the context. Light loss varies as the area while contrast varies as the diameter.


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Jon Isaacs
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Re: Reflector/Refractor equivalence formula new [Re: GlennLeDrew]
      #5774551 - 04/03/13 12:43 AM

Quote:

Eddgie,
I was recently given Suiter's 1994 edition by a friend. In it, the MTF chart is always normalized to the *fraction* of the maximum spatial frequency. This is appropriate when considering a telescope in the afocal configuration, where diffraction effects scale as the exit pupil.

My emphasis in this discussion is on the appearance of the image at the eyepiece and at given exit pupil. The better quality instrument, irrespective of aperture, will deliver the better quality view.

The eye sees an image, and knows not what is the aperture delivering it. All it 'knows' is whether the image is good or not so good as regards such things as diffraction and aberrations. If at some particular exit pupil one rates the view less afflicted by diffraction and aberrations for a smaller aperture, then that smaller aperture, in some respect at least, delivers by definition better contrast transfer.

Any two telescopes, no matter how much they may differ in aperture but which have identical MTF charts, will deliver identical contrast at the same exit pupil.




Glenn:

I am with Eddgie on this one... One needs to step back from what is "always done" and consider what one wants to know when attempting to analyze the difference between two scope that differ in aperture. This is the question as I see it:

For a given spacial frequency, which scope will provide the superior contrast. All we want to know is for a given detail on the surface of Jupiter, which scope will show it with more contrast. If you normalize by aperture, then the scale of the object must be normalized and that is not what we want, we are looking for absolute numbers for comparison.

In the case of the C-14 and the 6 inch, the same exit pupil occurs at 2.3 times the magnification, the details with the same contrast are much finer in the larger scope.

Jon


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Kevin Barker
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Re: Reflector/Refractor equivalence formula new [Re: Jon Isaacs]
      #5774684 - 04/03/13 03:42 AM

Interesting stuff. here is my 2c worth....

A crude rule of thumb for the equivalent obstructed and unobstructed equivalent aperture is take away the obstruction from the aperture for an obstructed scope. This seems to hold for up to 10-11 inches. And for obstructions from 20-35 %.

However obstructed scopes need to be well cooled, well baffled, perfectly collimated and have a very good figure if they are to produce similar contrast as an unobstructed "apochromat" equal to their aperture minus the obstruction. With this reasoning a 10 inch planetary Newtonian with a 2.6 inch secondary should be able to hold it's own against a 7 inch apochromat.

The apochromat could well seem to be more appealing visually and have a higher contrast to brightness than the Newtonian.

I have an 8 inch f-6 Dobsonian which has a 2 inch secondary. It does indeed show similar views to a good five inch apochromat when it is well cooled. The missing inch may be because of the less than perfect control of scattered light.

I think once achromatic refractors start to obey the f rule of 3 times the aperture in inches they also behave close to an obstructed aperture minus the obstruction.


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GlennLeDrew
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Re: Reflector/Refractor equivalence formula new [Re: Kevin Barker]
      #5774720 - 04/03/13 05:22 AM

Jon,
It's axiomatic that at given spatial frequency a larger aperture delivers better contrast. This is the essence of the aperture race. And as I stated, I am in complete agreement.

My emphasis is on what the observer sees *at the scale of the retina's resolving power*, so to speak.


We have two otherwise identical telescopes. A 2" is examining a 1st magnitude star and a 20" is examining a 6th magnitude star. Each is working at, say, the same 1mm exit pupil. The view through each eyepiece will be indistinguishable.

We have two optically excellent telescopes, one a 2" refractor and the other a 20" Cat. As before, each looks to a 1st and 6th magnitude star, respectively. At the same exit pupil, the Cat's image suffers additional diffraction. An observer conducting a blind test would judge it inferior.

This is the crux of my argument. Discounting the obvious increase in resolving power (and light grasp) which aperture affords, what is the *quality of the image on the retina* at any given exit pupil diameter?

We all know that resolving power scales directly as the linear aperture. This is so fundamental that once learned can be relegated to the back of the mind. The MTF chart is not concerned whatsoever with the actual, absolute resolving power, being normalized as it is to the theoretical maximum. The MTF chart is all about representing the departure from perfection of a same-size circular aperture. Two widely disparate apertures delivering the same optical quality will have identical MTF charts.

Concentrating on the *absolute* differences in resolving power resulting naturally from differences in aperture is all well and good. But that this scales linearly with aperture is so easily appreciated it hardly bears more than the briefest thought.

What we *really* desire to know is this; how far does my telescope depart from perfection? The MTF chart tells us clearly, and this is of direct relevance to the quality of the view over the range of exit pupils useable.

