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Equipment Discussions >> Cats & Casses

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Mike Harvey
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Reged: 03/01/04

Loc: Orlando, FL.
CO vs. All That "Other Stuff"!
      #5608522 - 01/06/13 02:25 PM

I didn't want to 'hijack' (or even divert) the Meade 600 CO thread but, there are so many other factors that affect the performance of a given SCT that need to be considered, it seemed like a new thread was called for.

Hopefully, those who have read the CO posts now have a better understanding of how the obstruction affects the scope's overall performance.
In my experience, there are other factors which are much more important considerations.
*Let me qualify my comments by stating that, over the past 40 years, I've owned or extensively used more than 30 SCT's. These include a variety of Celestron, Meade, Criterion, B&L and Takahashi.
The optical quality of ALL of the Criterion and B&L models (basically the same scopes) was inferior in just about every aspect. The size of the CO would not have mattered!
More than half of the Celestrons and Meades would have been rated 'poor' to 'mediocre' (again, the other shortcomings would have been vastly more important than CO). *Note: these were earlier models. Most of the Celestrons and Meades I've seen in the past few years have been of much higher quality.
The Takahashi TSC-225 proved to be the "gold standard" until the Meade ACF design came along. I don't yet have enough experience with the Celestron Edge to compare them with the ACF.

If you have an older SCT and are dissatisfied with it's performance, you may simply have a scope that came off the assembly line with very little QC exercised. These scopes must exhibit good optical quality on multiple elements: corrector plate, primary mirror, secondary, and diagonal.
PLUS you've got a primary mirror that must remain perfectly aligned even though it is MOVING up and down in order to focus!
This last item is always going to be a potential problem. It is the only weakness I've discovered in the ACF. Fortunately, there is a solution...
LOCK the primary in place at the exact point it should be separated from the secondary, then install a rack & pinion focuser. Trust me, it makes a difference!
There's also the question of collimation. I am constantly amazed at the number of SCT users at star parties who have collimation "issues" and either don't know it and think the soft images are just the price to be paid for having an SCT, or who DO know the images are not what they could be and blame some other aspect of the scope. From what I've seen THIS is the #1 problem for SCT users.
Until the newer secondary-holder design of the Meade ACF, most SCT's were notorious for becoming decollimated when moved around a lot.
Job One, before each observing session, was to collimate the scope!
Today, I'm still impressed every time I use the 10" ACF to discover that the collimation has NOT shifted AT ALL. With Uncle Rod Mollise's help, I precisely collimated this scope when I first received it some three years ago and, despite it being set-up, transported, taken down and set-up again dozens of times...I HAVE ONLY HAD TO TOUCH THE COLLIMATION ONCE...and that was just a near-infinitessimal turn of one screw!

SO - now you've got your SCT precisely collimated, locked the primary in place and installed the R&P. What then happens all-too-often is that the owner will insert a cheap diagonal into the focuser and undo much of the improvement he's made with the earlier tweaks!
You can have a near-perfect corrector, primary and secondary and STILL not achieve great visual results because you've 'bounced' the image off a rough diagonal mirror or misaligned prism.
GET THE BEST QUALITY DIAGONAL YOU CAN AFFORD!
I won't even take this thread into eyepieces because, hopefully, anyone who's taken the earlier steps to improve quality already knows that you need decent eyepieces.

After completing the steps listed above, my 10" ACF displays more planetary detail than any refractor I've ever owned (and that includes a
6" Takahashi FC-150, 6" f/15 AP Triplet and an 8" Alvan Clark). I'm assuming a 10" Zeiss would outperform it but you'd spend at least 10X as much $$$ just for the OTA (not to mention the ginormously expensive and heavy mount and the permanent observatory you'd want to keep it in)!

Mike


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Rick Woods
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Re: CO vs. All That "Other Stuff"! new [Re: Mike Harvey]
      #5608647 - 01/06/13 03:32 PM

Nice post, Mike!
Not much we can do about the CO; but all the rest of it is in our hands.


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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: Rick Woods]
      #5609117 - 01/06/13 07:42 PM

There seems to be two well defined camps in the astro community. One thinks any obstruction is bad - and not just bad but unforgiveable. These tend to be refractor owners. The other community thinks it does'nt make any difference. These tend to be people with scopes that have an obstruction. Bless them both.

The truth is of course more complicated. Many amateurs have both kinds of scopes and/or a better understanding of the action of an obstruction. This is the third camp!

You can come back here years from now - and someone will be asking the same question about CO! And the same arguments and discussions will follow.

It sort of reminds me of the StarTrek episodes featuring the Pakleds from the Alpha Quadrant. You know the guys that say "We are smart." They don't want to hear any thoughtful positions, they just want to collect stuff.

There also seems a tendency for people to get diverted away from practical matters as Rick mentioned. Your note on collimation is right on and as far as diagonals go - there are many good ones out there - and they really don't cost that much. A good one will not effect performance in any perceived manner.

Glenn


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doug mc
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Re: CO vs. All That "Other Stuff"! new [Re: Rick Woods]
      #5609151 - 01/06/13 08:01 PM

Ive only owned my c6sct for a few months now, and apart from the effects of a larger co., which are noticable when viewing bright double stars,not a problem so far, it clearly outperforms the acro refractors i had. 4,5,and 6inch on lunar and planetary detail. They were all synta scopes, so is the Celestron. My other scopes have been dobs 6,8and 10 inch. From my expereance optical quality is number one, much more than telescope type. The new Celestron cats would have to the best value for money scope going. Easy to mount (you can have a much bigger cat on that mount than other type of scope) . You have had some extra fine glass and are amazed by a scope thats much cheaper than many you mentioned. Nudge nudge wink wink.

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Loren Toole
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Re: CO vs. All That "Other Stuff"! new [Re: Mike Harvey]
      #5609252 - 01/06/13 09:21 PM

Quote:

Fortunately, there is a solution...
LOCK the primary in place at the exact point it should be separated from the secondary, then install a rack & pinion focuser.




Mike
I haven't followed the CO thread really carefully but your statement above seems to be a common belief among many SCT owners... the problem is, how can the correct spacing be determined easily without a heck of alot of testing? I'd guess you're proposing something like a Roddier test? Or, using the intra/extra focal patterns at different backfocus distances? All of this sound very time consuming and frankly may not be conclusive. My SCT images are often mushy, probably due to poor thermals and maybe collimation. I'd need to deal with all of that before even attempting what you're suggesting, yes?

Loren


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pstarr
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Re: CO vs. All That "Other Stuff"! new [Re: doug mc]
      #5609254 - 01/06/13 09:22 PM

Quote:

My other scopes have been dobs 6,8and 10 inch. From my expereance optical quality is number one, much more than telescope type.




A SCT with perfect optics and a 30% central obstruction can never give better that 1/4 wave performance. Not that 1/4 wave performance is bad. That said, you will never find a SCT, or any other design with perfect optics.


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5609289 - 01/06/13 09:43 PM

Sure, collimation is absolutely important. But, it's easy, as long as the optical axis is true and preferably orthogonal to the focal plane for best results. Getting that done can be a bit more time consuming, but tilting the secondary is easy. I did it each session, whether it needed it or not.

Cooling, same thing. Take precautions, prep the scope, and pray for moderate conditions the scope (all scopes) can stay in tune with. A good diagonal is an easy fix, especially with dielectric coatings, if it is a problem at all. Apparently not, not much anyway. Eyepieces, too. Same thing.

Personally, I am beginning to think the biggest fault, if you will, of a multiple lens/mirror design is veiling glare or scatter. On this, YMMV.

I am not versed on the advanced SCT designs, like ACF or Edge, but don't they use additional lenses to correct for coma? Meade does not say in this ad, but apparently they found a good "hyperbolic" system using the Schmidt corrector and primary.

"Fortunately, Meade engineers developed a radical new Advanced Coma Free design by combining a hyperbolic secondary mirror with a corrector-lens-and-spherical-primary-mirror combination that performs as one hyperbolic element. This Advanced version of the traditional CF design produces a coma-free, flat field of view that rivals traditional CF telescopes "

http://www.optcorp.com/product.aspx?pid=7836

I am wondering about the correction of the wave front on such a hyperbolic system, how far from ideal spherical does a hyperbolic system deviate? Not sure what the wave front looks like, but surely it meets one of the simpler diffraction limited criteria.

BTW, it does seem from anecdotal evidence (and my own experience) the newer CATs are better corrected and smooth these days. They seem to be more consistently capable of 0.95 aberrant Strehl (with a .3D CO means about 0.80 nominal, working Strehl.) Folks are very pleased with some aspect of them, be it sharper images and resulting contrast improvement (I appreciate that, despite a moderate CO) or flatter field.

And, again, this scope is optimized across the, uh hum, MTF with a huge secondary to suit a broader range of applications. It gains a little on the hi frequency end (tight, equal double star pairs), and gives up a little on the mid range (fine planetary and tight, unequal doubles) by changing the intensity structure through the Airy pattern and reducing peak intensity (probably below 80%.) The "aesthetics" of which can be and are hotly debated. But, this does affect contrast at small scales (for visual) down to about 4x the Raleigh criteria, if that scale matters to anyone. It matters somewhat to me, I push my scope hard and deep in better than average seeing. It's a trade off in the design, despite the off axis performance (which seems to be geared to larger imaging chips and not the eye.)

http://www.meade.ru/ser/product/qm-productId-eq-1279900254208048.htm

In any case, get a scope that suits your needs, control the induced aberrations (cooling, collimation, and de-focus) and enjoy it under steady skies. If it pleases you, then there is nothing wrong with that scope. Some folks probably do not collimate their scopes, no surprise. That's on them.

