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Central Obstruction Analysis by Everhart and Kantorski

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#1 hoa101

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Posted 02 June 2017 - 02:04 PM

I have run across quite a bit of discussion about central obstruction and spider vane thickness, yet I never see actual data provided. Apologies in advance if this is well-known and I simply missed it.

 

In terms of optics, the effect of central obstruction and spider vane thickness is a relatively straightforward thing to quantify. A good example is an old paper by Everhart and Kantorski:

 

Everhart, E. and Kantorski, J. (1959) “Diffraction patterns produced by obstructions in reflecting telescopes of modest size.” The Astronomical Journal, pp. 455-462.

(http://adsabs.harvar...AJ.....64..455E)

 

See the graph shown below. The horizontal axis is the ratio of the diameter of the secondary obstruction to the diameter of the primary. The vertical axis shows the Contrast Factor, a measure of the ratio of energy inside and outside the central disk. Each curve W represents a four-vane spider with the given ratio of thickness to primary mirror diameter.

 

 

everhart.JPG

 

 

For example, a 200mm newt with a central obstruction of 20% and a vane thickness of 1mm will have a Contrast Factor of approximately 3.2. Increase the central obstruction to 25%, and the contrast factor drops to roughly 2.6.

 

A couple observations from these data:

 

1) Most reasonable vane thicknesses I have seen for tensioned four-vane designs will be less than W=0.01, sometimes even approaching negligible thickness. Therefore the focus from a design standpoint should be on stiffness and collimation stability.

2) The often-recommend central obstruction of 20% or less is arbitrary. As we can see from the graph, the slope between 15% and 25% is relatively linear. There is nothing special about 20% in particular.

 

The paper is an interesting read even one does not have a math background. Hopefully some fellow astronomers find this useful.


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#2 havasman

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Posted 02 June 2017 - 02:23 PM

Therefore the focus from a design standpoint should be on stiffness and collimation stability.

waytogo.gif



#3 infamousnation

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Posted 02 June 2017 - 02:35 PM

A graph is worth a thousand words.


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#4 MitchAlsup

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Posted 02 June 2017 - 03:00 PM

1) Most reasonable vane thicknesses I have seen for tensioned four-vane designs will be less than W=0.01, sometimes even approaching negligible thickness. Therefore the focus from a design standpoint should be on stiffness and collimation stability.

The vanes on my 20" DOB are made from 0.007" galvanized steel (0.008 once the flat black paint dries).

This corresponds to 0.0004.

 

So the article is allowing for some very thick and heavy vanes.


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#5 havasman

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Posted 02 June 2017 - 03:30 PM

Yes indeed. That article fails when you actually measure modern vanes. They're thin. They need to hold collimation. That's a variable that still matters. Thickness is really not much of a practical matter.



#6 starcanoe

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Posted 02 June 2017 - 05:04 PM

For a long time, I have suspected a generally undetected optical culprit for reflectors is the vanes.

 

But NOT the thickness generally. It is that I suspect the vanes are often NOT "in line" with the incoming light. A vane may be thin, but it won't take much of a tilt to make a vane "look thick" optically speaking. And look how most spiders are installed. It's just hit or miss as to how well aligned the vanes are....Suiter's wobbly stack and all that...


Edited by starcanoe, 02 June 2017 - 05:06 PM.

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#7 Jeff B1

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Posted 02 June 2017 - 06:36 PM

Kind hah old news.  The results can be found within this:  http://www.alpo-astr..._Sec_Mirror.pdf

 

It was also an article in S&T many Moons ago, forget when, but it was the basis of my papers on central obstruction in Newtonians and  Cassegrains.  Thanks for digging it up again; maybe some will read and understand it.  smile.gif

 

Found it.  Bob Cox changed the subject title based on the article you referenced:  Cox, Robert E., "Spider Diffraction in Moderate-Size Telescopes," S&T , September 1960, 166-169.


Edited by Jeff B1, 03 June 2017 - 05:02 PM.