For an afocal instrument (with eyepiece, used visually), the quality of the view *as perceived on the retina* is what ultimately matters. In this context, then, contrast transfer must be rated with respect to the perfect wavefront emerging through a given exit pupil.

The importance of the telescope and eye *as a system* is too easily overlooked. The exit pupil is the coupling interface which locates the entrance pupil (objective) at the eye's pupil. The eye cares not a whit what other optics lie in front of it. All that matters is the pupil diameter and the wavefront passing through it.

If that wavefront is not aberrated, the dimension of the Fresnel pattern on the retina scales precisely as the f/ratio of the light cone defined by the exit pupil (or iris, if the smaller.) This is irrespective of the telescope aperture. And if any particular aberration or aberrations is present (say, 1/2 wave if spherical aberration), no matter the aperture, for given exit pupil it will have identical apparent extent on the retina.

This is why the exit pupil is so important. It is the normalizer for image surface brightness, diffraction and extent of aberrations.

If we assume for the moment that both systems are otherwise essentially perfect, how can we can say that the C14 delivers better contrast than a 6" APO when we know from its MTF chart that the additional obstruction impacts contrast??? At given exit pupil (smaller ones, of course) we will see in the C14 the degradation of contrast compared to the slightly cleaner image in the 6".

Yes, I know. The much larger image in the C14 WELL MORE THAN COMPENSATES for its slightly poorer contrast transfer. But just because that greatly larger aperture, with its commensurately better resolving piwer, so handily bests a superior but smaller instrument in no way means it delivers better contrast transfer.

If it did, then contrast transfer is to a *very* great degree merely interchangeable with resolving power, scaling almost purely with aperture. That's superfluous, don't you think?

To me, contrast transfer, at least in the context of an afocal system, is kind of like the Strehl ratio; it's related only to what a perfect, same-size, (in this case unobstructed) aperture could deliver.


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Mark Harry
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Re: Reflector/Refractor equivalence formula new [Re: GlennLeDrew]
      #5774747 - 04/03/13 06:31 AM

About the ganymede observation with 6+14" scopes---
***
Isn't the resolving power of a 6" around 1 arc-second?
I would think if so, an investigation why the features weren't seen is mandatory.
(Daves, and Marks remarks about rule of thumb- right on the mark!)
M.


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Jon Isaacs
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Re: Reflector/Refractor equivalence formula [Re: GlennLeDrew]
      #5774808 - 04/03/13 07:52 AM

Quote:


Concentrating on the *absolute* differences in resolving power resulting naturally from differences in aperture is all well and good. But that this scales linearly with aperture is so easily appreciated it hardly bears more than the briefest thought.




Glenn:

It seems that all too often, the fact that "it's axiomatic that at given spatial frequency a larger aperture delivers better contrast" is simply forgotten. This is particularly true in this forum, I see it stated time and time again that refractors, regardless of aperture, have better contrast than other scopes...

This is the issue I believe Eddgie is addressing, this is the issue I constantly address: That contrast for a given spacial frequency is a function of aperture, that in terms of planetary viewing, a 10 inch Newtonian with a 20%CO will have better contrast than a 4 inch anything. To try to explain this, I use phrases like "all scopes are obstructed", "by far, the most important diffraction effect that affects contrast is the result of the most important obstruction, the Outer Obstruction, more commonly known as the Aperture."

When evaluating a telescope, I am an observer, I am looking to see what I can see, the telescope itself, it ought to be a black box. I don't really care if it's a 4 inch scope that is as perfect as a 4 inch scope can be or a 10 inch scope that has average optics, what I want to know is which one will provide me with the more detailed views of Jupiter, which one will provide me with best view of Stephan's Quintet... which one will provide me with the best view of the North American Nebula..

When one normalizes by aperture, it's pretty apparent that an apochromatic refractor, because of the simple, unobstructed, will provide better contrast. What is not so clear though is that a somewhat larger scope with a central obstruction can overcome that advantage and provide equal or superior contrast to the refractor. An "Equivalance Formula" should be able to provide a basis for this relationship.

The value of MTFs, contrast transfer, is that if they are not normalized, then they can provide a basis for analysis to determine some sort of equivalency relationship. It's pretty apparent that a 12.5 inch F/6 Newtonian is going to have a big advantage in spacial contrast and resolution over the most perfect 6 inch refractor ever built, but how about an 8 inch Newtonian, how does it fit?

And then when one includes the practical aspects, thermal management in all it's many aspects, optical quality, sensitivity to seeing.. it gets really complicated.

For me, to understand that the contrast scales with exit pupil is interesting and worth understanding but it is also academic. What counts happens at the eyepiece, when comparing two scopes, I am not using the same exit pupil in both scopes, I am using the optimal exit pupil in each scope... What do I see looking at Jupiter with my 16 inch Newtonian versus my 4 inch apo?