So, if "all other stuff" includes collimation (plus mirrors shift) and a cheap diagonal, then feel lucky. Those are easy fixes. If a fixed focuser is key, find a sufficient back focus and induce ~1/24th wave over correction per inch of back focus. I doubt anyone will notice.


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GlennLeDrew
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5609495 - 01/06/13 11:55 PM

Loren,
If the radii on the two mirrors is reasonably close to the nominal design, then one can simply rely on the manufacturer's specification for the position of focus with respect to the rear opening. No need to laboriously test. Just place an eyepiece field stop at this distance, focus the primary and then lock it down.

Now, if one or both mirrors departs from nominal radius of curvature by some threshold, the resulting optimum position for focus will differ. There is some leeway before the wavefront is affected to any notable degree, and I should *think* these scopes are sufficiently well executed that reliance upon the maker's recommended nominal focus position will not steer you wrong.


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Mike Harvey
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Reged: 03/01/04

Loc: Orlando, FL.
Re: CO vs. All That "Other Stuff"! new [Re: Loren Toole]
      #5609502 - 01/07/13 12:05 AM

Quote:

Quote:

Fortunately, there is a solution...
LOCK the primary in place at the exact point it should be separated from the secondary, then install a rack & pinion focuser.




Mike
I haven't followed the CO thread really carefully but your statement above seems to be a common belief among many SCT owners... the problem is, how can the correct spacing be determined easily without a heck of alot of testing? I'd guess you're proposing something like a Roddier test? Or, using the intra/extra focal patterns at different backfocus distances? All of this sound very time consuming and frankly may not be conclusive. My SCT images are often mushy, probably due to poor thermals and maybe collimation. I'd need to deal with all of that before even attempting what you're suggesting, yes?

Loren




Hi Loren...assuming your scope does not have poorly figured optics, decollimation is probably the cause of your 'mushy' images.
In my opinion collimation is the FIRST thing to check.
An "artificial star" (point light-source) is invaluable for this purpose.

If you can't get your hands on one, try finding a point-source reflection of the sun off a bright shiny object about 100 feet or more away from the scope. Trying to 'chase' a star around in the dark to do the traditional 'star test' can be extremely frustrating if you don't have much experience (you have to keep re-centering the star after each adjustment) and poor seeing can make it difficult to accurately gauge the diffraction rings.

Yes, you're right about the calculations involved in determining the proper distance between the corrector and the primary. The math hurts my head!
With a LOT of help from smarter people than me, I found that the proper spacing for my 10" was such that the focal plane (at infinity) should fall some 3-1/2" behind the backplate of the scope. Knowing this allows the proper placement of the rack & pinion focuser.

Sometimes (depending on the scope and the R&P involved) you just can't make the two reach acceptable focus at the precise point. But a relatively small difference in the optimal vs. practical placement is not nearly as important to improved images as getting that primary secured in-place and perpendicular to the light path. That primary can, and does, flop around when it's being racked up and down the internal mounting tube. If you reach a given focal point and the primary mirror is even slightly off-axis, you've just UNdone your secondary collimation efforts and induced even more error into the system!

You know we're all crazy, right? I'm just not sure if we actually DO all this stuff because we're crazy...or if doing all this has made us crazy!



Mike


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Eddgie
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Re: CO vs. All That "Other Stuff"! new [Re: pstarr]
      #5609879 - 01/07/13 10:24 AM Attachment (27 downloads)

Quote:

A SCT with perfect optics and a 30% central obstruction can never give better that 1/4 wave performance. Not that 1/4 wave performance is bad. That said, you will never find a SCT, or any other design with perfect optics.




This really isn't quite the case, and should never be offered as a "Baseline" for comparing an obstructed instrument to an unobstructed instrument without at least a nod to the more complete story.

First, the effects of the central obstruction are most severe in the middle and higher part of the MTF curve (large and medium scale detail). Once you get past the elbow, where the smallest detail is to be found on the target, there is littel effect on the image.

The computational Strehl for a 30% obstruction is not .82 as is often written, but more like .88. This is considerably better than the Strehl of .82 that .25% of pure SA would result in.

I have plotted two curves.. One if for a perfect system with a 30% obstruction (left image), and the other is for a perfect system with .25 waves of lower order spherical abberation (right image).

The colored lines are sample points that show how much contrast is lost over the perfect system at each point in the linear resulution (spatial frequency) spectrum.

At the top left, it is easy to see that the obstructed telescope is performing slightly better than the .25 wave scope, and once you get past the elbow, where the most damage is being done, it is easy to see that the obstructed telescope pulls ahead and remains ahead.

This lower right hand portion of the MTF plot represents the finest scale detail the aperture can resolve, and it is ls abundantlhy clear that not only is the obstructed instrument ahead of the .25 wave instrument, it is also ahead of a perfect unobstructed instrument.

Now when the obstruction gets to .33D, the damage at the worst part of the curve is similar to the worst sag in the .25mm instrument, but once you get past the curve, the obstruction is clearly better.

Now the problem is that for visual use, the left half of the graph tends to be more important (often referred to as the important low and mid frequencies) because to get the smallest detail that the scope can resolve large enough for the visual observer to comfortably see, the exit pupil will get small enough that it starts to work against the observer for low contrast detail.

But the camera will show it easily. For imaging the finest scale detail the instrument can resolve, the central obstructoin has no damage at all in the image, and in fact can somewhat enhance the finest detai.

This is why large obstructions are OK for imageing scopes, but not so good for visual observation, but as the chart show, the 30% obstruction is superior to .25 wave over about half of the instruments spatial response frequencies.

I will be fair though and say this... The differences are so subtle that visually, the average observer would struggle to see them.

But the camera will.

That to me makes your statement somewhat innacurate. The CO = 1/4th wave is a good approximation for visual use, but somewhat overstates the damage that a 30% obstruction does.

I do agree with your sentiment on never finding an SCT with perfect optics, but no telescope is truely perfect.

Still, in the sentiment as it was intended, I agree that his is indeed the issue with the commercial SCT. Because it it starts wtih a 33% obstruction, anything other than quite minor optical imperfections will indeed quickly drive the scope to be truely worse than .25 pure LSA, and that is the real problem. To work well, the design has to be made to a very high tolerance. This means that any SA in the instrument combined with the contrast loss from the obstruction quickly pushes the scope into a poor performance envelope. Some SA would reduce the contrast below a perfect unobstructed aperture at both the low and high frequencies, and further deepen the sag we see at the elbow in the plot.

A truely excellent 33% obstructed SCT does little evident damage to the image. A small amount of contrast is lost in the mid frequencies, but the low frequencies are little changed, and the higest frequencies are improved.

But other defects lower the contrast across the entire spectrum, while an obstruction is the only device that can actually raise the contrast at any point in the spectrum over a perfect unobstructed instrument.

Bottom line... .25 SA is worse than a 30% obstructiion... Not much, and for visual use only, it is fair to compare them, but for imageing (and I personally belive for an experienced planetary observer), the 33% obstruction is not that important. The smallest, lowest contrast details available at the target are actually enhanced in the obstructed instrument (assuming good optics).

I routinely see very difficult detail in my 32% and 34% obstructed SCTs. Both have excellent optics, and both are excellent performers.

Side by side with my 6" APO, one has to look hard to see detail in the 6" APO that is not visible in my EdgeHD 8". I say this on the forums and people are skeptical, but people that have been to my house for star parties that have done side by side comparisons are usually shocked at how close the performance is. They have been led to believe that the big CO destroys the image, but the reality is that by itself, it does not have a huge impact.

The difference though is that my EdgeHD has about the best optics I have ever seen in a reflector. Similar to the Russian MNs I have owned. I would estimate a Strehl of over .95. No defect that is easily detectable in star testing, with almost perfect SA control. Not typical of the older SCTs I have owned.

Edited by Eddgie (01/07/13 10:27 AM)


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: Eddgie]
      #5610164 - 01/07/13 12:43 PM

Quote:

I routinely see very difficult detail in my 32% and 34% obstructed SCTs. Both have excellent optics, and both are excellent performers.



Makes sense. I imagine that's true because a reasonably good scope can still produce a peak intensity of about 80% (sort of a proxy for diffraction limited performance deemed acceptable) with an obstruction near .3D. Obstruction-less scopes perform with a higher peak intensity equal to their Strehl and the result is dimmer rings.

You are correct, the MTF curves are similar for 1/4 SA and .32D. However, SA affects the wavefront and the CO adds diffraction. With added diffraction, the central disc is smaller and brighter, so their Strehl equivalents are different: .82 and about .88, respectively. The CO has less impact on the image over the entire range, as I read it, especially at the high freq end.

Edited by Asbytec (01/07/13 12:59 PM)


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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5610922 - 01/07/13 09:18 PM

I think the comparison useful as long as you are careful to note that the obstruction does no damage to the resolving power of the scope. SA does some damage, only some of which is recoverable in imaging. That is the right side of the MTF (and yes MTF is a good indicator, phase plays an insignificant part in this situation) shows resolving power even enhanced a little with respect to a perfect unobstructed scope although in practice the difference would be difficult to discern.

