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How good are reflectors for resolving binaries?

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#76 Asbytec

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Posted 13 September 2013 - 04:49 AM

I dunno, Fred, how to answer that. One has to respect the experienced and expert observers and take what they say seriously. Anytime we observe hard and deep right at the limits of every variable present we risk false positives, our reputation, and our own integrity. No pain, no gain.

Good seeing here minimizes one of those many variables and offers some hope when cooled and collimated - leaving skill and luck remaining. The best I've done so far is 0.57" arc (72 Peg data as reported.) That turns out to be 0.57/0.92" ~ 0.6R normalized or ~0.7R with CO factored in. It wasn't entirely difficult, and suggests one can go even deeper.

That also implies, with CO, one might elongate Chi Aql in a 6" obstructed depending on it's real sep. That's a real test of 0.5R and CO affects. So far - one attempt in less than ideal conditions - has been negative. But, wouldn't that be a nice ob to have under your belt if it were possible and people believed you? :grin: How many look at it's reported data and immediately write it off as too hard or impossible? (That was my point with Io in another thread.)

And 7 Tau seems to suggest there is room to go beyond Dawes, too. All of this provides some allure for doubles and the challenge they pose is motivating. It's amateur frontier observing pushing technology and skill. That's exciting as it is risky.

#77 fred1871

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Posted 13 September 2013 - 08:38 AM

Norme, I agree about trying, to see what's possible. I hadn't thought I could see Zeta Bootis elongated, when it was down to 0.5R for my 140mm refractor, until I managed it. And I have no trouble believing some observers see hints of elongation, or something? ... at even closer (slightly closer) levels. Christopher Taylor's claimed best is ~0.4R with his 12.5-inch. Aitken's note on detecting doubles with the 12-inch at Lick goes down to ~0.45R...

The two doubles you mention after your success with 72 Peg are somewhat different types of critters - Chi Aquilae is at 0.5R for about a 7-inch scope based on separation (~0.4") - although delta-m of 1.2 will have some effect.

But 7 Tauri is wider, and more equal - mags 6.60 and 6.86 in the current WDS, 0.7" in 2012, and the ephemeris (gd 3 orbit) suggests 0.75" at present - so that's a 0.5R for about a 4-inch scope. I observed it last November, 140mm refractor, in rather unsteady seeing - elongation was visible at 285x, with star discs (peanut or notched effect) flickering in and out of visibility. That's at about 0.7R for 140mm. Some other doubles at about the same separation were clear flattened figure-8 pairs on nights with better seeing. At 0.6" - which is around 0.6R at 140mm, having a Rayleigh figure ~1.0" - I find elongation is clear enough if the seeing permits. It's consistently there at 400x; sometimes a bit less power will show elongation in the best conditions.

But below 0.6R things get noticeably tougher, and more demanding of steady atmosphere for allowing the certain identification of elongations, rather than uncertainty due to seeing variations. For me, 400x becomes necessary for definite identifications of elongation at this level.

Personally, I find it more interesting to try for the harder unequal pairs; but I'm happy to see others working on their limits for detectability of equal pairs. It's an interesting pursuit.

#78 WRAK

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Posted 13 September 2013 - 10:10 AM

...
The animated diffraction patterns item, posted above, is useful, but I'd love to see it as a set of diagrams, which would allow studying the effect at each level of CO. ...

Fred, with the old fashioned but free Microsoft GIF Animator you can see the single planes in the preview mode - or you could cut out each frame and save it as non animated image.
Wilfried

#79 Asbytec

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Posted 13 September 2013 - 09:35 PM

Personally, I find it more interesting to try for the harder unequal pairs...

Absolutely, I love the challenge they pose as well. They are interesting from that standpoint as well as interesting in optical theory of obstruction effects. This is one reason why I modified my scope, to press these babies, too. :)

Always a nice write up, Fred. As a newbie to doubles, I find them fascinating on many fronts, especially pushing the limits of man and machine while enjoying nature's beauty.