I think we both know the answer.

Jon


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Eddgie
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Re: Reflector/Refractor equivalence formula [Re: Mark Harry]
      #5775059 - 04/03/13 09:41 AM

Because while the resloving power is about 1 arc second, the detials will have lost most of their contrast at this size.

That is the whole point of MTF.

If you start out with a detail that has 100% contrast (Black on white) that is only one arc second across, it will have lost almost all of that contrast in the 6" scope!

That is what MTF is about.

All telescopes loose contrast.

By the time you get to detail this small, it will have so little contrast left that it is impossible to see unless it started with 100% contrast to begin with.

Lets take the example of the curve of Reggio Galilee. This is a Mare like feature on Ganymede. It describes a curve that is ony about 1 arc second in width and one side is flattened.

But the contrast of this area is very poor.. Perhaps ony 20% against the surrounding landscape (dark gray against light gray).

Becaucause this curve starts with low contrast, in the scope that can ony resolve a one arc second feture, 98% of teh contrast would be lost at the focal plane. A feature that started with 20% of the contrast at the target now ony has about .5% contrast at the focal plane. It has become invisible to the human eye, which requires between 2.5% contrast (brightly illluminted target) and perhaps 5% contrast.

In the C14 that has twice the spatical response, this feature that started with 20% contrast still at about .4 of the scopes maxiumum spatial frequency.

This means that a 1 arc second detail in this scope will still possess over 50% of the contrast that it started with.

A one arc second feature on Ganymede in this scope (regardless of the magnification used) will still show with 10% contrast at the focal plane.

As you can see, the feature has lost too much contrast to be visible in the 6" scope at all. If it is less than one arc second in size, it completely merges with the background.

But in the C14, it is still visible with 10% contrast. Difficult, but well within the eye's ability to resolve.

Contrast transfer has nothing to do with the observer or the eyepiece or the magnification.

This is the image at the focal plane being formed by the optics.

Resolition figures published with telescopes give you the resolving power for Double Stars.

A double star is a case where the contrast starts with 100% and reprsents the best possible case for the telescope because you are looking at a black seperation between two bright Airy Disks. That black "line" that appears between the two Airy disks represents the size of a feature where the contrast is almost completly gone. We only see it becuase the the contrast starts with 100%.

So, all of this other talk about magnification and image scale for different size telscope when viewed visually miss the point.

The point is that at the focal plane, different instruments transfer contrast (get detail from the target that starts with a given contrast and form the image on the focal plane with a lower contrast than on the target) at different rates.

By the time the 6" APO shows the image, unless it starts with 100% contrast (like the line between a double star) a one arc second detail will have lost so much contrast as to be inpossible to see.

The 14" aperutre will only have lost about 50% of the contrast detail for a target this size. If the detail started with 20% contrast, 10% will still remain.

That is how MTF charts work.

They tell you how much contrast a line pair of a given width will lose when it is rendered at the focal plane.

This can be used to infer how much contrast for a similar sized detail will be preserved.

Io in the 6" APO is almost featureless even on the very best of nights.

In the C14, it takes great patiance and excellent seeing, but there are occasions where I can resolve detail.

And I should be able to. THe C14 preserves far more contrast for these small sized details than the 6" APO does.

In fact, the C14 preserves more contrast for any size detail than the 6" APO does.

And that is what the MTF chart show you. They show that both instruments loose contrast on detail, but the sloping line shows you how much contrast is lost for a given size detail

The C14 has contrast transfer that is sperior across the entire range of detail size.

All planetary detail is shown with better contrast in the C14 than in the 6" APO.

Even on nights when seeing is less than great, large scale detail still stands out better in the C14 than the 6" APO. While small scale detail may be blurred out, the observer still enjoys the better contrast of the larger instrument.

Edited by Eddgie (04/03/13 09:41 AM)


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Re: Reflector/Refractor equivalence formula [Re: moynihan]
      #5775217 - 04/03/13 10:48 AM Attachment (9 downloads)

Quote:

The section continues, exploring various aspects of the central obstruction, equivalence formula, etc.
It appears that (from that section, and his formula on page 163), that all other things being equal (including the crucial element of seeing...) that the unobstructed equivalent of a 14" with a 32% would be 9.52", according to Suiter. On that score, the 34% CO equivalent of a 6" unobstructed aperture would be a tad more than 9 inches?




To harken back to the OPs question, the formula is really only general, and works better for visual observing than for imaging. For imaging, it is not at all accurate because the obstruction doesn't matter for the finest detail the scope can resolve. Even a large obstruction doesn't loose much additional contrast past about .7 on the MTF plot meaning that for the finest detail, the size of the obstuction doesn't matter.