Strehl however has more limitations than most people realize. A 0.95 strehl scope is clearly superior to a scope of 0.85. However two scopes with the same aperture and obstruction and identical strehl can yield different results in imaging.

Glenn


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: Eddgie]
      #5611363 - 01/08/13 04:13 AM

Quote:

Bottom line... .25 SA is worse than a 30% obstructiion..




This is somewhat a side issue - but are your plots based on 0.25 SA without optimal defocus? If the only error in the wavefront is 0.25 SA, you can compensate for it almost entirely by a shift in focus. In Suiter, for example, 0.25 SA actually refers to about +1 wave of SA and -1 wave of defocus. So if you have about 1 wave of SA, you can defocus so the resulting wavefront, combining defocus with SA, has an overall P-V error of about 1/4 wave.

So I think either your plot does not include defocus, in which case it makes 0.25 SA worse than it really is, or it does include defocus, and the actual SA term is closer to 1 wave - which is a big error in the optics.

Either way - it's hard to compare two different systems based on a single number or a single plot. The higher values of MTF at the high end may pass individual spatial frequencies well, but in an actual view of jupiter's bands, for example, they could look ugly and distorted.

Frank


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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5611369 - 01/08/13 04:57 AM

The 1/4 wave in Suiter is the traditional terminology going back to Rayleigh. That is the peak to valley deviation in optical paths across the wavefront, from the ideal gaussian, which reduces intensity at the central peak to a level of 80% compared to a perfect optic.

Perhaps to avoid confusion we should state that 1/4 wave in Suiter is comparable to 0.0745wv rms for low order spherical aberration. Thats approx 0.8 strehl. Because different aberrations are distributed differently, and in real optics not in a perfectly smooth fashion, equivalences between PTV and RMS values are fairly complex.

The focus is shifted yes, and the resultant PSF and MTF should be evaluated at best focus, which it is in Suiter.

Spherical aberration is a true resolution killer, nominal obstruction is not.

Glenn

Edited by DesertRat (01/10/13 03:46 PM)


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5611374 - 01/08/13 05:29 AM

Quote:

The 1/4 wave in Suiter is the traditional terminology going back to Rayleigh.




No - it isn't, since the Seidel form of the aberration terms has taken over. Rayleigh includes defocus as a form of aberration, and he describes the impact of defocus by itself on an image. If you always speak in terms of optimal focus, then you can never have aberration due to pure defocus.

The total aberration from combined spherical and defocus is:

W = a040p^4 + a020p^2

The first coefficient, a040, is the amount of spherical aberration and the second, a020, is the amount of defocus aberration. I can point, and already have, to many texts that state that you can tolerate nearly a full wave of spherical aberration when it is compensated by defocus to keep the total wavefront error below 1/4 wave P-V. Suiter is a rare exception that glosses over the difference between the Seidel definition of each third order aberration term and the Zernike form - normally those things are kept distinct to avoid confusion. It is due to this ambiguity and confusion that I asked what exactly is being shown above - since "1/4 wave of spherical" is very different from "1/4 wave total wavefront error due to combined spherical and defocus."

You can have a given amount of spherical aberration and combine it with coma and astigmatism and defocus and end up with any crazed amount of total wavefront aberration. But the amount of spherical inherent in the wavefront remains the same - given by the coefficient on the p^4 term.

If a telescope is guaranteed to have 1/4 P-V wavefront error - the amount of spherical aberration could be much larger than this. Or it could be less and involve some mix of other aberrations. All you know is that at best focus, the wavefront will have 1/4 wave P-V total error from all the terms.

Frank


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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5611381 - 01/08/13 05:39 AM

Yes the 1/4 wave of SA we are talking about is the amount that would lower the strehl to approx. 0.80. The MTF above is using that figure, which does go back to Rayleigh.

Yes a telescope has a mixture of aberrations and all the terms do add, albeit differently. Perhaps since there is some confusion we should stick to rms equivalents, which I like anyway since they are easier to do calculations from.

Since not many here want to plod through Born & Wolf we should try to keep the explanations at a useful level, with emphasis towards practicality.

Glenn


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5611498 - 01/08/13 08:29 AM


Here is a pretty good write up of aberration theory and Seidel terms, and it shows plots of PSF's due to spherical aberration alone in 8.40. Note that the upper left image of W040 = 0.25lambda is an image of pure spherical, whereas Suiter's non-conventional figure shows SA=0.25 - and in fact corresponds to something different from 8.40 since it is a picture of 1 wave SA combined with -1 wave defocus.

I can answer my original question of "which is being shown in the figure above - 0.25 SA with no defocus, or 1 wave SA with -1 wave defocus?"

This page is not an amateur optics page and is from Wyant at the U. of AZ Op. Sci. Center. If you enter 0.25 lambda spherical alone, you will get a strehl of 0.8 and a corresponding MTF. If you enter 1 wave spherical combined with -1 wave defocus, you will also get a strehl of 0.80, and the MTF is a better match to the plot in this thread. Therefore I conclude that plot actually shows a full wave of spherical aberration combined with defocus to yield 0.25 lambda P-V total wavefront error. At paraxial focus, this same system would have had much lower strehl - around 0.09 - for the same 1 wave of spherical.

Frank


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Eddgie
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5611595 - 01/08/13 09:43 AM

The plots were done at best focus.

As for the rest, I can only say that my experience matches MTF plots farily well.

The EdgeHD 6" Vs the 6" APO, when plotted, suggests that the EdgeHD should maintian about the same contrast as the 6" APO for the finest details, and I find this to be the case.

For example, Cassini is every bit as crisp and as sharp in the EdgeHD as it is in the 6" APO. Likewise, thin band structure on Jupiter appears to be very similar to the 6" APO.

Larger, fainter festoons though, like in the equitorial band on Jupiter, don't show quite as well in the EdgeHD 8". These are larger(mid frequency) details that would be more at the center and left side of the MTF chart, and they are less easily visible in the EdgeHD 8" than in the 6" APO.

And likewise, these large, low contrast details are much more easily seen in the C14 than in the 6" APO.

These large festoons are all within the angular resolution limit of all three scopes, and are a classic (to me) example of "Mid Frequency" performance. While they are angularly large, they start with very low contrast.

The more contrast the aperture looses, the more difficult they become to see.

But my experience has been very consistent. The scopes with more clear aperture tend to show them better than scopes with less clear aperture.

As for refocusing, that might work on a point source, but I have my doubt that it would be effective on a complex extended target. Maybe. I just don't know.

But a CO does damage the image. I do not at all disagree. And maybe it does do as much damage as 1/4th wave of pure SA (I have my doubts, but don't keep a 1/4th wave scope around to compare to).

But in the overall scheme of things, the CO is easily offset by simply adding a bit more aperture.

And this is the benefit of large SCTs. It makes it possible to simply get the performence of a smaller scope using brute force and still having an affordable, compact, (relatively) light, and easy to use instrument.

But CO does damage the image with respect to aperture. I realized how bad it was the first time I compared a C9.25 to a MN61. One would think that the C9 would do better because of the 50% increase in aperture, but there was no contest.. The MN61 was blazingly good in comparison. About as close to my 6" APO as I have seen in a similar or smaller size scope.

Plotted on an MTF chart though, it was easy to see that the C9 would have had to start with perfect optics to be in the game. But the 37% obstruction I think was the major cuplrit in the C9s failure to perform better than the MN61.


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: Eddgie]
      #5611690 - 01/08/13 10:40 AM

I think your plot shows 1 wave of spherical aberration at minimum RMS focus - or -1 wave defocus. Given that amount of spherical aberration, you could focus it in other ways shown in my links above: paraxial focus, minimum rms, least square ray error, and smallest circle of confusion - i.e. there is no single best amount of defocus, and it is good to keep it separate from the problematic aberration itself, which is 1 wave of spherical. The key is that the inherent spherical aberration is fixed and you can adjust focus separate from it to alter all the main metrics: P-V, RMS, Strehl, and MTF.

Since you and other people interested in MTF often point to the high frequency stuff and how it relates to "resolution" - note that if you increase defocus beyond -1 wave (min RMS/max Strehl) you will boost the high frequency part of the MTF in exchange for the mid-frequencies. This may well be what you do when you focus in on the belts of jupiter - it's hard to say. But the amount of spherical aberration (1 wave) is fixed here, and you can alter the PSF and MTF to get the best view of a given object based on the spatial frequencies you are studying. This may end up increasing RMS and reducing Strehl - but it does boost the higher frequencies in the same way an increased CO does - if that is something you want to do.

Frank


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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5612042 - 01/08/13 02:18 PM

Best focus for a scope with low order spherical aberration (LSA) would be where the central maximum of a star is at its highest. This is often referred to as diffraction focus. A primary aberration evaluated at that point is called balanced, the balancing performed by an equal amount of defocus.

Most amateurs chase focus all night at levels that exceed the needed amount of balancing defocus due to seeing effects as well as thermal changes. In typical applications one will find a user chasing somewhere from best focus to smallest blur and back again. Operationally the user has no idea where paraxial focus is, and in any event a scope with 0.25 wv ptv LSA at either paraxial focus or marginal focus at the other end would be simply awful. Knowing the defocus term in backyard astronomy is not a useful parameter.

