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Jon Isaacs
Postmaster

Reged: 06/16/04

Loc: San Diego and Boulevard, CA
Re: Resolution, magnification and seeing. [Re: Starman1]
#5657673 - 02/02/13 08:03 AM

Quote:

Hence, a 4.5" scope can resolve a 1arc second distance, and a 9" scope 0.5arc second.
I was also taught that, for "comfortable" viewing, the apparent separation in the eye for those two points should be 8' of arc. Since 8' is 480", that means a magnification of 480X would have to be used on that 4.5" scope to view the 1" separation "comfortably".
No way. That's 107x/inch.

Better to use 4' as a practical apparent separation. 4' is larger than the maximum resolution of the eye with good acuity (usually 2-3'), and would prove difficult for only a fairly small percentage of observers

Don:

I consider myself a dedicated double star observer. Here's a few thoughts and experiences.

- To split a 0.5 arc-second double requires 0.5 arc-second seeing. The magnification necessary to make the split is immaterial, that depends on the eye.

- The double double is about 2.3 arc-seconds. 4 arc-minutes at the retina corresponds to about 104x. This is certainly a comfortable magnification if one is using a 3 or 4 inch scope where the airy disks are considerably smaller than the separation but even then higher magnifications can show the separation better. If the seeing is not optimal, higher magnifications may provide a cleaner image.

- The Rayleigh criteria is the separation when the two Airy disks are just touching, this is given by 5.45 inches/aperture. To see whether they are actually touching or not requires finer resolution of the eye than just the separation.

- If one is working at the Dawes limit (4.56inches/Aperture), the Airy disks are overlapping, and the observer is trying to see a 5% drop in brightness that appears as a thin dark line. This is a low contrast object and very difficult to see, quite different from the double-double in a 3 or 4 inch scope. In my experience, magnifications on the order of 80X/inch are necessary to see that thin line and "split" a Dawes limit double. A couple of years ago, when Zeta Bootes was right at the Dawes limit for an 10 inch scope, several observers in the double star forum were able to make the split but all used magnifications on the order of 800x or even more.

Sidgwick in his 1950s discussion of maximum magnification derives the 25x/50x rule but says that double stars may require significantly higher magnifications.

- Generally floaters are a problem for me but for some reason they are not so problematic splitting doubles at very high magnifications.

Just some stuff to think about.

Jon

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Starman1
Vendor (EyepiecesEtc.com)

Reged: 06/24/03

Loc: Los Angeles
Re: Resolution, magnification and seeing. [Re: Jon Isaacs]
#5657920 - 02/02/13 11:08 AM

Epsilon Lyrae makes an interesting test of your eye's resolution.
Can you see it as double with the naked eye (separation about 3')?
How low a magnification in the scope shows all 4 stars?

I've done the test:
1) I can *just* make out epsilon as double with my naked eye.
2) Using the 3' separation figure for my eye's resolution, that translates to a magnification of 78X to see all 4 stars in the scope.
3) I have eyepieces at 59X and 87X. I find the 4 stars easily split at 87X, which goes along with the naked eye test. I find the stars also split at 59X, which means that, theoretically, I can resolve objects at a naked eye separation of 2.26'.
4) Actually, I can't see epsilon as a separated double star with the naked eye--I see it as an elongated image.[My driving glasses separate the star into 2 points, but since they provide a half diopter of magnification, that doesn't count] What allows the separation to be seen at 59X is not primarily the magnification, since this image's exit pupil matches that of my naked eye, nor the brightness of the images in the scope. What does it is the star images are round tiny points in the scope and slightly flared, out of focus, images to the naked eye.

I wonder if there is another test of the eye's resolution in a naked eye double. Any ideas?

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GlennLeDrew
Postmaster

Reged: 06/18/08

Re: Resolution, magnification and seeing. [Re: Starman1]
#5657968 - 02/02/13 11:34 AM

Don,
If your eye is the weak link, through the scope at an exit pupil equal to or larger than your eye's pupil the image should be equally bad. The telescopic image at best provides an image of fidelity approaching the direct view. In other words, even if the scope delivers to your eye a perfect wavefront, your eye will 'mangle' it just as badly as when no instrument is placed before it.