Here is a plot that shows what is going on.

This is a plot for a perfect 9.25" 36% obstructed instrument

The red line would show how much contrast would be lost for even a perfect 9.25" apeture.

The dashed red line shows how much contrast would be lost for the obstructed instrument.

The blue line shows how much contrast would be lost for the perfect 6" instrument.

Now the forumla for S' Max would indicate that the 9.25" scope will have lost almost all contrast for a line frequencey of 2 line pair per arc second on the target.

The S' Max for the 6" apeture (if you have been following along) is 1.32 arc seconds per line pair on the target.

First, no one should be able to argue that the angular resolution is better for a 9" scope than a 6" scope. There are numerous formulas out there that show that, and contrast transfer is after all, a function of angular resolution. It describes how far away from the geometric center of the Airy Disk light energy will fall. Everyone knows that the Airy Disk is smaller as apeture grows (all other things being equal).

Back to the chart. The 1 on the X axis indicates that the 9.25" instrument can resolve 2 line pair per arc second on the target.

The 6" instrument cannot reasolve lines this small at all. It can only reslove line paris that are 1.32 arc seconds indicated by the fact that the S' max is only 65% of the S' Max of the 9.25" scope.

Now, follow the graph over to where you see the little green line between the obstructed and perfect aperture lines.

This represents line pairs that are about .33 of the S' Max of the 9.25" Scope, or lines that are about .66 lines per arc second (in other words, line pairs about 1.5 arc seconds wide at the target).

What the MTF chart shows for line pairs (or detail about 1.5 arc second in size at the traget) is this.

If these lines started as a 1.5 arc second wide line pair with 100% contrast on the target as black and white alternating sine waves, in the perfect 9.25" scope at .33 S' Max, they will have lost about 39% of their contrast.

They will appear as very dark gray lines alternating with very light gray lines, but the contrast is high ehough that they will still appear to the eye as almost black and white.

Continue down to where the green line is between the two scopes in question. Note that the perfect 6" aperture will show those same lines with only about 46% contrast. Now, rather than looking more black and white, they are starting to look more medium dark gray and medium light gray. They are starting to blend together because the light from the Airy Disks coming from the points along the white line are spreading into the area of the black lines, causing the contrast to lower.

Now, follow the green line down to the obstructed apeture.

In this case, the contrast as fallen to 43% maybe.

Now this is not a lot of contrast difference at all. Even the very very best observers will struggle to see a difference this small, though on a brightly illuminated target, people can often judge contrast differences as small as about 2.5%.

This graph shows though that a 9.25" 36% obstruted instrument is not quite as good as a perfect 6" apeture for details that are bigger than about 1.4 or 1.5 arc seconds in size on the target.

And the 6" aperture retains that contrast advantage for all lareger size detail though as the detail gets larger, the advantage dwindles. It peaks for line pairs about 1.3 to 1.5 arc seconds wide though.

But past about .5 of the S' Max of the bigger scope notice that it quickly gets back to even footing with the perfect apeture.

This represents contrast for the smallest possible detail the scope can resolve.

And this should make perfect sense if you use a double star as an example.

The space between the double stars can represent a feature on the surface of a planet.

Suppose you had a feature that was the same length as the spacing between a pair of double stars that was 1.5 arc seconds from geometric center to geometric center.

In a small aperture, the big extension of the Airy Disks would cause them to meet very near the center of this line.

If you used a bigger scope, the Airy Disk would be much smaller, and as a consequence, you would see more of the dimension of that line that was not covered by the Airy Disk of a star at either end.

And that is what you get when you viewin a planet. Each point of every feature emits ligth that speads out the distancee of the Airy Pattern based on the size, quality and obstruction of the telscope that forms the image.

If the telescope that forms the image conentrasts that energy in a smaller circle, or keeps more of the energy in the Airy Disk itself rather than in rings far away, it may preserve more enegy from the point that formed it.

MTF describes how this energy is distrubuted around the geometric point that formed it.

So, a 9.25" 36% obstructed aperture, when used visually, will have conrast transfer that is fairly close to a 6" perfect apeture.

This is a crucial qualification though. Again, this is only if the obstucted scope is perfect.

Finding 6" APOs with perfect optics is not difficult. No leanding manufacturer is going to sell you an expensive APO that is less than near perfect.

Near perfect C9s though are not the norm. And when you add the typeical inperfections, it can cause the MTF line to further sag.

And it doesn't take much for the line to sag enough so that the contrast falls to a 10% difference.

And when it does, the difference starts to show at the eyepeice.

If you know the amount of error though, you can model it.

Edited by Eddgie (04/03/13 10:54 AM)


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