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How bad a view can an unusually large CO produce?

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#1 stargazer193857

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Posted 31 July 2014 - 09:30 PM

Say if a 47mm secondary mirror were placed in an 114mm Newtonian. How bad would that make the mirror? This is a Frankenstein question. Is there any data on resolution with CO significantly greater than 33%?

#2 Stephen Kennedy

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Posted 31 July 2014 - 11:02 PM

By diameter that would be a CO of 41% and by area it would be a 17% CO. For Comparison, my 210 mm F7 Newtonian with a 55 mm secondary mirror has a 26% CO by diameter and a 6.8% CO by area. 114 mm is a fairly small aperture to begin with so losing 17% of the light to the CO would probably be noticeable in terms of a dimmer image with less contrast.

If you can find and afford a 150 mm Newtonian reflector with that same 47 mm secondary mirror, the CO would be down to 31.3% by diameter and 9.8% by area. I think these would be fairly typical figures for a 150 mm Newtonian. As the aperture increases, the effect of the CO diminishes.

#3 jzeiders

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Posted 31 July 2014 - 11:23 PM

Just to give you an idea, I tried a 1-1/4" 35mm wide field in 8" f/4 Meade Schmidt-Newtonian last weekend. About half the field of view was obstructed by this huge shadow from the secondary. It was unusable. A 24.5mm wide field worked fine.

The F/4 SN is built as an astrograph and optimized for taking photos. It can be used visually.No shadow at all on a full frame 35mm field photographically, just a little vignetting around the edges.

Bottom line, use the correct size diagonal for your intended purpose and you will achieve better results.

YMMV

Jack

#4 jzeiders

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Posted 31 July 2014 - 11:23 PM

Just to give you an idea, I tried a 1-1/4" 35mm wide field in 8" f/4 Meade Schmidt-Newtonian last weekend. About half the field of view was obstructed by this huge shadow from the secondary. It was unusable. A 24.5mm wide field worked fine.

The F/4 SN is built as an astrograph and optimized for taking photos. It can be used visually.No shadow at all on a full frame 35mm field photographically, just a little vignetting around the edges.

Bottom line, use the correct size diagonal for your intended purpose and you will achieve better results.

YMMV

Jack

#5 Asbytec

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Posted 01 August 2014 - 02:51 AM

Say if a 47mm secondary mirror were placed in an 114mm Newtonian. How bad would that make the mirror? This is a Frankenstein question. Is there any data on resolution with CO significantly greater than 33%?


There is plenty of data out there...here.

As a matter of being correct, the obstruction does not make the mirror bad. It affects the image in some ways, good and bad. To ask how bad the view is seems to suppose the obstruction is in itself a bad thing. It does affect resolution (good), but I suspect your question above is about contrast which most folks talk about when they discuss the CO as being a bad thing.

What the CO does is add diffraction as well as shade the primary as mentioned above. All aperture diffract, including unobstructed ones. The obstruction is simply another aperture with additional diffraction added to the diffraction caused by the objective. Diffraction in every scope causes a point source image to form as a central disc and a series of rings. The addition of an obstruction changes the distribution of light between the rings and the central disc. The disc is dimmer and the rings are brighter with an obstruction.

It's this first bright ring that primarily reduces contrast on extended objects supposedly made up of an infinite number of point sources. If you could imagine an LED screen showing a picture of Jupiter. If just the LEDs were bright, the image would be full of contrast. However, if each LED was a bit dimmer and had a ring around it, you can image the image would not be as clear. By clear, I do not mean sharp as in focus, but it might appear slightly blurry because it's points are not as well contrasted with one another. For simplicity, the bright ring of one point overlaps the LED of another. It gets a little more difficult to see each LED. That's the bad.

Added diffraction has a positive effect on resolution. In this case, each LED is around 10% smaller (ball park.) The Airy disc of a star is set by the aperture (and the wavelength of light, normally yellow-green.) For example the Airy disc of a star (or point source) is a 114mm objective is 138.4/Dmm or 1.2" arc. When two Airy discs are close enough together so there is no dark space between them, this is the limit of resolution. The smaller the Airy disc, the better the resolution because you can "split" to points closer together. The CO diffraction makes the Airy disc smaller in a given aperture thus enhances resolution.