For some applications a quarter wave ptv of LSA is a lot. For high resolution imaging it is too much, for when the other aberration terms which are surely there are added the usage of the scope will be limited to widefield or low power use. LSA is a resolution killer. Central obstruction is not.

In the case of the SCT it is even more complicated by the fact that in all probability the scope has a minimum amount of LSA at a given wavelength. I've seen a lot of SCT's corrected in red and showing pretty severe overcorrection in blue. One of the reasons the Edge HD series seem to be star testing so well visually is that they tend to be very well corrected in green. Before the SCT users out there protest too much, I hasten to add I've seen a lot of supposedly premium refractors fail on the blue end as well.

There is no doubt from my analysis and from experience that the central obstruction effects on image quality are usually overstated. But they should be understood and the MTF displays the effect very well.

Glenn


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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5612418 - 01/08/13 06:07 PM

Another excellent thread, with more good theory than I have time to absorb in full at the moment.

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...

Of course, CATs do require attention to detail - for starters, the importance of good collimation is hard to over emphasize. That last "whisker" of adjustment can make all the difference, yet the mechanisms aren't so user-friendly to the newcomer. Furthermore, based on experience with both my CATs I note that mechanical assembly can fall short of what is needed to get the best out of essentially blameless optics. Tilted baffle tubes & primary mirrors, off centre secondarys and the like can really spoil the show. However, many users will be unable to recognise, or be unwilling to investigate & tackle these problems. I'd love to know how many good sets of optics have been compromised by non optimum assembly - could this have contributed to some of the received wisdom regarding CAT performance? As the writer and broadcaster Sir Patrick Moore would have put it "well, we just don't know", but I have my suspicions.

What I do know is that when I got my C8 properly "sorted" to the best of my abilities - ensuring that everything was coaxial, squared-on and collimated - I was amazed by its planetary performance. This was quite different to its "as received" capability, despite seemingly succesful attempts to collimate with the secondary mirror screws. My Orion 127 Maksutov also benefitted from similar treatment, if not to the same degree.

I've rambled on long enough, perhaps too much, but will finish in saying that good execution of a design is as important as a good design.


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: Ed Holland]
      #5612926 - 01/08/13 11:29 PM

Yea, this is an interesting thread, especially the discussion between Glen and Frank. A lot of that is difficult to grasp, at least the importance of it. Yes, all aberrations such as seeing, collimation, cooling, and everything have to be absolutely minimal if not perfect to squeeze that bit of performance from a scope. And any amount of de-focus from best diffraction focus counts, too.

What's interesting to me is the idea an obstructed scope has a smaller Airy disc that is a bit brighter than it would normally be if it's intensity were spread over 1.22 Lambda/D. This, in my understanding, is what differentiates CO diffraction and spherical aberration. This is what causes an obstructed scope to exceed a perfect unobstructed aperture on very small scales (near the radius of the Airy disc.) And it is what allows, under very minimal induced aberrations, to actually exceed Raleigh and Dawes limits by about half an arc second.

The peak intensity is a bit higher for an obstructed scope with good correction than with one with 1/4 wave SA. SO, yes, a scope with an aberrant Strehl of 0.95 can be very good while the CO reduces peak intensity (not aberrant Strehl) further to about 80% (a peak intensity comparable the Raleigh limit) or less depending on the combined affects of both the wavefront error and added diffraction.

The scale of these effects seem to be over rated for general viewing because we're talking scales to about 4x the Raleigh limit. But, for critical viewing, they can be important. On Airy disc scales, this is where obstructed scopes rule. On slightly larger scales is where unobstructed scopes rule with peak intensity (nominal, system Strehl) equal to their aberrant Strehl. CATs do not enjoy this trait.

But, we're focused on the CO and not the "other stuff" such as veiling glare and scatter in CAT optics (including reflectors), which happen to be obstructed.


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siriusandthepup
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Re: CO vs. All That "Other Stuff"! new [Re: Mike Harvey]
      #5613042 - 01/09/13 01:16 AM

I have pretty much the same opinion as Mike on the SCT's.

Optical quality rules and is THE most important factor.

Now I've heard the argument about the 1/4 wave derating for the 30% CO and it's overblown. Let's discuss it. In the case of the 10" SC with 30% obstruction, is it as good as a 10" perfect APO? No. Obstructed scopes will always take a performance hit for the obstruction. Do you really want to compare it to a 10" APO? Get real! A 10" SC with a 30% CO will only perform about as well as a 7" perfect APO. I can live with that...


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5613087 - 01/09/13 02:21 AM

Hi Norme-

I haven't been talking specifically about CO stuff but more to encourage formal terminology in these discussions, and references to optics textbooks. The nomenclature has been honed over centuries to avoid some of the ambiguities that come up in these discussions. I think there is over confidence in going by a few metrics of a system performance, when things like Strehl and MTF are meant more as guides and figures of merit rather than hard performance metrics that allow systems to be ranked against each other.

When someone looks at an object in an eyepiece, the resulting image involves the object itself, the optics, the perceptual process, and the personal preference for choice of focus. Much of that is not captured in fixed metrics of the optical system alone, but it's all playing a role.

I am always amazed at how different jupiter looks at different powers in the same telescope. If I put a big image of jupiter on the wall and view it from close or far, I don't see much change in detail - but with different eyepieces and magnfications, the colors and spatial frequencies all have different impact - and I always adjust focus to bring out optimal (for me) detail. You could say that at low power I bias the focus so that MTF emphasizes the mid-range, since mid-range is higher frequency at low power; and at high power I bias it toward the high frequency part. But either way - there is a lot going on just in changing powers with a given telescope - let alone comparing two with different CO's. And in terms of the MTF or Strehl of the OTA itself at "best" focus - nothing should be changing at all.

Frank


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Jon Isaacs
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5613159 - 01/09/13 05:35 AM

Quote:

What's interesting to me is the idea an obstructed scope has a smaller Airy disc that is a bit brighter than it would normally be if it's intensity were spread over 1.22 Lambda/D. This, in my understanding, is what differentiates CO diffraction and spherical aberration. This is what causes an obstructed scope to exceed a perfect unobstructed aperture on very small scales (near the radius of the Airy disc.) And it is what allows, under very minimal induced aberrations, to actually exceed Raleigh and Dawes limits by about half an arc second.




It is my understanding that the central disk is slightly smaller than it would appear in scope without a CO because there is more energy in the rings and less energy in the central disk. One thing to remember is that hidden inside every scope without a central obstruction is a scope with any sized central obstruction one desires.

Jon


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: Jon Isaacs]
      #5613183 - 01/09/13 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-optics.net/obstruction.htm


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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5613214 - 01/09/13 07:27 AM Attachment (17 downloads)

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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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5613365 - 01/09/13 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.

Edited by Asbytec (01/09/13 09:41 AM)


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maknewtnut
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Re: CO vs. All That "Other Stuff"! new [Re: Mike Harvey]
      #5613501 - 01/09/13 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).


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Darren Drake
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Re: CO vs. All That "Other Stuff"! new [Re: maknewtnut]
      #5613732 - 01/09/13 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.

Edited by Darren Drake (01/09/13 02:54 PM)


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Joe Cepleur
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Re: CO vs. All That "Other Stuff"! new [Re: Ed Holland]
      #5613778 - 01/09/13 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:

Quote:

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!


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5613907 - 01/09/13 03:12 PM Attachment (13 downloads)

Norme wrote:
Quote:

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

Edited by DesertRat (01/09/13 03:47 PM)


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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5614476 - 01/09/13 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.


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: GlennLeDrew]
      #5614655 - 01/09/13 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.

Edited by Asbytec (01/09/13 10:53 PM)


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5614786 - 01/10/13 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


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: GlennLeDrew]
      #5614909 - 01/10/13 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


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freestar8n
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5614911 - 01/10/13 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


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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5615128 - 01/10/13 09:43 AM

Quote:

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.


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Re: CO vs. All That "Other Stuff"! new [Re: Eddgie]
      #5615190 - 01/10/13 10:25 AM

Quote:

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!"


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Re: CO vs. All That "Other Stuff"! new [Re: Joe Cepleur]
      #5615669 - 01/10/13 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.org/wiki/Contrast_(vision)

Glenn


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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5615680 - 01/10/13 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

Edited by DesertRat (01/10/13 03:44 PM)


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Alph
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5615765 - 01/10/13 03:48 PM

Quote:

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.

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Re: CO vs. All That "Other Stuff"! new [Re: Alph]
      #5615834 - 01/10/13 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


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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5615848 - 01/10/13 04:37 PM

Quote:

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.


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Re: CO vs. All That "Other Stuff"! new [Re: Alph]
      #5615912 - 01/10/13 05:16 PM

Quote:

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


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cn register 5
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5615937 - 01/10/13 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


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Re: CO vs. All That "Other Stuff"! new [Re: cn register 5]
      #5615951 - 01/10/13 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


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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5617641 - 01/11/13 05:37 PM

Quote:

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.org/wiki/Contrast_(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.


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Re: CO vs. All That "Other Stuff"! new [Re: Joe Cepleur]
      #5617734 - 01/11/13 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.


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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5618500 - 01/12/13 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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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5618529 - 01/12/13 07:20 AM

I own two unobstructed telescopes one a 20inch f 8 for 4 years and a 17inch f 9 and I know there is a improvement in the image .One only needs to look at the HST images the central obstruction effects are easy to see .The effect on long focus newts is small but there I think a .3 CO =1/4 wave error . All good telescopes work great not saying anything bad on any design .