#80 azure1961p

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Posted 13 September 2013 - 11:11 PM

For the record I was joking about the 250x showing .21". I didn't see any chortles or chuckles so I'm guessing it was taken without humour .

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#81 WRAK

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Posted 14 September 2013 - 07:23 AM

Fred's statement "...Zeta Herculis, as observed with my two scopes - just elongated this year with 140mm..." made me aware that Zeta Her would be a very interesting object for testing different CO values. With a separation of 1.3" (or ~1.2" according the 6th orbit catalog) the companion should sit directly at the first diffraction ring when using a 140mm scope. Thus I could check with which CO value the brightness of the first ring is ident with the brightness of the secondary giving a hint for the magnitude of the ring in terms of a part of the ring comparable to the spurious disk of a star and not for the ring in total.
What surprises me here is the statement "elongated" as this would mean a separation of less than 1".
Its now already a bit late in the season for me to observe Zeta Her in reasonable altitude so I need the next clear sky night rather soon.
Wilfried

#82 fred1871

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Posted 14 September 2013 - 09:22 PM

Wilfried, the reference to Zeta Her should have been Zeta Bootis - sorry. Both are doubles, but Zeta Her is easy; Zeta Boo is not at present. Having looked at both recently, along with all the diuscussions of 90 Herculis etc etc, I apparently wrote "Herculis" when I meant "Bootis". Zeta Boo is at 0.5" this year (2013.5); hence just elongated with 140mm, barely split (discs virtually touching) with 235mm.

That should eliminate any puzzle in the matter.

Yes, Zeta Her could be a test object for the secondary on the first diffraction ring if it's at 1.3".

#83 fred1871

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Posted 15 September 2013 - 08:34 PM

A follow-up on Zeta Herculis - the magnitudes are 2.95 and 5.40 (WDS), separation 1.3" (2011). With a grade 1 (definitive) orbit, of only 34.45 years, the ephemeris should be pretty accurate - it suggests ~1.2" this year. Need for a slight revision to the orbit? - without a full list of measures, especially recent ones that are presumably of higher accuracy due to better techniques, not possible to say.

I looked at Zeta Herculis in July this year with the 140mm refractor - my notes from the night include "at 160x the companion shows as a disruption to the first diffraction ring, occasionally as a spot on the ring...". The varying aspect was due to seeing fluctuations; on the night seeing was generally flickery, and where I'm located zeta Her only rises to about 23 degrees altitude.

So you're quite right Wilfried - it's an interesting one for 140mm (at present) because the secondary is on the first diffraction ring. But it showed quite well despite that and a delta-m of 2.45 - however the brightness of the secondary star I'm inclined to think, helps with bright pairs like this. When the secondary is at similar delta-m, but a lot dimmer - say mag 8 or 9 - it can be more difficult.

#84 WRAK

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Posted 25 September 2013 - 02:35 AM

After weeks clear sky last night. Started rather early to get Zeta Her with reasonable altitude but seeing was really bad with Pickering rather 4 than 5 - so no resolution with 140mm. Hoped for improvement and continued the session in Her trying 90 Her and 99 Her - as to expect negative. Proceeded then to STF2166 2.3" +8.8/9.08mag - easy resolved with x75, smallest resolving aperture was 70mm. Switched then to the CO mask (means back to 140mm) using x200:
CO 0.1 - no obvious effect on the image
CO 0.15 - disks a tad smaller and crisper
CO 0.2 - no obvious change
CO 0.25 - no obvious change, disks may be a tad smaller
CO 0.3 - first hints of diffraction rings, else no obvious change
CO 0.35 - diffraction rings brighter, disks fainter, impression of less crisp resolution.