The additional diffraction created by the obstruction changes the diameter of the Airy disc at the expense of adding light to the rings. The effect of robing the central disc of it's peak intensity and distributing some of it's light into the rings is very similar in effect to an aberration. However, the CO does NOT affect the optical quality of the scope, it's diffraction only affects contrast and resolution (and shading some of the light from reaching the objective) in a way that is similar to an aberration. For example, contrast with a 33% CO in a perfect scope is equivalent to about 1/4 wave of spherical aberration in an unobstructed scope of the same aperture.

However, the CO affects are generally felt over very small scales. Contrast is affected mostly at the first diffraction ring and resolution is enhanced at smaller scale of the Airy disc. We're talking a paltry 2" arc, give or take, in a 114mm aperture. These effects can only be appreciated at fairly high magnification. When you're talking images the diameter of Jupiter, approaching 50" arc in diameter, contrast between unobstructed and obstructed becomes increasingly the same. So much so, they are basically unchanged and we're only left with the 17% (in the example above) shading of the obstruction affecting the brightness of the view. At lower powers, there are no visible obstruction effects outside of the minor light loss.

Now, if you already have a bad mirror, say one with 1/4 wave SA, the obstruction and the aberration factor together to really drag down performance. For example, the diffraction limit results in about 80% of the available light being in the central disc and the remaining 20% in the rings. This kind of defines a minimum standard for what we might consider to be a good image with descent contrast and resolution. This is also what we get with a perfect optic and a 33% obstruction (approximately) or an unobstructed scope and 1/4 wave SA. If you have both in the same scope (obstruction and SA), then the light in the central disc (peak intensity) falls off to well below 80% and the rings brighten similarly. This reduces contrast between neighboring points (while actually boosting resolution a tiny bit.) In such an instrument, the high power image might be unacceptable because contrast at very small scales near the Airy disc is getting worse. Some argue contrast on much larger scales is degraded, too.

So, lets run the numbers on the OP. The CO will, I trust, dim the image by 17%. It will also improve resolution by (1 - co^2) or about 15% (very approximately as a CO this large has a better mathematical approximation to work with.) If it were a perfect optic, and the CO being already greater than 33%, we already know the light loss from the central disc will exceed 20% meaning the central disc will be well below 80% and the diffraction rings somewhat brighter producing less contrast. If the scope is not perfect, and it's likely not, the degradation due to the obstruction and aberration combined will be larger. But, then again, primarily only at the highest magnifications starting above 30x/inch (or 1.2x/mm) being about 140x. Below that Jupiter will be quite nice, relatively speaking for the aperture, but higher than that and it will have some notable contrast loss when compared to an unobstructed aperture - should you care to make such a comparison between a >$1000 refractor (of 114mm aperture) and a $300 Newt.

So, in a 114mm aperture of reasonable optical quality, you might have the contrast of a good 80mm refractor, the resolution of a 127mm aperture, and the throughput of a 102mm unobstructed scope (approximately using common apertures for comparison.) That is an approximation without running the exact math (which would include an unknown Strehl) to give an idea of what the obstruction does.

The CO is both good and bad, and often not so bad. If you can keep aberration low and the CO modest, then peak intensity of the central disc will hover around 80% (20% rings) and you will have an image you should like very much. So, CO's are not entirely all bad and arguments about CO are often over rated. But, they can be bad when combined with a bad mirror - because the CO does not make the mirror bad, only the image worse.

Just to give you an idea, I tried a 1-1/4" 35mm wide field in 8" f/4 Meade Schmidt-Newtonian last weekend. About half the field of view was obstructed by this huge shadow from the secondary. It was unusable. A 24.5mm wide field worked fine.


Excellent point. You do not wanna go too low on magnification.

Bottom line, use the correct size diagonal for your intended purpose and you will achieve better results.

Yep. Or find a descent optic with a smallish CO to break into good scope territory.

By diameter that would be a CO of 41% and by area it would be a 17% CO.

As the aperture increases, the effect of the CO diminishes.


Two excellent points.

#6 Jon Isaacs

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Posted 01 August 2014 - 06:42 AM

Just to give you an idea, I tried a 1-1/4" 35mm wide field in 8" f/4 Meade Schmidt-Newtonian last weekend. About half the field of view was obstructed by this huge shadow from the secondary. It was unusable. A 24.5mm wide field worked fine.