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Re: CO vs. All That "Other Stuff"! new [Re: kfrederick]
      #5618656 - 01/12/13 09:25 AM

Frank, you always make an interesting argument. The MTF basically puts contrast onto the focal lane in a linear fashion in accord with diffraction. How we observe it is, apparently, non linear. But, with average vision, normal color perception, and normal contrast sensitivity most can expect to see pretty much the same thing. That is, pedagogically, at very small scales expect some higher resolution and at slightly larger scales expect the brighter rings to wash out some contrast. Of course, that can change from person to person or even between scotopic and photopic vision. But, on the focal plane just as in any linear imaging device, the MTF and PSF describe what's there well enough for amateur observing purposes, IMO.

I do understand how defocus can improve the image with some amount of LSA, but I cannot fathom how 1 wave can possibly produce a Strehl of 0.80. I am not saying your wrong, just not sure how that can be. Seems 1 wave SA would put so much light into the rings that peak intensity should be far less than 0.80 Strehl even at best focus. Maybe it depends on where you draw the reference sphere, I apply it at best focus not Gaussian focus.

Anyway, it does seem application of the MTF is important. If you're imaging a white picket fence from across the street, it should be no problem. Imaging fine print with a photo copier, maybe. Observing close, unequal doubles seems to obey the same contrast as planetary viewing because they are on the same scale. If it's not on the focal plane, it cannot be seen by anybody.


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Re: CO vs. All That "Other Stuff"! new [Re: Starman1]
      #5618932 - 01/12/13 12:01 PM

Quote:


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.




Amen Don!


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Re: CO vs. All That "Other Stuff"! new [Re: maknewtnut]
      #5618984 - 01/12/13 12:29 PM

Quote:

Quote:


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.




Amen Don!




That ought to be graven into a stone tablet somewhere, preceded by "Thou Shalt..." .


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Re: CO vs. All That "Other Stuff"! new [Re: Rick Woods]
      #5619103 - 01/12/13 01:49 PM

In my neck of the woods, transparency and seeing seems to be more of a factor than the CO
With a 10" SCT, what level of seeing/transparency does it require to get to the point that the CO makes a difference?
It's one thing to look at all the math and plots based on a magical perfect scenario, but the real world in my back yard seems to throw me the biggest curve.


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Re: CO vs. All That "Other Stuff"! new [Re: shawnhar]
      #5619115 - 01/12/13 01:55 PM

One can't argue the physics of the MTF. However, execution of an optical system, combined with the ability of a system to approach it's potential is 'what it's all about'.

As for CO, IMHO it plays a bigger role in consistency of high mag performance than anything else. When seeing isn't ideal, larger obstructions seem to play a synergistic role in limiting a system's performance (ie, limiting it's potetial).


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5619156 - 01/12/13 02:16 PM

Quote:

How we observe it is, apparently, non linear. But, with average vision, normal color perception, and normal contrast sensitivity most can expect to see pretty much the same thing.




The human eye response to light intensity is approximately base 10 logarithmic. If you plotted modulation/contrast in a base 10 logarithmic scale, then the MTF graph would be mostly flat, and the difference between %30 and %50 obscuration would be barely noticeable. Maybe Rat could generate a couple of graphs for comparison in a base 10 logarithmic scale.


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Re: CO vs. All That "Other Stuff"! new [Re: maknewtnut]
      #5619181 - 01/12/13 02:30 PM

Quote:

One can't argue the physics of the MTF. However, execution of an optical system, combined with the ability of a system to approach it's potential is 'what it's all about'.

As for CO, IMHO it plays a bigger role in consistency of high mag performance than anything else. When seeing isn't ideal, larger obstructions seem to play a synergistic role in limiting a system's performance (ie, limiting it's potetial).




After owning several sct and trying to get high resolution planetary views, "execution" of these systems seemed like a good idea.


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Re: CO vs. All That "Other Stuff"! new [Re: shawnhar]
      #5619184 - 01/12/13 02:31 PM

Well, sure, seeing trumps everything. But, your scope is always transferring contrast at all times according to the conditions its working with. That's what scopes do.

Remember, seeing can be modeled using the MTF, too. And each aberration, induced like seeing, cooling, collimation, and focus, are added to the MTF of the CO and inherent aberrations. So, each time one of those variables increased, the contrast transfer worsens. Even though one might be much more significant, one does not trump the other. Yes, seeing is significant (and complex), but each affect adds to the others.

In my neck of the woods, seeing is normally very good in a 6" aperture. With moderate temperatures, cooling is never a problem. And great seeing allows essentially perfect collimation and, best I can tell, perfect focus. Those are the jaw dropping moments when your scope is performing close to where it should be hampered only by the obstruction and inherent aberrations. So, induced aberrations are minimal at worst. In this case, and when doing high power, critical observing (such as very tight and unequal double stars and fine planetary detail) the CO matters somewhat.

Still, the affect is over relatively small scales for point sources (Airy disc scale) and a bit of contrast fall off on extended objects (first ring out to about 4x Raleigh) that can be seen under the best conditions.

For example, the Dawes limit for a 150mm clear aperture is 0.77" arc. My 150mm obstructed aperture has split 7 Tau at (as reported) 0.74" arc with a clear fall off in contrast between both stars just as MTF theory predicts (preliminary, anyway, higher spacial frequency above that of an unobstructed aperture.) It might go deeper, but I have not found a suitable pair to split below that (other than 72 Pegasi elongated at 0.57" arc.) If seeing were to "add" additional contrast transfer problems below some figure, it would never accomplish anything near that. I probably would not worry much about a CO, either.

(But, please don't ask if removing the CO will improve the image in bad seeing, cuz I dunno. Maybe. )


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5619204 - 01/12/13 02:46 PM

Quote:

For example, the Dawes limit for a 150mm clear aperture is 0.77" arc. My 150mm obstructed aperture has split 7 Tau at (as reported) 0.74" arc with a clear fall off in contrast between both stars just as MTF theory predicts (preliminary, anyway, higher spacial frequency above that of an unobstructed aperture.)



MTF applies to extended objects only. MTF does NOT describe point sources.

BTW The Dawes limit is off the MTF chart anyway.


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Re: CO vs. All That "Other Stuff"! new [Re: Alph]
      #5619346 - 01/12/13 04:04 PM Attachment (13 downloads)

Quote:

MTF applies to extended objects only. MTF does NOT describe point sources.

BTW The Dawes limit is off the MTF chart anyway.




Alph, neither statement is correct. Raleigh is 0.82 and Dawes ~ 0.97. The MTF describes diffraction of exactly that: point sources (either singularly or in infinite numbers.)

Here's a rough scale of things, even though both obstructed and unobstructed are normalized to 1. Really, obstructed is compressed horizontally by a factor of (1 - CO^2).

"In effect, an aperture D with central obstruction oD acts as a larger aberrated aperture, D/(1-o2), with its Strehl-like number (in the sense that it indicates both, normalized peak diffraction intensity and relative loss of energy to the ring area) given by (1-o2)2."

http://www.telescope-optics.net/obstruction.htm

Credit for the illustration (I added the Airy disc roughly to scale so the first ring roughly corresponds to the huge drop off. And you can even see how the CO intensity peaks closer to 1, meaning the Airy disc is smaller.) Pretty small scale, really, when working with tight doubles. Now, imagine infinite point sources scattered over Jupiter's surface and you can see the effect of additional light in the first ring, as a minimum.

http://www.handprint.com/ASTRO/ae3.html#centobs

Edited by Asbytec (01/12/13 04:15 PM)


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5619397 - 01/12/13 04:34 PM

Norme,
That is one cool looking graph. Thanks! Very clever and well done. Yes you are correct Dawes is clearly on the graph, although barely, as I showed earlier. And thanks for the reference to Vlad's site, his site is a treasure, and I hope he publishes a book someday.

Frank & others,

Optics is a complicated subject filled with approximations, conventions, regions of validity, criteria and a host of special conditions. It has a long and colorful history. Of all the mathematics one has to master as a student of physics it ranks up there in difficulty with some of the more challenging subject areas.

The convention of describing wavefront error referenced to an ideal spherical wavefront is not just found in Suiter but scores of other books. It is also used by those that make optics for telescopes, for example Texereau, Ingalls, and many others. Amateur astronomers, professional astronomers in the field of binaries (like Couteau), reference aberrations observed in terms of what they see as quarter wave spherical, eighth wave coma, etc.

The figure of 1.0 wave you quote is the aberration coefficient of balanced spherical Ai=As(p^4-p^2) for a strehl of 0.8. But the same term is 0.25 for spherical alone Ai=As*p^4. And the wavefront error for both at strehl 0.8 is 0.25. See Mahajan for example pg 85 of "Aberration Theory Made Simple" 2nd edition. I love that title!

Can we at least agree that a scope with no error other than 0.0745wv rms low order spherical (yes I know this is an unlikely case) would yield a strehl of 0.8? If not, then well, I have nothing to add. I choose to use the convention used for many years that amateur astronomers can relate to and that people that make telescopes aim for and see in their tests.

As far as MTF, I never wrote or implied that MTF was "all-encompassing". In fact what I said was that in some contexts it makes no sense as in coherent imaging, significant phase shifts, some fields of microscopy, etc. And obviously when you add an eyepiece or barlow, a detector or the eye, all the MTF's of each component are essentially multiplied.