Switched then to Aql and had a look at Pi Aql 1.5" +6.34/6.75mag. Clear resolution with x140, limit aperture 65mm giving a notched rod. Switch to CO mask (aperture 140mm, magnification x200):
CO 0 - no rings, clear resolution
CO 0.1 - no change
CO 0.15 - image tad crisper, resolution seems enhanced
CO 0.2 - similar image with first hints of diffraction rings
CO 0.25 - disks smaller, rings brighter
CO 0.3 - disks smaller, rings brighter
CO 0.35 - more of the same, resolution still intact.

Switched then to STF2616 3.3" +6.85/9.64mag means larger delta-m. Resolution with x75 but companion as to expect rather faint, did not check limit aperture, only CO.
CO 0.1 - same image
CO 0.15 - companion tad fainter
CO 0.2 - companion barely visible
CO 0.25 - companion resolution only with moving through field of view
CO 0.3 - diffraction ring of primary gets brighter than companion, resolution only when moving
CO 0.35 - resolution of companion only when moving very difficult and only for fractions of seconds.

Next object A1663 1.3" +8.89/9.25mag - resolution with x140, did not check limit aperture, only CO.
CO 0.1 - same image
CO 0.15 - crisper image, better resolution
CO 0.2 - no visible change
CO 0.25 - slight degradation of image back to CO 0 resp. 0.1
CO 0.3 - no visible change
CO 0.35 - disks smaller but a bit fuzzy, resolution somewhat worse than without CO.

First conclusions:
- Will make an additional CO 0.4 insert to verify my impression that CO 0.35 seems a critical value for image quality
- Small CO 0.1 to 0.25 effects seems conform to diffraction theory meaning enhancing resolution for equal bright binaries to some degree
- CO 0.3 seems to be the break even point for equal bright pairs
- CO 0.35 leads already to some degradation making resolution a tad more difficult but not seriously
- for unequal doubles with delta-m larger 2 CO 0.3 and larger makes resolution more difficult and can get a limiting factor
- bad seeing has certainly influenced this observations so this conclusions are to be taken with caution.

Hope for better seeing next time to continue with this experiment.
Wilfried

#85 Erik Bakker

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Posted 25 September 2013 - 03:40 AM

Very impressive report on the effects of increasing CO on doubles. The rewards of an increasing CO are more compactness and, compared to refractors, less color. Currently I have three instruments, with different CO's:

4" f/8 apo CO=0
16" f/5 dob CO=0.17
5" f/11 SCT CO=0.37

I like them all.

The image quality the 5" is capable of, with it's large 0.37 CO, is what continues to surprise me. When the skies clear, I will make a direct comparison between the 4" and the 5". Just had this scope for 2 weeks. Of course, the CO lowers the peak intensity of the Airy disk, while at the same time pushing more light in the brighter rings. That is obviously visible in the 5" SCT.

The same effect is already very difficult to observe in the 16" Newt. Under good conditions, that scope behaves more like a hypothetical 16" apo with 0 CO. Doubles are stunningly pure and clear with perfect chromatic correction in my bino with the 16" on those good nights. That too has surprised me.

Per inch of aperture, the 4" rules. With it's excellent peak intensity and very little energy in the rings, the images are of unmatched clarity. But only per inch of aperture. The overall high correction in this small scope makes itself known in very high contrast and great tranquillity of the images it presents to the observer.

All in all, your findings are very similar to what I've seen at the eyepiece so far. Keep up the food work and let us know what the 0.40 CO does to the image in your scope!

#86 azure1961p

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Posted 25 September 2013 - 07:24 AM

Erik,

I agree the SCT (mine being a 6") will show surprisingly fine doublestar views when seeing cooperates - and - its cooled and well collimated of course. The rings are brighter of course, but the optics are so very good I honestly don't mind. It'd be a bother if a faint companion were interfered here by them but for all others Ive enjoyed some very pleasing views here too. Porrima was stunning!!! Wilfreid nice defines the effects of CO here and on a number of pairs but from a personal standpoint I can forgive a 37% CO when the optical train is top shelf.