That was most likely due to the size of the exit pupil, 8.8mm with the 35mm and 6.2mm with the 24.5. I believe the 8 inch F/4 Meade SN has a 3.1 inch secondary, 38.8%.

The shadow of the secondary is 38.8% of exit pupil... with the 35mm, it's 3.4mm.. if your eye is open to 7mm, that's nearly a 50% shadow...

The primary effect of a large CO is to reduce the fine scale planetary contrast because it transfers energy from the central spurious disk to the outer rings. A 47mm secondary in a 114mm scope is a 41.2% CO, not much larger than the 8 inch F/4 Meade and would have a noticeable effect.

Jon

#7 Jon Isaacs

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Posted 01 August 2014 - 07:08 AM

The CO diffraction makes the Airy disc smaller in a given aperture thus enhances resolution.



For equal magnitude sources, this can be a slight help though one never hears of adding an obstruction to scopes without of a CO or with a small CO to gain resolution even though it is easily done. For unequal magnitude sources, the energy transfered from the central disk decreases the contrast and makes splitting unequal double stars more difficult.

However, the CO affects are generally felt over very small scales. Contrast is affected mostly at the first diffraction ring and resolution is enhanced at smaller scale of the Airy disc. We're talking a paltry 2" arc, give or take, in a 114mm aperture. These effects can only be appreciated at fairly high magnification. When you're talking images the diameter of Jupiter, approaching 50" arc in diameter, contrast between unobstructed and obstructed becomes increasingly the same. So much so, they are basically unchanged and we're only left with the 17% (in the example above) shading of the obstruction affecting the brightness of the view



If the CO is 20%, the differences are small. In this case, the CO is 41% and the differences between an obstructed 114mm and an unobstucted 114mm are significant. Typically Jupiter is about 40 arc-seconds in diameter.. Drawing with 2arc-second pixels, that's only 20 points across and the smearing of those pixels caused by the CO will definitely affect the crispness and contrast of Jupiter.

Below that Jupiter will be quite nice, relatively speaking for the aperture, but higher than that and it will have some notable contrast loss when compared to an unobstructed aperture - should you care to make such a comparison between a >$1000 refractor (of 114mm aperture) and a $300 Newt.



The issue here is not comparing an inexpensive Newtonian to a $1000 refractor, rather it is understanding how a 41% CO will affect the performance of that 114mm Newtonian. The old clear aperture rule of thumb suggests that would have the planetary contrast of a 67mm clear aperture..

It is worth comparing a 114mm Newtonian to an expensive 4 inch refractor for the simple reason that a well executed 114mm Newtonian with a small CO can be an excellent planetary scope. But a large CO definitely scatters/smears light.. One can actually perform this experiment.. add a 41% CO to an existing scope.. I will experimenting with COs something I have done.

Jon

#8 dave brock

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Posted 01 August 2014 - 07:19 AM

Now, if you already have a bad mirror, say one with 1/4 wave SA, the obstruction and the aberration factor together to really drag down performance.


I would think increasing the size of the secondary would reduce the spherical abberration by blocking out more of the central rays. Sort of similar to blocking out a turned edge with an aperture mask.

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#9 Pinbout

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Posted 01 August 2014 - 07:23 AM

not really, the central portion of a mirror adds less to the airy disc than from .7zone to the edge.

#10 Asbytec

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Posted 01 August 2014 - 08:44 AM

Hi Jon, and thanks for grinding through that essay. :)

For equal magnitude sources, this can be a slight help though one never hears of adding an obstruction to scopes without of a CO or with a small CO to gain resolution even though it is easily done.

Yes, thanks for saying so. It helps for equal close pairs, not so good for unequal wider pairs.

If the CO is 20%, the differences are small.

Also true, IMO. And any gain in resolution above 40% is somewhat minimal, too, as I understand it. And maybe in practice, as well.

Drawing with 2arc-second pixels, that's only 20 points across and the smearing of those pixels caused by the CO will definitely affect the crispness and contrast of Jupiter.