The real MTF is a measured data set, scanning the PSF for example and taking the transform or simply scanning a test image. This is what the Zeiss firm did for many years. Zeiss also published MTF's with their lenses combined with the best B&W films of the time.

The calculated MTF is for purposes of indicating tendencies, not indicating quantitatively measured results. It does take some investment of time to appreciate what the MTF provides when applicable. Also it should be noted the MTF's I supplied assumed a vertical banded test chart. For spherical aberration or spherical obstructions that's ok. For astigmatism (or any aberration with an angular component like coma) however you have to add orientation data. Hopefully what I posted had some educational value, if not then I failed, not a singular event I must say!

Glenn

Edited by DesertRat (01/12/13 07:34 PM)


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5619769 - 01/12/13 08:25 PM

Quote:

neither statement is correct. Raleigh is 0.82 and Dawes ~ 0.97. The MTF describes diffraction of exactly that: point sources (either singularly or in infinite numbers.)




I stand by my statements. I should have chosen my words more carefully though.
The MTF in the last 3% of the frequency range (Dawes limit) rapidly approaches zero and is equal to the MTF of an unobstructed aperture. There is no increase or decrease of contrast in that range that could be attributed to aperture obstruction.

A point source becomes a PSF in the image. The PSF is the impulse response of an optical system. OTF (Optical Transfer Function) is Fourier pair of PSF. MTF is the modulus of OTF. However, the MTF is interpreted as the ability of an optical system to transfer spatial modulation (contrast) of an extended object to the image (focal plane). A source point has only one light intensity level.

All, check out this cool MTF and PSF demonstration implemented in webMathematica.


Quote:

Here's a rough scale of things, even though both obstructed and unobstructed are normalized to 1. Really, obstructed is compressed horizontally by a factor of (1 - CO^2).




I was referring to contrast plotted in a logarithmic scale (human eye response). See Fig. 3.6 in Suiter 2nd edition. It's a wash


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Re: CO vs. All That "Other Stuff"! new [Re: Alph]
      #5619910 - 01/12/13 10:13 PM Attachment (10 downloads)

Alph,

Thanks for the Wyant calculator link, I had seen that before but had not saved it.

At Dawes criterion the MTF does not clearly describe whats happening because it is bunched up over there and frankly was not intended to. I hasten to add the Dawes criteria is normally described for an unobstructed scope and contains the 1.22 factor we all grew up with. For obstructed scopes the distance to the first Airy minimum is somewhat smaller and becomes essentially unity at 50% obstruction.

A blown up MTF shown here indicates some real added contrast at the Rayleigh line for these high spatial frequencies. Actually seeing it and proving the case is another matter. Atmospheric seeing normally prevents demonstrating this effect visually, although I think it could be done with a camera and unbiased processing and analysis. Since the laws of diffraction have been proved countless times on the bench without a seeing problem, I'll leave that experiment to a student!

For a point source it is often better to examine the actual PSF or blink/animate them as I had shown previously in this thread. If one can appreciate the concept that an image is the 'smearing' or convolution of the object with a PSF then it becomes clearer.

Glenn


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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5620044 - 01/12/13 11:59 PM

Quote:

The MTF in the last 3% of the frequency range (Dawes limit) rapidly approaches zero and is equal to the MTF of an unobstructed aperture. There is no increase or decrease of contrast in that range that could be attributed to aperture obstruction.




Thanks for clarifying, I don't totally disagree.

Well, yes, that's true. But the contrast at the Dawes level is "off the chart" at a higher spacial frequency than normalized at 1. In the charts shown, both obstructed and unobstructed aperture maximum spacial frequencies are normalized to 1. In reality, an obstructed aperture has a maximum spacial frequency of about D/(1-o^2) at zero contrast. So, the curve for an obstructed aperture actually hits zero contrast a bit beyond the normalized 1.00 max frequency. That would be the improved contrast (higher resolution) attributed to an obstruction. Again, the curves only collapse at 1, seemingly becoming equal at that point, because they are both normalized for max spacial freq. An obstructed scope has a higher max spacial freq.

Excellent comments, Glenn. Thank you for making a few things more clear.
Quote:

Optics is a complicated subject filled with approximations, conventions, regions of validity, criteria and a host of special conditions.

...in some contexts it makes no sense as in coherent imaging, significant phase shifts...

The real MTF is a measured data set...

For astigmatism (or any aberration with an angular component like coma) however you have to add orientation data...

Dawes criteria is normally described for an unobstructed scope and contains the 1.22 factor we all grew up with. For obstructed scopes the distance to the first Airy minimum is somewhat smaller and becomes essentially unity at 50% obstruction.



As I understand it, amateur apertures are, for all intents and purposes, coherent in a range near peak sensitivity. And since phase is responsible for intensity distribution, it is at least somewhat accounted for. One can model asymmetrical aberrations by rotating them to the point of maximum affect, but it would be difficult to capture the aberration fully. The CO is symmetrical, and SA is assumed to be, as I understand it.


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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5620243 - 01/13/13 07:39 AM

Quote:

The figure of 1.0 wave you quote is the aberration coefficient of balanced spherical Ai=As(p^4-p^2) for a strehl of 0.8. But the same term is 0.25 for spherical alone Ai=As*p^4.




Huh? The W040 term is the Seidel term for spherical aberration alone, and it can have a value of 0.96 lambda and still be diffraction limited, with defocus. That's why in the Wyant aberration tool I cited earlier, when you enter 1 for the Spherical aberration and -1 for the defocus, you get an acceptable wavefront. If the spherical aberration is "really" 0.25 - why does he want us to enter 1? This is all aberration theory 101, and I don't find the math hard at all - especially compared to nonlinear and quantum optics.

As an example - how much spherical aberration did the HST have when it was launched? Here is a nice description by Wilson. He draws a simple diagram and demonstrates that the surface error amounts to having the edge flattened by 2.17um, which means the spherical aberration is 4.34 microns. That corresponds to the departure of the wavefront from the Gaussian sphere at the edge, and across that wavefront it will vary as the r^4. Either way, the Seidel wavefront error, or departure from the Gaussian sphere, has both a coefficient of 4.34 um, and a maximum value of 4.34um across the surface. You mentioned earlier that you calculated relative to a Gaussian sphere - albeit a shifted one - but that makes no sense since there is only one Gaussian sphere, and it is the paraxial one - and that is what Wilson uses as the reference.

Separately, Roddier (Appl. Opt. 1993) reported the spherical aberration of the HST with, "The amplitude of the spherical aberration term was estimated to be -0.294-um rms..." The fact that he doesn't just say "-um" but "-um rms" means he is measuring departure from a mean surface and is implicitly including defocus and the meaning is fairly clear, if awkward since it is unusual to place a negative value on an rms. But the context is clear enough, and one can think of it as a net rms error at min rms focus, or as an inherent flaw in the wavefront with r^4 dependence that can be largely cancelled by -r^2 defocus.

The rms value is related to the w040 spherical aberration term by a factor of 1/(6*sqrt(5)).

Unfortunately a lot of optics and aberration theory has different conventions and it isn't always clear which is being used. As Wilson says, "The above figures reveal how
essential it is to define exactly what definition
is being used, otherwise serious
confusion results." In amateur astro there is total confusion over RMS vs. P-V, and even a blanket disregard for aberration theory by including coma as a "field curvature" term. I think it's important, and clarifying, not to confuse the Seidel forms with the Zernike polynomials - particularly when discussing a fixed amount of spherical aberration combined with varying defocus and its impact on MTF.

How bad is an f/9 Newtonian with a spherical mirror? Well, it has almost a full wave of spherical aberration due to the departure of the sphere from a perfect paraboloid, but with defocus the resulting wavefront has lambda/14 rms, yielding a Strehl of 0.8 - even though the wavefront arriving at the image plane is almost a full wave off from the Gaussian sphere.

When I plug such a system into Oslo, I get 0.95 waves for the Seidel w040 spherical aberration term. When I plug that same value into the Wyant tool, where it says "spherical", I get the same result - and a Strehl of 0.8.

Frank


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5620274 - 01/13/13 08:14 AM

Quote:

As I understand it, amateur apertures are, for all intents and purposes, coherent in a range near peak sensitivity. And since phase is responsible for intensity distribution, it is at least somewhat accounted for.




Norme - I'm sorry but statements like these really need to be backed by a good reference - either a textbook or journal article. There are many amateur write ups on these topics that make no reference to literature - and I don't know what they use as a basis. On topics such as Fourier optics and its suitability to visual observation in low light near the diffraction limit, at the least you would need to cite a text on Fourier optics - and it is even more challenging since it also folds in optical physics, in terms of coherence, biology, in terms of the eye response, and psychology, in terms of the final perception.

I regularly cite relevant texts and I wish others would also. I have cited these before but I will try again.

Here is Gaskill on MTF:

"The characterization is incomplete... Loss of phase information can be quite significant because the effects of phase distortion are frequently more severe than amplitude distortion."

On coherence and MTF:
"... caution is once again in order for incoherent imaging situations. Light emitted from an incoherent source becomes partially coherent as it propogats, and may invalidate the assumption that each of the intermediate images behaves as an incoherent object for the following system."

This means that the whole basis of Fourier imaging falls apart and you can't think of it as simply the product of individual MTF's. This isn't due to *phase* but to partial *coherence*. It is a separate problem.