Wil, an excellent account and on a revealing variety of doubles . The poor seeing was actually appreciated as its part of the observing condition - particularly where I live during winter.

Pete

#87 WRAK

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Posted 25 September 2013 - 03:42 PM

To avoid misunderstandings - I do not intend to make anybody feeling bad about his or her scope with CO 0.35 or larger. I just want to get a better understanding of how CO influences resolution of unequal binaries to enhance my current RoT algorithm showing a weakness here. It also seems that potential negative effects of large CO values are enhanced by not this good seeing and may be neglectable with very good seeing.
Wilfried

#88 Asbytec

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Posted 25 September 2013 - 03:54 PM

Wilfried, it interesting you mention a peal performance near a 0.3D. As Erik says, the CO of course reduces peak intensity. For an optic of Strehl 0.95, it can maintain a 'diffraction limited' peak intensity of ~.80 when the CO is about 0.3D. This was my motivation to get my CO down from about 37% effective to about 31% real (at full aperture, and since it has such a small FOV, anyway.)

A CO larger than 0.3D, aberration less than 0.95, or both begins to reduce peak intensity below 0.80. It should begin to become noticeable in performance, if we're to believe the Raleigh criterion (anything less than 1/4 P-V SA can be considered diffraction limited - equivalent CO induced diffraction.)

You can approximate the peak intensity using comax~[0.6-(0.6Sn/S)]^1/2, where Sn is the peak intensity desired and S is the Strehl. It turns out in my own scope, Strehl 0.94, to maintain 0.8 peak intensity the CO must be 0.3D. Mine is 0.31D, so just a tad under 0.8 peak intensity (normalized.) The equivalent wavefront error can be estimated using w~0.21co for 0.4D and smaller. For example, a 0.3D is approximately equivalent to 0.063 RMS for the left side of the MTF.

The right side MTF resolution is still 1/(1-co^2) times better - about 10%, even though peak intensity falls below 'diffraction limited' performance. The latter effect is what I suspect you're beginning to notice at 0.3D, peak intensity falls off below the standard 'diffraction limited' performance. This is due to both obstructed light loss and added diffraction contributing more light to the rings.

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

So, I am not really surprised by your findings. The sound consistent with theory some of which being empirical, too. That you're noticing a drop off in perceived performance, noting the changes in the central disc, is a testament to the idea diffraction limited is indeed minimal performance.

Edit:

...make anybody feeling bad about his or her scope with CO 0.35 or larger.

Of course not, CO as large as 0.4D are optimized for performance along the entire MTF as well as providing wider fully illuminated FOV for improved versatility. If anyone wants feel bad, my small and tight fully illuminated FOV is estimated to be about 10' arc.

#89 WRAK

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Posted 26 September 2013 - 01:27 AM

... This was my motivation to get my CO down from about 37% effective to about 31% real (at full aperture, and since it has such a small FOV, anyway.)...


Interesting ... how did you manage this?
Wilfried

#90 Asbytec

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Posted 26 September 2013 - 01:46 AM

...how did you manage this?


Cut off the secondary baffle reducing the size from ~53mm and 140mm effective aperture to ~47mm and 150mm full aperture.

So far, no ill effects from stray light. The un-vignetted field is very small with the diagonal and the remaining primary baffle is very tight. A little flocking along the primary baffle through the visual back and stray light is pretty much eliminated.

I was a bit concerned over exposing the image to peak aberration from the primary's edge. Star testing and visual observation show no significant additional aberration.

#91 WRAK

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Posted 26 September 2013 - 05:11 PM

... For an optic of Strehl 0.95, it can maintain a 'diffraction limited' peak intensity of ~.80 when the CO is about 0.3D ... A CO larger than 0.3D, aberration less than 0.95, or both begins to reduce peak intensity below 0.80. It should begin to become noticeable in performance, if we're to believe the Raleigh criterion ... You can approximate the peak intensity using comax~[0.6-(0.6Sn/S)]^1/2, where Sn is the peak intensity desired and S is the Strehl... http://www.telescope...obstruction.htm
...