This would be an interesting topic as extended object resolution is really not that simple. There is something weird going on, I think, that makes it more complicated that this. I guess we could say contrast is reduced on this scale, but resolution behaves differently. Each pixel is not equally bright across that diameter, it's brighter in the middle. I am sure you understand that, but there's something I do not really understand: why could I resolve a small crater that has at least bright point on the rim whose FWHM maybe have covered at least half of the grey pit? And why was the pit grey instead of black? After observing it, I sat for a long time working on the infinite point source model trying to understand why resolution was so high. One explanation is FWHM of each bright point must have been very small, smaller than expected. The entire crater fit easily within the Airy disc and inside the first ring comfortably. Yet, it's pit was certainly seen. The point is, something weird is happening on extended objects, IME.

It seems the best thing to do is to have a pretty well made scope and a modest CO to get the peak intensity back up to 80% and resolution and contrast will be just fine. You can do that with mid 90's Strehl and 30%-ish CO.

#11 Asbytec

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Posted 01 August 2014 - 08:46 AM

I would think increasing the size of the secondary would reduce the spherical aberration by blocking out more of the central rays. Sort of similar to blocking out a turned edge with an aperture mask.

Dave


It does. There is less energy in the center of the mirror relative to the edge (as Danny points out), but it helps with the total wavefront deviation. Someone smarter than me can chime in on RMS, which can be a long topic.

#12 planet earth

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Posted 01 August 2014 - 08:46 AM

not really, the central portion of a mirror adds less to the airy disc than from .7zone to the edge.


The area is equal at (.7071 times the radius squared times pi) to the edge, as is the centre of the mirror to the .7071 radius. So the inner area subracting the secondary circular shadow is quite important as it has quite a bit of area.
Yes/No :)
Sam

#13 Nils Olof Carlin

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Posted 01 August 2014 - 09:32 AM

I would think increasing the size of the secondary would reduce the spherical abberration by blocking out more of the central rays. Sort of similar to blocking out a turned edge with an aperture mask.

Dave

not really, the central portion of a mirror adds less to the airy disc than from .7zone to the edge.


At best focus, the amount of light in the Airy disk (at best focus) is maximized when the average (Mean Square, or RMS squared) phase deviation from all parts of the wavefront is minimum. This does not depend on where in the aperture the phase error is - any part of the aperture contributes equally.
The combined effect of obstruction and figure errors is not easily guessed, but a program such as the Aberrator will give a good answer.

Nils Olof

#14 Jon Isaacs

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Posted 01 August 2014 - 09:40 AM

It seems the best thing to do is to have a pretty well made scope and a modest CO to get the peak intensity back up to 80% and resolution and contrast will be just fine. You can do that with mid 90's Strehl and 30%-ish CO.



Based on my understanding and my experiences, I would say that the smaller the CO the better, the higher the quality of the optics the better. The difference between a 30% CO and a 20% is significant in terms of fine scale contrast.

Of course, the "outer" obstruction, i.e. the aperture, is most important in determining the fine scale contrast, or "contrast transfer." So much is made of the central obstruction but that is only relative to the Airy disk. The aperture determines the size of the Airy disk so doubling the aperture means that the Airy disk structure, rings and all, is half the diameter..

Jon

#15 Asbytec

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Posted 01 August 2014 - 10:44 AM

...any part of the aperture contributes equally.

Okay, that makes sense.

Based on my understanding and my experiences, I would say that the smaller the CO the better, the higher the quality of the optics the better. The difference between a 30% CO and a 20% is significant in terms of fine scale contrast.

No doubt smaller CO and better optical quality are better. With enough of each, it begins to approach refractor-like performance in terms of peak intensity (contrast transfer.)

Say you have a Strehl of 0.95 and a 30% CO (that's about what I have now) you have about 80% light in the Airy disc and some in the rings. With a better optic at the same CO, you might have 85% in the central disc and a little less in the rings. A 5% increase might be noticeable over time - maybe - IME with 7% improvement which really took time to maybe notice it on planetary low contrast detail. My guess is there is some improvement, but it's hard to tell whether I just gained more experience during that time or using a bit better magnification helped. But, over time, my sketches are more detailed for some reason after the modification.

Decrease the CO of that better scope to about 20% and you are above 90% peak intensity. I'd say you could notice that 10% to 12% improvement more readily. I'd be interesting to know how easily one can notice the gain from 80% to just over 90% and how significant that 10% to 12% gain might be in practice. I have no experience comparing that much difference in a similar aperture.