People keep talking about how the MTF is "physics" - but it is actually more engineering stripped of the physics that makes it complicated - which involves coherence. General landscape photography doesn't push these issues as much as amateur astro at the diffraction limit, so astro has to be even more careful.

Holst/Lomheim in "CMOS/CCD sensors and camera systems": "An image where the MTF is drastically altered is still recognizable, whereas large [phase] noninearities can destroy recognizability."

More specifically on topic, here is Shannon "Art and Science of Optical Design" on the role of central obstruction and MTF:

"The obscured-aperture OTF shows an apparent increase in contrast for high spatial frequencies as the obscuration is increased. Although this effect certainly does occur, it is a change in contrast, not in total signal level... In cases where obscured apertures must be used, the loss of total signal must be considered in system analysis."

And - I have already cited Rutten on the role of changing brightness on the effective MTF of the eye.

If you have other references either in texts or journal articles I'd be happy to look at them.

Frank


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5620472 - 01/13/13 10:40 AM

"Since, according to Van Cittert-Zernike Theorem, light arriving from stars is coherent in amateur-size telescopes, as long as it is near monochromatic, it is an interesting question how much this coherence factor, combined with the coherence-lowering polychromatic spectrum and OPD differential between two close stars influences their actual resolution limit in the field."

http://www.telescope-optics.net/telescope_resolution.htm
http://home.myfairpoint.net/vzeeg3o2/id4.html

"For photopic eye sensitivity, there is little difference between monochromatic and polychromatic MTF."

"At any given frequency, MTF is a ratio of the output (image) to input (object) modulation amplitude. Mathematically, it is a Fourier transform of the aperture's PSF (more specifically, it is an integrated sum of the PSFs for every point over its intensity distribution profile, i.e. convolution of object's Gaussian image and aperture's PSF)."

http://www.telescope-optics.net/mtf.htm

The statement on phase was inferred from the presence of the diffracted pattern for a perfect optic and an aberrant one. The convention is to rotate the MTF to the angle (on the pupil) of maximum phase.

"Contrast transfer function alone shows the efficiency of contrast transfer from the object to its image for a single orientation in the aberrated image, normally that along the axis of aberration."

"Still, despite the MTF being standardized to a single object form sample and brightness level, it is considered to be a reliable general indicator of the effect of wavefront aberrations - or any other factor affecting wave interference in the focal zone - on image quality."

http://www.telescope-optics.net/mtf.htm

You make great points, Frank. I read the references (links) you post (reading about the Hubble after this.) Most of what I say is studied, processed and regurgitated from credible sources, too, to the best of my ability to understand (as I often cite), interpret, and convey it.

The bottom line is, there is a fall off in contrast with a CO and "all that other stuff." Whether or not anyone can see it depends on so many factors, but it is there. And whether one wishes to use MTF or another model is up to them. I lay my hat on the reference above that states, for our purposes in amateur sized (and quality) scopes, the MTF is a useful tool to discuss aberration and interference.

It is not perfect description of the detector (eyeball or CCD chip) but it describes pretty well what is on the focal plane. I see what I see, others see what they see, and a chips see what they see. The entire subject can become so complex, for example discussing infinite emitters on the wavefront and the resulting phase, that no discussion can occur on any level.

Anyway, it's a great discussion. I know what I need to know, at the moment, and am exploring, "...OPD differential between two close <unequal> stars influences their actual resolution limit in the field." <Insert is mine.> So far, it seems pretty consistent with the MTF/PSF (visual observation in excellent seeing.) I'll leave it to others to decide what they need or want to know.

Some easy reading here...
http://www.handprint.com/ASTRO/ae1.html


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5620681 - 01/13/13 12:25 PM

Hi Norme-

For an in-depth topic like this I encourage references to textbooks and journal articles as I have provided. If you are interested in these topics, and you appear to be, I recommend Linear Systems, Fourier Transforms, and Optics by Gaskill. Since people were citing Mahajan, I think Gaskill was Mahajan's thesis advisor - and I believe Goodman was Gaskill's. Anyway, it's a standard text on Fourier optics and is often cited. For coherence stuff, there is Born and Wolf.

Frank


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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5620907 - 01/13/13 02:21 PM

Yes, thanks, Frank. Living abroad, often good reference material is difficult to come by - shipping can be expensive, no references to peruse living in the sticks. So, I rely heavily on what resources are readily available. I have some books on order to pick up when returning to the US next month. I will look over those you reference. As you know, what sparked my interest 2 years ago and since was star testing my scope, then later that monster effective aperture thread.

But, in closing, I do have to say that observations in better than average seeing are pretty much consistent with what MTF suggests, if imperfectly. Namely, reduced diffraction effects improving my CO ratio from 37% to ~28% at full aperture (yea, I did the unthinkable...:)), and splitting stars /reported/ at below Dawes with noticeable contrast between the peaks. No immediately apparent improvement in planetary contrast, however, there may have been some. All of this is pretty much consistent. I am not an MTF crusader, but I do understand what it's telling us.

You are correct. You can have 1 wave PV at paraxial focus and, with defocus, correct to 1/4 PV at best focus. But we do not focus at paraxial, we add defocus aberration when observing. That is where the curve above was drawn.

By the way, reading the Hubble link above, it's apparent to me Nelson was at smallest blur to get his 100% "geometric" light figure within 1.5" arc. I am sure the previous 70% measurements were at best focus with the correspondingly larger blur radius. And he seems to imply half wave of error in red light, which is probably closer to the reported error at 5500 angstroms. There must be a typo, he gives longitudinal error at 40mm. He must mean microns, and without doing the math that may explain Suiter's report of 1.7 PV at Gaussian focus.


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5620923 - 01/13/13 02:29 PM

Quote:

But, in closing, I do have to say that observations in better than average seeing are pretty much consistent with what MTF suggests, if imperfectly. Namely, reduced diffraction effects improving my CO ratio from 37% to ~28% at full aperture (yea, I did the unthinkable...:)), and splitting stars /reported/ at below Dawes with noticeable contrast between the peaks. No immediately apparent improvement in planetary contrast, however, there may have been some. All of this is pretty much consistent. I am not an MTF crusader, but I do understand what it's telling us.




Hi Norm-

Thanks - I really value reports at the eyepiece coupled with interpretations. I am not anti-theory at all - but when a system is as complicated as I think this topic is - I like to go by observations first, backed by theory - rather than just go by theory.

Thanks,
Frank


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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5620974 - 01/13/13 02:49 PM

Cheers, Frank. You made me brush up on LSA.

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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5621371 - 01/13/13 06:12 PM

Frank,

Mahajan shows images of PSF's for balanced spherical aberration As(p^4-p^2) in his book noted earlier. They match pretty closely to what Suiter shows for 0.25wvPTV given As = 1wv. Mahajan shows (As=1) == (Wp-v=0.25) for balanced spherical aberration in table 8-2 pg 85 in book referenced.

I think it clear you are speaking of a coefficient. I should have realized this by noting you don't say 0.95wv PTV but just 1 or 0.95 wave. My code aberrates the wavefront with components given in waves rms or they can be alternately set to PTV values. I prefer this method as it corresponds to what the wider community of amateurs and telescope makers are familiar with.

The reference sphere I referred to above probably was not made clear, a drawing could help but my skills there are limited. I reference the diagram fig 1.2 in Suiter as an alternative.

My references to the quarter wave criteria go back to Rayleigh. He wrote that performance begins to degrade when the total wavefront error exceeded 1/4 wv of yellow-green light. For this description I can cite the following, they are not Phys Rev but for the community here of amateur astronomers useful:

Ceravolo et. al. "Optical Quality in Telescopes" , Sky & Telescope March 1992 pg253
Texereau "How to Make a Telescope" 1951 , republished 1984 Willmann-Bell Inc.

I understand you might not like their treatment, or Rayleigh, or Suiter's, but I would argue they are more valuable for our purposes here than Goodman (from which I used to code angular spectrum methods for microscopy applications), Gaskill etc. I think it important to note that Suiter is an experimental physicist, not inclined to mislead the community. The scrutiny his work has received far exceeds that which a lot of professional journals provide.

It would be useful to focus (!) on 2 questions:

1) Does a Strehl ratio of 0.8 result from an aberration of approx sigma = lambda/14 ?

2) Given a sigma of 0.0745wv rms what is the corresponding PTV error for low order spherical ? Assume any approximations or qualifications as you see fit.

I'd like to focus on those 2 questions, and maybe we can clear this all up. Later we can discuss coherence as it applies to standard backyard astronomy!


Norme,
Thanks for the link to Vlad's work on coherence as it relates to telescope resolution. I'll have to review that!


General audience (are you still here? )

On MTF
A calculated MTF does a decent job of describing obstruction, effects of smaller amounts of low order spherical and astigmatism (if careful to include orientation data). However for coma it is not that useful, since the OTF has a significant imaginary part in that case. Also for very large amounts of defocus it does not apply well. In both those instances contrast reversal is possible, the phase portion is too large to ignore.

Glenn


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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5622085 - 01/14/13 04:03 AM

I am referring to third order spherical the same way Oslo, Wyant, Wilson - etc., refer to it - as the wavefront discrepency from the Gaussian sphere. It is both a coefficient and an actual distance you can see. For the Hubble telescope, it is about 4.3 um, or 8 waves at 0.5um lambda. In Wilson's write up - he is not referring simply to an abstract coefficient - he is measuring something in a figure. I can only conclude you think he is wrong to say the HST has 4.3um spherical aberration.