Norme, thanks for this informations - very useful, especially the formula for Peak Intensity depending on Strehl and CO size and the connex with the Rayleigh criterion. So far theory is conform with my observations and I am waiting for the next clear sky to continue. Currently I am very interested in the effects of CO for doubles with a fainter companion in or very near the first diffraction ring and with which CO value the companion is no longer to resolve - the result would enable an educated guess regarding critical delta_m values of unequal binaries and a better interpretation of the effect of the amount of energy in the first ring of the primary. Several sources indicate a delta_m between central disk and rings but so far I have found no clear explanation how these values are derived and how they are to interprete (for the whole ring or for each point of the ring corresponding to the size of a central disk of a companion).
Wilfried

#92 WRAK

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Posted 26 September 2013 - 05:30 PM

... the 16" Newt. Under good conditions, that scope behaves more like a hypothetical 16" apo with 0 CO. Doubles are stunningly pure and clear with perfect chromatic correction ...


Erik, meanwhile I think Newtons with f/9 or larger focus ratio and small CO may be perfect scopes for resolving doubles as counter intuitively a small amount of CO seems to enhance the image quality for this purpose. Only two arguments against them: Too large for easy handling and demanding regarding seeing.
Your positive report regarding a f/5 Dobson for resolving doubles surprises me somewhat as such a small focus ratio should be combined with reasonable coma.
Wilfried

#93 Asbytec

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Posted 26 September 2013 - 07:58 PM

Wilfried, yes, that's an interesting problem locating a binary companion on the first ring (or any ring) relative to delta_m. I'd like to know more about that as well.

#94 fred1871

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Posted 26 September 2013 - 10:33 PM

Wilfried, a useful study, despite the limited number of objects, and the separate variable of seeing, interacting with CO. Not surprising that you note the "bad seeing has certainly influenced this observations" - so we'll look forward to seeing what results you get in better seeing conditions. It's been an accepted principle for a long time that seeing interacts with CO to create less good images, so one would expect with your methodology that inferior seeing more strongly affects your telescope (adversely) when you're using a large CO, compared to no CO. It will be useful to look further at the CO effect, 0.30 vs 0.35 vs 0.40, in better conditions. At 0.40 I'd expect markedly inferior image quality (compared to zero CO) if the seeing is mediocre or poor - and less deterioration in good seeing despite the large CO.

Looking at your results, I'm assuming that "CO 0.2 - no visible change" refers to comparing with 0.15 CO, the previous line, not with zero CO.

One result of particular interest is that 0.15 CO resulted in several cases with "crisper image, better resolution". With those doubles, the magnitudes were nearly equal. A different result with STF 2616, where delta-m is 2.8 magnitudes - there, the 0.15 CO result was "companion tad fainter" and 0.20 CO gave "CO 0.2 - companion barely visible". Quite a different effect, and similar to Christopher Taylor's comments on his observation of a larger-delta-m pair, with 0.17 CO.

Your current impression that "CO 0.3 seems to be the break even point for equal bright pairs" , if it continues to fit your observations, may well be a useful finding for observers wishing to maximise resolution of equal pairs. So observers with, say, a Newtonian that has 0.15 or 0.20 CO might add a central disc to enlarge CO to 0.30 when observing very close equal pairs. With unequal pairs, the smaller CO would do better.

More thoughts on this later.

Erik Bakker's 16" f/5 - I'm wondering if he uses a coma corrector... the diffraction-limited field for an f/5 of that aperture is quite small.

Another issue with Newtonians, apart from coma (short f/ratio) and bulk (long f/ratio) is tube-currents and cool-down. I've seen major problems with some Newts because of those factors, more troublesome than with refractors.