Of course if you have no CO, then your peak intensity is equal to the Strehl which we normally assume to be quite high for a quality refractor at say 98%. I am sure we can notice that 18% improvement from 80% easily enough. There is likely not so much immediately recognizable (8%) difference between >90% with better correction and smaller CO and a 98% Strehl APO. That seems inline with my own experience with a similar 7% difference in CO diameters (which seems to show some improvement noticed over time but not immediately, IME. I mean, to me 7% was not shocking. It is subtle.)

So it seems minor, single digit improvements can be noticed with care, and larger improvements from 80% all the way to perfect aperture (without a CO) even more so. Perfect scopes with smaller CO less so, but still noticeable.

Here's a math approximation one can play with from Vla's site to calculate an optimized CO for low contrast features: COmax=SQRT(0.6-((0.6SN)/S)). See eq 64.

SN is what Vla calls nominal Strehl, the peak intensity on the focal plane which is an indication of how much light is sent to the rings and thus contrast transfer. S is the Strehl of the optic. Plug in what peak intensity (SN) you desire, say 80%, and the Strehl of the optic and it /approximates/ the CO diameter that will give you the desired contrast.

#16 kfrederick

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Posted 01 August 2014 - 02:15 PM

The obstruction and spider scatters the light making the background not as dark . I have a 17 inch unobstructed reflector and that was the feedback I was getting was the dark background . There are some telescopes with huge obstructions that image very nice so I am not saying it does not work.

#17 Nils Olof Carlin

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Posted 01 August 2014 - 02:40 PM

With an ideal aperture, 84% of the total light is in the Airy disk, the other 16% is in the rings. One could think of it as 5/6 of the light forms a sharp image (by the Airy disk), and 1/6 of the light forms an unsharp image on top.
With Strehl 0.8, barely meeting the Marechal or Rayleigh criteria, at least approximately 0.8*84% = 67% is in the peak and 33% in the rings: 2/3 sharp, 1/3 unsharp. Little wonder this is clear under good seeing.

Nils Olof

#18 Pinbout

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Posted 01 August 2014 - 03:56 PM

This does not depend on where in the aperture the phase error is - any part of the aperture contributes equally.



thats true for 4th order but... as you go up in orders the errors become smaller and more localized?

do they dominate as equal to 4th order?

#19 Asbytec

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Posted 01 August 2014 - 09:17 PM

With an ideal aperture, 84% of the total light is in the Airy disk, the other 16% is in the rings. One could think of it as 5/6 of the light forms a sharp image (by the Airy disk), and 1/6 of the light forms an unsharp image on top.
With Strehl 0.8, barely meeting the Marechal or Rayleigh criteria, at least approximately 0.8*84% = 67% is in the peak and 33% in the rings: 2/3 sharp, 1/3 unsharp. Little wonder this is clear under good seeing.

Nils Olof


That's true. What you've illustrated is the difference between a perfect ideal aperture without an obstruction and a scope that has any combination of Strehl and CO achieving only 80% on the focal plane. That could be an unobstructed optic with about 1/4 PV SA, or it could be a scope with mid 90's Strehl and 30% CO. Both have about the same intensity distribution on the focal plane.

That performance between 80% (normalized) and 100% should be easily noticeable in good seeing. But, if you obstruct the perfect, ideal, unobstructed example it no longer puts the full 84% of 84% light into the disc. Its performance drops off somewhat and any performance advantage narrows relative to the scope that only puts 67% of the 84% max (80% normalized) of the light in the central disc.

The question then becomes, at what point does difference in final intensity distribution on the focal plane (caused by the CO and aberration - and seeing, too) can one notice it in moments of very good seeing? Can it be readily noticed at all when seeing is average or worse as it drags (probably) both scopes down below that 80% threshold?

#20 Asbytec

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Posted 01 August 2014 - 09:25 PM

I have a 17 inch unobstructed reflector and that was the feedback I was getting was the dark background.

:bow: Yea, I bet it's nice.