#8 Eddgie

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Posted 03 June 2017 - 08:46 AM

The typical 4 vane spider lowers contrast uniformly across the angular resolution range by only about 2%.   No one can see a 2% loss in contrast when using scoptopic or mesopic vision and even with photopic, it is near the absolute bottom of the floor for contrast sensitivity for most people.  

 

I think that 10% is about the minimum that is required for most observers to really positively see contrast differences when viewing under nighttime conditions and you would need pretty thick spider to do this much damage (though there are some scopes with cast spiders that probably approach this level of spider diffraction). 

 

The 20% figure is important because it is hard to keep good field illumination if you go to a secondary mirror much smaller than this.  For planetary, you can get a bit smaller, but for DSO, you will loose considerable off axis illumination by doing so which means that there is a practical limit to how small you an go with a general use instrument and still have wide, well illuminated fields. 

The MN 66 is a great example of this.   The secondary is only about 17%, but this scope cannot well illuminate the field of a 35mm Panoptic.  You don't notice it under dark skies, but most suburban and city skies, the use of a 31mm Nagler or 35mm Panoptic gives you a very doughnut backgound sky being much brighter in the center than at the outside.  The field literally looks like you are viewing though a doughnut.  Again, under dark skies, this slips past, but under brighter skis, it makes the view look weird at low power. 

 

For most people though, the thickness of the spider is simply not enough to see and chasing an ever thinner spider is not worth the sacrifice in the stiffness of the secondary support.

 

Often people suggest that the spiders be replaced by optical windows. This of course is a big mistake because the window would likely do more damage than the spider vane.   You can see this on modern SCTs where the float glass is polished on only one side.   The streaks in the glass probably do about as much damage to the image as spider vanes do.  

 

The typical spider used today simply does not do enough damage that eliminating it would produce a change in contrast that was big enough for even the best observer to see. 


Edited by Eddgie, 03 June 2017 - 09:05 AM.

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#9 Jeff B1

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Posted 03 June 2017 - 04:31 PM

I have posted similar stuff, but back in the 1970’s Don Parker and I made several different size disks to simulate secondary obstruction of 12%, 20%, 25%, 33%, 40% and made visual and photographic image of Mars.  The results were predictable, at least for us, whereas one could readily see a perceptible le difference in each case.  Yes, obstruction makes a big difference in image contrast. 

 

Another time we took Don’s 6” f/4 with two secondaries giving 25% and 26% obstruction, photographed the Rosetta and not only was contrast higher with the smaller mirror, more reddish color was imaged.  Well, we showed it to the club and got some oh hums.  It took them many years to find out on their own that we were right.



#10 Mike Lockwood

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Posted 03 June 2017 - 05:12 PM

For the first one, the 12-40% obstruction, what size telescope was it?

 

As for the 25% and 26%, likely the secondaries had different coatings to cause the red color shift.  There is no other logical explanation for that.  You're not going to notice 1%.  I'm calling BS on that one.

 

As I always say, if you're worried about the contrast loss due to your obstruction, just buy a slightly larger mirror (which automatically has better contrast) and forget about it.  That's good for the telescope builder and for my business.  :)


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#11 Starman1

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Posted 03 June 2017 - 05:30 PM

The arbitrary figure of 20% obstruction comes from observers of the 19th century, who wrote that a 20% obstruction is little different than

no obstruction at all.

That is more or less borne out by the mathematics behind the obstruction:

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

There is very little difference between a 10% obstruction and a 20% obstruction but the curve gets steeper after that.

20% is somewhat arbitrary, but I guess the visual observers back then could see a negligible difference between that and a 0% obstruction.

It could be a historical accident of telescope choice, or target chosen.

A larger aperture, even an obstructed one, reveals smaller details than a smaller aperture.

But see Ed's comment regarding what % difference really counts.

This whole discussion just perpetuates the paranoia so many ATMs have regarding the secondary size.

Even some commercial scopes use too-small secondaries for that reason.

If secondary size were the most critical factor in a telescope's performance, no one would use a Schmidt-Cassegrain.


Edited by Starman1, 03 June 2017 - 05:34 PM.