#95 Erik Bakker

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Posted 27 September 2013 - 02:37 AM

Erik Bakker's 16" f/5 - I'm wondering if he uses a coma corrector... the diffraction-limited field for an f/5 of that aperture is quite small.

Another issue with Newtonians, apart from coma (short f/ratio) and bulk (long f/ratio) is tube-currents and cool-down. I've seen major problems with some Newts because of those factors, more troublesome than with refractors.


I don't use a coma corrector. On-axis, images are superb anyway. In my bino at 150x and higher mags, a sizable portion of the field is sharp. The images in the 16" f/5 are so very refractor like. Unlike in my Questar 7, where the first ring was so "large obstruction" like. In the Q7, unequal doubles where hindered by the lowered peak intensity and fat first ring. Not in the 16" f/5.

It's minimalist design works very well thermally too. Ever seen a fast cooling 16" apo refractor :lol:
And yes, the 4" apo cools faster. But the Q7 a lot slower.


#96 WRAK

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Posted 27 September 2013 - 04:38 AM

Looking at your results, I'm assuming that "CO 0.2 - no visible change" refers to comparing with 0.15 CO, the previous line, not with zero CO ...


Yes, correct

... Your current impression that "CO 0.3 seems to be the break even point for equal bright pairs" , if it continues to fit your observations, may well be a useful finding for observers wishing to maximise resolution of equal pairs. So observers with, say, a Newtonian that has 0.15 or 0.20 CO might add a central disc to enlarge CO to 0.30 when observing very close equal pairs. With unequal pairs, the smaller CO would do better...


Fred, language is tricky, this is a misunderstanding: Break even means crossing the line to the worse compared with zero CO, not turning point of the peak.
My impression so far is that for equal binaries the peak performance (means better than refractor) is between 0.15 and 0.2 CO. With 0.25 CO you have first evidence of a slight degradation compared to the peak but you can still expect refractor like performance with somewhat brighter first diffraction ring and over 0.3 CO troubles begin at least for fainter equal binaries. To some degree this can be compensated with larger aperture but with CO values above 0.4 things get this bad that not even larger aperture can compensate the negative effects - such a scope is then only useful for bright equal pairs and especially for very faint wide pairs (also a very interesting field, you just have to know it).

For unequal binaries the rules change and depending on separation and delta_m already small CO values have a negative impact as a secondary with less peak intensity can get lost in the brighter diffraction rings.

Disclaimer: This are first impressions from a few observations with rather bad seeing and the conclusions may be premature.
Wilfried

#97 fred1871

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Posted 27 September 2013 - 09:27 AM

Thanks for the clarification, Wilfried. I got in ahead of the further data collecting. Though I am wondering if a CO of 0.30, or near that, might prove to be useful for equal pairs when the seeing is good - reducing the diffraction discs, but not suffering too much loss of quality in better conditions, and with the enhanced diffraction rings not being too dominant, at least for the brighter doubles. We shall see.

Very large CO - 0.4 and bigger - I've never thought good for visual use. Twenty years ago I got to use a 16-inch RC with large CO - probably a bit above 0.4 - and thought it less good on globular clusters than a C14 I was familiar with.

Yes, "conclusions may be premature".

#98 fred1871

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Posted 27 September 2013 - 09:41 AM


Erik Bakker's 16" f/5 - I'm wondering if he uses a coma corrector... the diffraction-limited field for an f/5 of that aperture is quite small.

Another issue with Newtonians, apart from coma (short f/ratio) and bulk (long f/ratio) is tube-currents and cool-down. I've seen major problems with some Newts because of those factors, more troublesome than with refractors.


I don't use a coma corrector. On-axis, images are superb anyway. In my bino at 150x and higher mags, a sizable portion of the field is sharp. The images in the 16" f/5 are so very refractor like. Unlike in my Questar 7, where the first ring was so "large obstruction" like. In the Q7, unequal doubles where hindered by the lowered peak intensity and fat first ring. Not in the 16" f/5.