If someone says they have a telescope with an overall wavefront rms of lambda/14 I would deduce they are referring to the rms measured relative to diffraction focus, and I would conclude that if the only aberration is spherical, then they could have up to 0.96 waves of spherical.

If they said they had about a full wave of spherical based on an interferometry report, I would tell them it could still have a Strehl of 0.8 since defocus would compensate for most of the aberration.

If they said it had lambda/14 rms, again I would assume they mean at diffraction focus, and if the only aberration was spherical, I would conclude they have about 1 wave of spherical, and the P-V error would be 1 wave at paraxial focus, but about 1/4 wave at diffraction focus. If the lambda/14 is measured at paraxial focus, I would say they had very good optics since an adjustment of focus would take it down further.

Regarding "what Rayleigh said" - I spent some time on this a while ago actually reading his papers and realized that, in his own words, he regarded 1/4 wave as a limit early in his publications, but later he did empirical measurements and concluded the true limit is 1/2 wave. This is an example of why I think it's important to refer to primary sources - particularly when referring to what someone was thinking in the past. There is no question people refer to the Rayleigh 1/4 wave rule, and he did allude to that in his papers - but later he measured how much error was allowed before it was noticed in an image, and concluded it was 1/2 wave.

In Rayleigh's experiment, he used defocus as an aberration and measured how much he could tolerate before he noticed the loss of image quality. That is exactly in line with the way I regard defocus - as a separate aberration term that can be varied independent of an intrinsic amount of third order aberration. I disagree with his conclusion that it's about 1/2 wave though - and would put it more at 1/4 wave, P-V.

I did not cite phys. rev. letters - I cited optics textbooks and journal articles by people well known in the optics community. Since the discrepancy here involves convention - it's important to cite people in optics rather than physics, particularly when they are self taught.

Frank


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Re: CO vs. All That "Other Stuff"! new [Re: freestar8n]
      #5622290 - 01/14/13 09:03 AM

I get the feeling you are both correct in the context from which you argue the point.

"...gives the aberration function for paraxial focus, or so-called classical aberrations. Advance in calculation methods revealed that Gaussian image point is not the best focus location...requires shift from the Gaussian image point to their respective best focus location, where the central intensity of diffraction pattern is at its maximum (thus, best focus location is also called diffraction focus). Primary aberrations evaluated at best focus location are called orthogonal or balanced primary aberrations."

"For spherical aberration, the amount of defocus from paraxial focus needed for the shift to diffraction focus location is given by P=-S, with P and S being the peak aberration coefficients for defocus and spherical aberration, respectively..."

http://www.telescope-optics.net/lower_order_spherical.htm


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Re: CO vs. All That "Other Stuff"! new [Re: pstarr]
      #5622358 - 01/14/13 09:57 AM

HST

Quote:

Quote:

My other scopes have been dobs 6,8and 10 inch. From my expereance optical quality is number one, much more than telescope type.




A SCT with perfect optics and a 30% central obstruction can never give better that 1/4 wave performance. Not that 1/4 wave performance is bad. That said, you will never find a SCT, or any other design with perfect optics.




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Re: CO vs. All That "Other Stuff"! new [Re: Peter Natscher]
      #5622522 - 01/14/13 11:40 AM

Quote:

Quote:

My other scopes have been dobs 6,8and 10 inch. From my expereance optical quality is number one, much more than telescope type.




A SCT with perfect optics and a 30% central obstruction can never give better that 1/4 wave performance. Not that 1/4 wave performance is bad. That said, you will never find a SCT, or any other design with perfect optics.




That's likely true in general while observing, the difference is probably too hard to tell at any distance from max spacial frequency. Still, it is somewhat misleading. I only mention it because it's interesting and it leads to the very reason obstructed scope perform differently. Contrast transfer can be comparable to 1/4 PV SA in terms of performance, but only over a very small range. The effect on the Airy disc is different for an obstruction than LSA, and this gives rise to a perfect obstructed scope's advantage.

With perfect obstructed optics, the Strehl-like peak intensity can be about 89% with co = 0.32D. This is due to the added diffraction effects with cause the Airy disc radius to become smaller and a bit brighter than it normally would be (if it remained at 1.22 Lambda/D.) It's not, it's at 1.11 Lambda/D for 0.3D. Actually, the contrast transfer equivalent of a perfect obstructed system can be approximated (co </= 0.4) using w ~ .21co ~ (.21 * .3) ~ 0.063 RMS of LSA, a bit better than 0.074 RMS for 1/4 PV SA.

Toss in some aberration, say a very good S = 0.95 Strehl, and Strehl-like intensity falls to Sn ~ S * I, with I = (1 - co^2)^2, ~ 0.95 * 0.83 ~ 79%. That figure is normalized to 1, just as an unobstructed scope's peak intensity is equal to it's Strehl (0.838 * S, also normalized to 1.) This gives a peak intensity of ~98% vs ~79% for the obstructed scope (with accompanying ring brightness.) This is the advantage refractors share along with very good Strehl on the high end.

There is a reason perfect obstructed performance exceeds perfect unobstructed performance at higher frequencies. You can begin to see how the (1 - co) rule of thumb for mid range frequency resolution came about. Truth is, an obstructed scope might perform close to (1 - co) in the mid range but exceeds performance at high frequencies by D/(1 - co^2.) This is the advantage obstructed scopes share, provided reasonably good Strehl.

It turns out, obstructed approximation for equivalent aperture over mid ranges is about 0.67D (for co = 0.33D) and for 1/4 PV SA is more like 0.58D over the same range. If the CO is less than 0.33D, then the equivalent performance increases to > 0.67D (until, of course, the CO becomes zero with 1.0D equivalent aperture as expected.) Add some aberration in both samples, and things change. So, Yes, optical performance means a lot.

In effect, an obstructed scope has the mid range performance of a smaller aperture and the high end resolution of a (~8%) larger /aberrant/ aperture. And this is due to the diffraction effects that differ from 1/4 PV LSA over most of the MTF, especially the right hand side.

http://www.telescope-optics.net/obstruction.htm

So, while it might be true performance across some of the spacial frequencies approximates 1/4 PV SA, it's not true entirely. The difference can be important depending on how critical one observes, the type of observing, and the conditions one observes in. But 'quick look' observing or 7/10 seeing might not distinguish between the two and the difference can be considered roughly the same, I'd say.


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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5622584 - 01/14/13 12:19 PM

Nice points But..BRAIN HURTS NOW.

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Re: CO vs. All That "Other Stuff"! new [Re: orion61]
      #5622639 - 01/14/13 01:00 PM

It quits hurting once numbness sets in, like mine.

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Re: CO vs. All That "Other Stuff"! new [Re: Asbytec]
      #5622727 - 01/14/13 01:51 PM Attachment (9 downloads)

Looks like we are in agreement now, hopefully its clear now to others the different ways to view aberrations.

From the standpoint of an amateur astronomer viewing a star inside and outside of focus he can get some idea of the wavefront error with all the qualifications Suiter describes. Rayleigh was primarilly investigating the appearance of a star in focus, and that would indeed be difficult but not impossible to determine 1/4wv vs 1/2wv LSA PTV.

Add some defocus on an obstructed scope the situation is quite different. See attached view of only 2 waves for LSA 0.10wv PTV.

Glenn


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Joe Cepleur
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5622768 - 01/14/13 02:15 PM

Quote:

hopefully its clear now to others the different ways to view aberrations




What's clear is how complex the subject is, and how much I have to learn!


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: Joe Cepleur]
      #5622840 - 01/14/13 03:02 PM

The eye even more so, that would make for some great debate: scale, illuminance, resolution, photopic through scotopic vision, etc. The eye can perceive color, the MTF doesn't treat color very well. What I mean is, once you learn to discern subtle color differences on Jupiter, so much more resolution is open to you, for example, than simple sinusoidal contrast transfer. This very thing occurred to me recently, and now I see Jupiter in low saturation but very distinct hues. Its amazing to distinguish not just brown from white, but varying tones of gray from each other, white from Tawney, blue from ruddy, etc. Here, brightness and image scale play a role as well as contrast.

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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5623089 - 01/14/13 05:13 PM Attachment (4 downloads)

Quote:

A blown up MTF shown here indicates some real added contrast at the Rayleigh line for these high spatial frequencies. Actually seeing it and proving the case is another matter.



From your graph, the MTF is no greater than 0.02 at the Dawes limit.
I have created a simple graph using sagemath to depict in red what is left from the original signal at the Dawes limit. The sage command is
(sin(x)).plot(xmin=0,xmax=20*pi)+ (0.02*sin(x)).plot(xmin=0,xmax=20*pi, rgbcolor=Color('red'))


Edited by Alph (01/14/13 07:25 PM)


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DesertRat
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Re: CO vs. All That "Other Stuff"! new [Re: Alph]
      #5623157 - 01/14/13 05:56 PM

Alph,

Interesting, but as you see in your quote that I referred to Rayleigh, not Dawes. Even so recording or measuring there would be a delicate operation.

Glenn


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Asbytec
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Re: CO vs. All That "Other Stuff"! new [Re: DesertRat]
      #5623708 - 01/15/13 12:42 AM

Again, Alph, that graph occurs at a higher spacial frequency than for unobstructed apertures.

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