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#12 Jeff B1

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Posted 03 June 2017 - 05:34 PM

or the first one, the 12-40% obstruction, what size telescope was it?

 

As for the 25% and 26%, likely the secondaries had different coatings to cause the red color shift.  There is no other logical explanation for that.  You're not going to notice 1%.  I'm calling BS on that one.

 

As I always say, if you're worried about the contrast loss due to your obstruction, just buy a slightly larger mirror (which automatically has better contrast) and forget about it.  That's good for the telescope builder and for my business.  smile.gif

Was a 12.5" f/6. 

 

Was a typo for the 6" scope, should be: "25% and 36%."  

 

Since Don is at room temperature he is not here to discuss it.  We demonstrated this using various telescopes instead of using optical engineering talk; but some people have thick skulls.

 

Right after Chick Capen retired in 1984 he ordered a 20” Classical Cassegrain from an optician our west and after the primary was finished we tested it as a Newtonian in a temporary tube.  First the surface was so rough the dog biscuits barked and the figure was very off.  The optician test results were anything but what was actually observed.  After he sent it back and got his money back we had a local optician do him a 16” set.  Not too happy with some folks you see.  I have observed with some so-called high quality telescopes at several events and not too impressed with many “professional” jobs. Sorry, just my experience (and belated, Don Parker's as well).


Edited by Jeff B1, 03 June 2017 - 05:52 PM.


#13 Jeff B1

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Posted 03 June 2017 - 05:38 PM

The arbitrary figure of 20% obstruction comes from observers of the 19th century, who wrote that a 20% obstruction is little different than

no obstruction at all.

That is more or less borne out by the mathematics behind the obstruction:

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

There is very little difference between a 10% obstruction and a 20% obstruction but the curve gets steeper after that.

20% is somewhat arbitrary, but I guess the visual observers back then could see a negligible difference between that and a 0% obstruction.

It could be a historical accident of telescope choice, or target chosen.

A larger aperture, even an obstructed one, reveals smaller details than a smaller aperture.

But see Ed's comment regarding what % difference really counts.

This whole discussion just perpetuates the paranoia so many ATMs have regarding the secondary size.

Even some commercial scopes use too-small secondaries for that reason.

If secondary size were the most critical factor in a telescope's performance, no one would use a Schmidt-Cassegrain.

Maybe you do not perceive a difference from10% to 20%  obstruction; however, we (me and Parker) observed planets for 50 and 60 years using apertures from 2" to 88" and we could see the difference.  Oh well..........



#14 Starman1

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Posted 03 June 2017 - 06:02 PM

I also have 54 years of observing under my belt, with both refractors (0%) and reflectors (18-45%obstruction widths),

And for sure, for a given aperture, I can see the difference between a refractor and a reflector

Of course, I have very little experience with small reflectors under 5", and very little experience with refractors over 5".

 

Note that for any given f/ratio, the larger the scope is, the smaller the secondary %.

The problem I see is that all-too-often, in the pursuit of a smaller obstruction, ATMs use a too-small secondary for the aperture and end up

stopping the scope down to a smaller diameter, defeating the purpose for which they chose a smaller secondary in the first place.

 

The difference I read between the relative peak intensity of the Airy disc at a 10% obstruction and 20% obstruction is not zero, but it's about 6%

That's a pretty small difference to see and see reliably with more than a random-chance determination.

Could you see the difference in a star image in a Strehl ratio of 0.98 versus 0.92?  Maybe with test instrumentation (Ronchi, Foucault, Lyot, IF), but visually?

 

Well, since the obstruction does affect the MTF, I'm willing to believe the difference could be visible in certain limited circumstances.

I presume your "disc obstruction" tests were done with a refractor, since no reflector I've ever seen had an obstruction as small as 12%.



#15 Mike Lockwood

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Posted 03 June 2017 - 06:23 PM

It would be interesting to see photos of the differences on the 12.5" telescope.  As for the 6", that's a significant difference if the light spectrum changed, there was some other difference like coatings.