#21 Nils Olof Carlin

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Posted 02 August 2014 - 10:15 AM

What determines detail contrast due to diffraction effects, is not the height of the Airy disk alone, but rather the ratio of sharp (Airy disk) to blurred (due to the rings).
For ideal aperture, 5 to 1 as shown. For sph abb lowering the Strehl by 0.2, only 2 to 1. Here, seeing will lower Strehl by an amount independent of the Strehl in perfect seeing, and another 0.2 due to seeing will lower the contrast to 2 to 1 as well.
The combination, Strehl lowered by sph abb from 1 by 0.2 (this is approx 1/14 wave RMS) and 0.2 from seeing gives Strehl 0.6. The Airy disk contains 0.6*84%=50%, and contrast 1 to 1.
I would guess if seeing is good enough, you could clearly tell the difference.
These results are approximate, but should give some idea of what detail contrast you can expect. But you seldom if ever know the parameters very well.

Nils Olof

#22 wh48gs

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Posted 02 August 2014 - 07:16 PM

What determines detail contrast due to diffraction effects, is not the height of the Airy disk alone, but rather the ratio of sharp (Airy disk) to blurred (due to the rings).



It's not that simple. What really determines contrast level is the relative brightness over intensity distribution of the diffraction pattern. For instance, most of the energy lost to the central maxima due to central obstruction ends up in the first bright ring, but it increases in size, opposite to the central maxima, which shrinks, retaining nearly unchanged physical brightness level. In other words, the relative increase in brightness of the first bright ring is significantly less than what the energy numbers alone indicate. The size of central maxima itself also matters for the contrast/resolution level.

This is why MTF shows that obstructed apertures have higher contrast than perfect aperture in the high frequencu range. Spherical aberration shows contrast recovery toward high frequencies as well, but remains below perfect aperture because it shrinks the central maxima significantly less.

It is established by the diffraction theory that the averaged MTF contrast directly scales with the Strehl. Hence, 0.80 Strehl implies 20% contrast loss over the range of MTF frequencies. Sure, it is strictly valid only for the sinusoidal pattern, but it doesn't change significantly if we use square wave instead. MTF is considered to be a good general indicator of image quality (contrast), and using the Strehl as the contrast indicator is even simpler than the energy arithmetic.

Vla

#23 gnowellsct

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Posted 07 August 2014 - 03:47 AM

Well for one thing, if you go to a 100% central obstruction the image will suffer.

 

The Palomar 200 inch scope with it's observing cage is about a 50% central obstruction.



#24 Glen A W

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Posted 08 August 2014 - 06:38 PM

My Vixen 260 has a monster up front.  I did not buy it to look at planets, but that's what I do.  It has wonderful contrast and sharpness.  It really changed my opinion of the compound designs.  Glen



#25 gnowellsct

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Posted 10 August 2014 - 03:11 PM

My Vixen 260 has a monster up front.  I did not buy it to look at planets, but that's what I do.  It has wonderful contrast and sharpness.  It really changed my opinion of the compound designs.  Glen

 

The issue achieves exaggerated significance because the non-SCT (or compound scope user) *instantly* assumes that any discrepancy in performance between the larger vs. smaller CO scope is due to the secondary's size.  Even if it is a simple thing like collimation the scope's performance will be passed off on the secondary.

 

There are in fact a host of *other* issues...collimation for example is not an easy issue.  You collimate on a star, you swing the scope to Saturn or Jupiter to enjoy...seems obvious.  But it is a test many SCTs won't pass because with a loose lock nut on the primary the scope will no longer be collimated  when you arrive at the new target.  Loose secondary screws will do the same.  A number of scopes have been opened by people who haven't re-oriented secondary and corrector plate to the correct original position.  Any resulting image defects from these issues *at all* will, on a compound design, be attributed to the secondary's size.  There is also the issue, to be frank, of shoddy quality control on mass produced SCTs, but *even so*, the resulting image deficiency is *not* due to secondary size. 

 

Quality control is itself an issue because if someone looks through a 1984 SCT he will make generalizations about all SCTs based on that experience.  But if I look through a bad 1965 Newt or a bad 1985 Newt I *do not* generalize about all Newts based on that experience...as a matter of their design.

 

One weird consequence is that Newtonian scope owners over-react and try to cut their secondaries to excessively small sizes, sacrificing eyepiece illumination for non-existent gains on planets.   Fortunately with today's larger apertures many Newts give decent edge of field illumination regardless of secondary sizing.  


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