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Riddle me this

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#1 loo27

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Posted 18 July 2005 - 03:16 PM

I just read somewhere that a 33% obstruction adds 1/4 wave error to the optical train. I've had 4 SCT's, two of which I've star-tested. One was definitely 1/5 wave or better, the other one I'm less certain because of seeing, but I believe it was also 1/5-1/6 wave.

Am I seeing things? Is this technically possible? I've seen some write their best planetary images were in SCT's or Mak's, how is this possible with the big central obstruction?

#2 Starman1

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Posted 18 July 2005 - 04:49 PM

The effects on contrast of small-diameter details is about the same as adding 1/4 wave of defects to the wavefront. This can be seen in MTF (modulus tranfer function) graphs.
But that does not mean the wavefront from the mirrors is reduced in quality, merely that the final wavefront is damaged.
But that is in comparison with an unobstructed aperture, not another obstructed aperture with a somewhat smaller secondary. The newt with the 20% aperture blockage has some deleterious effects to its wavefront, too.

Fortunately for us, wavefront accuracy isn't the whole story.
If your newt has 2 mirrors with +/- 1/8 wave accuracy, P-V, a simple summation says the final wavefront could be +/- 1/2 wave! Fortunately, it is the relative average (RMS) of the surface which more accurately predicts the final wavefront product. And, there is serendipitous wavefront error cancellation at work, as well. In an SCT, they even adjust the mirrors to get as much of that as possible.

What is the wavefront accuracy that determines the minimum usability? IT ISN'T SPECIFIED IN ANY LITERATURE.
If we went by what is often stated in books, a 1/4 wave wavefront error at the focal plane, then SCTs would have to have perfect mirrors to meet this criterion. And most newts would have to have 1/25 wave or better to meet the minimum. Clearly, this requirement is too stringent. Adequate views can be seen through poorer optics. Certainly +/- 1/10 wave mirrors result in a good image, but this can result in a wavefront error at the focal plane of well over 1/2 wave!

And it depends on how the mirror's error is measured. Peak-to-valley? RMS? On the surface or reflected wavefront? All result in different figures.

I would not worry about the secondary size if you have taken steps to optimize the size for the usage.
Worry instead about how to collimate it. Miscollimation results in more poor telescope images than poor surface accuracy.

And seeing has an even bigger effect. Even a perfect telescope will be seeing limited.

#3 Guest_**DONOTDELETE**_*

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Posted 19 July 2005 - 01:27 AM

I wouldn't worry about it too much. The manufacturers all claim certain statistics but there are different ways to measure and GET those stats even! Most of the big observatory scopes have some type of obstruction as well (correct if I'm wrong here) and they do just fine. The huge apertures will definitely help when dealing with any obstruction. Whether a Newt or an SCT or Dob, there's SOME obstruction that's going to get in the way and WILL introduce some type of imperfection. The only design I believe that won't is the refractor and nobody's going to make a 6 meter refractor! :)

A lot of the new designs are cells of mirrors, many in a hex shape I believe. This way they can get around grinding a 20' mirror to perfection, for example. But these scopes too will have a central obstruction and I'm sure that the separations between the cells introduce SOME kind of errors as well. I think it mostly comes to a tradeoff. A 16" SCT will be quite a bit more compact and easier to handle than a 16" Newt. Does it make THAT big of a difference with the obstruction size when you start talking bigger apertures like that? I don't think so. At least in my viewing, it doesn't matter and my 10" with that obstruction will still gather more light than a smaller unobstructed APO, for example. There are other tradeoffs, but I do have an aperture advantage that does count for something, at least. Not a bash at any design, but just an attempt to illustrate that some design and practicality will inevitably introduce some type of error that has to be weight against the benefits of that size. Hey, I'd love to have a 10" APO, but I'll probably never get one as the cost would simply outweigh the commitment I'm willing to put into the hobby.

I think that's one reason Dobs are so popular. They have all the benefits of Newtonians, a small obstruction (relatively) and a simplicity and ease of use that an Alt-Azumith or Equatorial mount simply can't match. Now they can even be given goto functionality. You lose the tracking reliability of an EQ mount and possibly even the Alt-Az, but the ability is there. And for a lot of people that ability is "good enough." That and the price advantage due to the lack of mount, tripod, etc. makes them a very easy, enjoyable scope that at large sizes is within reach of even MORE people than a Newtonian and especially an SCT or Mak design. Just my 2 cents...

#4 loo27

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Posted 19 July 2005 - 09:18 AM

A 16" SCT will be quite a bit more compact and easier to handle than a 16" Newt. Does it make THAT big of a difference with the obstruction size when you start talking bigger apertures like that?