It's minimalist design works very well thermally too. Ever seen a fast cooling 16" apo refractor :lol:
And yes, the 4" apo cools faster. But the Q7 a lot slower.


Useful information, Erik; though I'm inclined to think the large apeture helps make up for the coma limitations for visual use, if you're only looking at the centre of the field. At 150x, observers typically see to about 1" resolution, so the 1" field is much larger than the diffraction-limited field for a 16-inch. Even at 300x that remains true, though the size of the 1/2" field is obviously smaller (though enlarged more for the observer at that power).

A quick calculation suggests diffraction-limited field for 16" f/5 is about 75" (1.25') - not very large. But because coma scales with f-ratio for Newtonians, the 1"-defined field is about 4.5' wide, much more substantial.

So I'm not surprised that, with small CO, the images are refractor-like. A good Newtonian does do that, as I've seen with some Newtonians I've owned, and others I've looked through, over the years. However one of the more impressive short Newtonians I've looked through in recent years was an f/4.5 with coma corrector added, and a superb mirror - very refractor-like indeed.

#99 Asbytec

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Posted 27 September 2013 - 11:42 PM

It's been an accepted principle for a long time that seeing interacts with CO to create less good images...

Fred, that's an interesting point, though I am not aware of any sources that speak to that nor what mechanism would cause an image to be worse with a CO. It's reasonable seeing affects the wavefront in the field reducing image quality. If a scope has a high Strehl, it might be more resistant to seeing induced aberration up to a point.

In that case, seeing seems to affect the wavefront pretty much equally in a given aperture despite the presence of the CO which has already done it's damage. A CO adds to diffraction effects but does not affecting the wavefront (other than improving it slightly by masking the center of a spherical optic.) Induced wavefront error is more affected by aperture relative to R0.

However, since obstructed scopes are already close to a nominal operating peak intensity closer to the diffraction limit, it could be that seeing pushes peak intensity below that level quite easily thus "damaging" the image. Still, in smaller apertures where D/R0 ~ 1 (about 8/10 Pickering), the image is still diffraction limited despite the CO.

It's a curious aspect of seeing and I have not run across any studies speaking to the effect of a CO. Most studies discuss he affects on aperture and do not discuss the CO. It's intuitive, however, to understand how peak intensity might be affected as the wavefront is affected (generally.)

#100 fred1871

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Posted 28 September 2013 - 03:25 AM

Norme, I came across this idea - that CO interacts with seeing to reduce image quality - long ago, in the 1st edition of Jean Texereau's How to Make a Telescope, a copy of which my local library had on the shelves.

More recently, as in 1980s :grin: I bought a copy of the 2nd edition, still available I think from Willmann-Bell. From that some quotes:

p.310: ...in reflectors, the central obstruction makes the instrument somewhat more sensitive to turbulence..."
Taking an extreme example, on pp 140-141, where various CO levels are discussed, the case of 0.5 CO: "the first ring is so reinforced that with the slightest added residual zonal aberration, or the least turbulence, it is no longer the radius of the first dark ring, but that of the second which fixes the resolving power. Thus, a 16-inch telescope with an obstruction of 0.5 will hardly be better than an unobstructed 6-inch, and may even be much worse if turbulence increases appreciably...."

Texereau treats turbulence as being similar to defects in the optics, producing reduced wave-front quality in the instrument. Early in the book (p8) he notes that "...A. Danjon has pointed out that under actual conditions [of using the telescope] it is the total wavefront imperfection we must consider: that we must take account of atmospheric disturbances superimposed on the defects of the objective..." Where an objective has defects approaching a quarter-wave [Rayleigh tolerance] "...such an objective is therefore much more sensitive to atmospheric disturbance than an otherwise similar perfect objective...".
A CO is in effect a form of optical imperfection, reducing the wavefront quality. Suiter (Startest) has similar comments.

A further point of interest in Texereau's comments is that better optical quality, other factors being equal, will reduce sensitivity to seeing.






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