 

I am sorry that you have had bad experiences with "professionals".  All I can say is that things are very different now than they were a few decades ago.

 

And just FYI, even in the fastest Newtonians today, typically central obstruction does not exceed 25%, and is usually less than that.



#16 Jeff B1

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Posted 03 June 2017 - 06:27 PM

As a retired dude with many years as an engineer and/or technician, astronomer, computer programmer and mathematician I like theory as much as anyone.  But when the rubber hits the road (clever TV clique) practical experience trumps all.  We did a lot of gazing and a lot of planetary observing over the years and just did not believe the conventional wisdom; it was not good enough so we strived (strove ?) to improve our machines. Parker was producing film images long before just about anyone else using CCD’s were rendering planets as good as his photographs; he improved and went electronic and it should not be too far off saying his images were about the best in the business.  He didn’t get there by believing conventional wisdom.  Neither do I.  More clever clique to come smile.gif

 

Don's estate is out of my hands but Sheldon Faworski I think is going through his astronomical stuff and maybe out of the tens of thousands of photos they maybe be found.


Edited by Jeff B1, 03 June 2017 - 06:32 PM.


#17 Jon Isaacs

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Posted 03 June 2017 - 07:07 PM

The results were predictable, at least for us, whereas one could readily see a perceptible le difference in each case.  Yes, obstruction makes a big difference in image contrast.

 

 

I have done a few experiments myself with an ED/apo refractor using disks to add a central obstruction. Like many here, I spent much of my life doing science in the laboratory and like many in these forums, I am an author on a number of peer reviewed papers, most of which I did not write, I developed the experimental techniques, made the measurements, did the basic analysis and allowed some other "fortunate" individual to write the paper.  Oh such joy..   

 

In the "objective" terms I prefer to use, to my eye, the difference in contrast between no obstruction and a 40% obstruction is "significant" but most everything visible without the obstruction will still be seen with the obstruction in place.  

 

In my world, a "big" difference in contrast, that's the Veil using an O-III filter under 18.6 MPSAS skies.  Or even the Veil under Magnitude 21.5 MPSAS skies, that big too.  

 

Jon Isaacs


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#18 Redbetter

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Posted 03 June 2017 - 08:03 PM

One of the advantages of large aperture is being able to achieve full illumination of a large spot with acceptable levels of vignetting on the widest field eyepieces, while still keeping the central obstruction diameter less than 20%.  When you are down close to 15% obstruction the loss to the rings is not all that great.

 

The spider vanes on the 10" and 20" we have are of such low impact that Sirius B shows up easily even when it is right on a diffraction spike.


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#19 Redbetter

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Posted 04 June 2017 - 04:41 AM

Here are the values I get from the Telescope optics.net website for different CO's, with some intermediate values added by me based on a polynomial curve fit (better than interpolating.)

 

There is also one small effect not accounted for, the slightly smaller diameter of the inner minima as % CO increases. 

 

CO = linear central obstruction fraction.  EE = encircled energy within minimum of airy disk, as a fraction of total. 

 

CO...........EE

0.0 ____ 0.838

0.10 ___ 0.818

0.15 ___ 0.795 (curve fit)  20" f/5 Obsession is 0.155 CO

0.20 ___ 0.764

0.25 ___ 0.726 (curve fit) Common for mainstream Dobs like the Zhumells with tall focusers.

0.30 ___ 0.682

0.35 ___ 0.635 (curve fit) Close to 8" SCT

0.40 ___ 0.584

0.50 ___ 0.479

 

The thing that sticks out is that the increase in lost energy from the airy disk going from 10% to 15% CO is not much with 10% CO already being below a practical lower bound for an obstructed scope for anything other than dedicated planetary...and perhaps not even achieving so low with full illumination of a small central spot even there.  Going from 15% to 25% results in about two and a half times as much additional light being sent into the diffraction rings relative to one another vs. obstructed.  Not that this is just the incremental effect.  The relative light lost overall compared to unobstructed is only about 70% more at 25% CO vs. no obstruction and only ~27% more for 15% CO vs. none. 