I believe when you get in the 12"+ range (or 10"+ range?), with decent optics, the sky is the limiting factor in all but 2 or 3 nights out of your lifetime.

I was just wondering why my star test say one thing, but this fact about c.o. says another.

#5 Art Jacobs

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Posted 19 July 2005 - 02:29 PM

Cliff,

I think that the source you are quoting is a little misleading. What they should have said is that the 33% central obscuration degrades the contrast of the image by roughly the same amount as what you would get from having a 1/4 wave error on the mirror. This shouldn't be interpreted to mean that the CO distorts the wavefront by 1/4 wave, only that the effect of the CO on contrast is equivalent to what you get from a 1/4 wave error. The decrease in contrast due to the CO is separate from (and additional to) whatever decrease in contrast you get from wavefront error.

#6 loo27

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Posted 19 July 2005 - 03:44 PM

The confusion in my mind is there a distinction between 1/4 wave error in contrast as opposed to spherical aberration? Does this wave error in contrast show up in a star-test.

If the answer is no,then it makes sense.

#7 Art Jacobs

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Posted 19 July 2005 - 08:02 PM

Cliff,

This is a confusing subject. I'll try to explain using some plots I generated with Zemax (optical design software). To see the plots you will need to open the attachment called Airy Patterns.jpg.

First, I need to explain how a star test tells you something about the contrast of the image: The more light that is concentrated in the central spot of the Airy pattern the better the contrast will be. That having been said, the attachment shows some plots of what you would expect to see if you did a star test on a 10" f/8 parabolic mirror.

Case #1 is what you would see at the center of the field of view if the mirror was perfect and there is no central obscuration. This case represents the absolute best that nature will allow.

Case #2 shows what you would see if the mirror was still perfect, but now there is a 3.33" central obscuration. Although the differences between Case #1 and Case #2 appear subtle, you may notice that the first Airy ring is brighter in Case #2, which will lead to lower contrast because some of the light has been shifted from the central spot (where you want it) to the first ring.

Case #3 is what you would expect to see with no central obscuration, but where the mirror now is no longer a perfect parabola, but instead has 1/4 wave of spherical aberration. This case looks a lot like Case #2, which leads us to believe that image contrast for Case #2 and Case #3 will be very similar.

In summary, the answer to your question is (if I understand your question correctly): You can see the effect of a 33% central obscuration in a star test. You can also see the effect of 1/4 wave of spherical aberration in a star test. The star tests for these two cases look very similar, which suggests that these two cases will suffer a similar degradation in image contrast when compared to the perfect/unobscured case.

Hope this helps!

Attached Thumbnails

  • 523320-Airy patterns.jpg


#8 loo27

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Posted 20 July 2005 - 10:44 AM

Art -

That does help tremendously. The next question is are the errors additive, multiplicative, etc?

#9 Starman1

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Posted 20 July 2005 - 11:55 AM

Cliff,
Unfortunately, additive.
Some wavefront error cancellation takes place, but it's well known that the image deteriorates with increasing secondary diameter.
Many books state the effect on the star image is negligible when the secondary is 20% or smaller of the primary diameter.
However, this presumes perfect mirrors.
But it points out some rules of thumb:
--get as good a primary as possible.
--get as good a secondary as possible
--keep the secondary size no larger than what is required to illuminate the edge of the field to 70% of the 100% illuminated center.
It's easy, but it's a difficult 3 rules.
Fortunately, there's rule 4:
--observe the sky in a dark site and forget about rules 1-3.

#10 Art Jacobs

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Posted 20 July 2005 - 03:59 PM

Cliff,

The effects of spherical aberration and a central obscuration are somewhat additive. That is, their combined effect is worse than either one of them alone. However, I don't think that it is twice as bad. Attached is a new picture illustrating what I mean.

Case #1 is with no CO and no spherical aberration. Case #2 is with CO only. Case #3 is with spherical aberration only. Case #4 is with both CO and spherical aberration. To me Cases #2, 3, and 4 all look pretty much the same. However, I would bet that if I were to do a more careful analysis that Case #4 would be somewhat worse that either Case #2 or Case #3.

Attached Thumbnails

  • 524565-Airy patterns2.jpg


#11 Starman1

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Posted 20 July 2005 - 04:16 PM

One of the paradoxes of obstruction (and it's dimly seen in your examples) is that the visible part of the Airy disc gets smaller as more light is thrown into the diffraction rings. This can make the resolution of extremely close double stars easier rather than harder.
It has to be mentioned that this is just about the only advantage to larger obstructions, though.

#12 Art Jacobs

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Posted 20 July 2005 - 06:11 PM

Hmm...... The idea that a central obscuration might actually help you to resolve closely spaced double stars never occurred to me. Has anybody confirmed this with actual observations?


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