 

This makes shooting for a design somewhere in the 15-20% CO range appear attractive to me for a custom/premium scope.  Of course busting some other critical constraint or compromising usability to go from 21% to 20% CO would be nonsensical, but the range seems a good initial target for large scopes. 



#20 Starman1

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Posted 04 June 2017 - 08:58 AM

Yes, for large scopes, this is practical.  It allows for shorter f/ratios with a still-acceptable secondary size.

As scopes get larger, illuminating the same size field stop becomes easier because the field stop gets to be an ever-decreasing percentage

of the aperture.

For scopes in the 6-12" class, however, where illuminating a large field stop requires a higher percentage obstruction,

<20% is rarely possible unless the f/ratio is longer.

Still, even the size of obstruction in the small reflectors is radically exceeded by most catadioptric scopes.

 

One other consideration: secondary size is not equal, in many cases, to obstruction.

On my 12.5", the exposed secondary surface is in the 2.45" range (hard to measure accurately), while the mirror is 2.6" and the outside diameter of the secondary holder is

closer to 2.65".  So obstruction is 2.65" (21.2%) while the secondary size used in secondary calculations is only 2.45" (19.6%).

I use a secondary holder that has a lip around the edge of the secondary all the way around, reducing the amount of exposed surface.

If you are being really fussy about your calculations, you have to take the secondary holder into account. 


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#21 Cotts

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Posted 04 June 2017 - 09:32 AM

Maybe you do not perceive a difference from10% to 20%  obstruction;

 

I'm curious - trying to imagine a telescope with only a 10% central obstruction....   Would this be something like an f/10 or longer newtonian?

 

As for telling the difference between 10% and 20% obstruction, a proper test of this would have to involve using either two otherwise identical telescopes or to use a scope with a 10% obstruction and adding a cardboard disc of 20% size.   

 

How did you do your tests with Don Parker?  Under the above single-variable-controlled conditions?  

 

Dave



#22 Jon Isaacs

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Posted 04 June 2017 - 10:47 AM

As for telling the difference between 10% and 20% obstruction, a proper test of this would have to involve using either two otherwise identical telescopes or to use a scope with a 10% obstruction and adding a cardboard disc of 20% size.

 

 

The easiest way I know to do this is with a refractor and paper disks to provide the central obstruction.  

A 4 or 5 inches refractor also has the advantage that thermal and seeing issues are minimzed..

 

The only challenge is holding the disk in place... I do not recommend crazy glue.. :)

 

Jon



#23 Starman1

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Posted 04 June 2017 - 12:21 PM

Thread attached to the back of the cardboard disc can be stretched around the edges of the dewshield and taped in place.

It would also add diffraction spikes to the bright stars.



#24 Cotts

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Posted 04 June 2017 - 02:08 PM

Thread attached to the back of the cardboard disc can be stretched around the edges of the dewshield and taped in place.

It would also add diffraction spikes to the bright stars.

Seems to me an excellent single-blind test could be rigged up using a 5" or 6" refractor:  

 

1. Manufacture three or four "Obscuration Disks" with thread as Don described above. They could be built into 'cells' that fit over the dewshield for easy attachment/removal.  Obstructions of 0% (just threads), 10%, 20% and 30%  Name them something non-identifying - say, Galileo, Fraunhofer, Schmidt and Maksutov....

 

2.  Have a 'neutral' test-operator (non-participating as an observer)  put the Disks in place randomly while keeping track. (Several runs, each in a different order)  Have the observer(s) look at any targets they like, at any magnification they like and attempt to rank the obscurations from least to most. Observers not allowed to 'peek' at the obscuring disc in place, of course - they would just be told its 'name'.

 

I wonder who could really tell what from a test like this....  (My own bias says that this will be an extremely difficult test for just about anyone...unless image brightness came into play in the case of the 30% obstruction....)

 

I really love the idea of blind testing...

 

Dave


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#25 Jeff B

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Posted 04 June 2017 - 04:27 PM

A graph is worth a thousand words.

And this is just the start.  

 

About a million words to follow.....




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