Epsilon Lyrae is not the best test for this purpose, as each naked eye component is a not-bright 5th magnitude. Were they a bit brighter, the resolution as a pair would be easier. And the apparent brightness of the naked eye test subject should be the same as the telescopic one. Through even a 60mm aperture, any one of the four components is rather brighter in appearance than the whole lot together with the unaided eye.

This in another example of how subject brightness goes most directly to the matter of resolution.

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Starman1
Vendor (EyepiecesEtc.com)

Reged: 06/24/03

Loc: Los Angeles
Re: Resolution, magnification and seeing. [Re: GlennLeDrew]
#5657994 - 02/02/13 11:56 AM

Quote:

Don,
Epsilon Lyrae is not the best test for this purpose, as each naked eye component is a not-bright 5th magnitude. Were they a bit brighter, the resolution as a pair would be easier. And the apparent brightness of the naked eye test subject should be the same as the telescopic one. Through even a 60mm aperture, any one of the four components is rather brighter in appearance than the whole lot together with the unaided eye.

This in another example of how subject brightness goes most directly to the matter of resolution.

That's what I think, too.
I've seen what the limit of the eye's resolution can be--a 10 year old boy spotted the directions the "horns" of Venus pointed when Venus was nearing inferior conjunction. A few of us confirmed his sighting with binoculars that showed he had the orientation of the crescent just right.
Since the tips were, at that time, about 1' apart, he was obviously able to see the tips as separated. Incredible acuity. And no shortage of brightness, either. [Not to mention excellent seeing conditions]

Glenn, do you know any other separations that would be a better test for the naked eye?

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GlennLeDrew
Postmaster

Reged: 06/18/08

Re: Resolution, magnification and seeing. [Re: Starman1]
#5658317 - 02/02/13 03:08 PM

Don,
The only test subject which comes to mind--and it's a severe one at that--is the 1 arcminute, equal pair, nu Draconis.

The ideal is if course equal or near-equal brightness pairs, the components having a brightness somewhere about 3rd magnitude (which will be a short list), going to as faint as 5th. A routine to search the Hipparcos catalog, looking for such pairings in the 1-4 arcminute separation, would make short work of the task. In essence, each star of suitable brightness is searched for neighbors not exceeding a defined magnitude delta and which have a calculated separation in the range sought. Later, on-line images could be inspected so as to ascertain no other neighbors which could compromise or 'contaminate' the view; an example would be a suitable pair found in a bright cluster or crowded association.

Or there might already exist a list compiled for just this purpose.

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Jon Isaacs
Postmaster

Reged: 06/16/04

Loc: San Diego and Boulevard, CA
Re: Resolution, magnification and seeing. [Re: Starman1]
#5658366 - 02/02/13 03:35 PM

Quote:

3) I have eyepieces at 59X and 87X. I find the 4 stars easily split at 87X, which goes along with the naked eye test. I find the stars also split at 59X, which means that, theoretically, I can resolve objects at a naked eye separation of 2.26'.

I normally can convince myself that I see the split at 60x, there are nights when it has seemed possible at even lower magnifications. But it is definitely a clear split with space between the pairs at 90x and wide open at say 120x.

But this using a scope that itself is not challenged by the split, the pairs are widely separated at the focal plane and in the exit pupil. When one is working at the Dawes limit, double stars are very different objects..

By the way, the Dawes limit for a 5mm aperture is about 23 arc-seconds... According to Skytools 3, the separation of the pairs is 3.5 arc-minutes. This means that for a 5mm aperture optic, i.e. the eye, the epsilon 1 and epsilon 2 are approximately 10 times the Dawes limit, an easy split.

With "easy" splits like the double-double in a 3 or 4 inch scope, relatively low magnifications can be used. But the 2.3 arc-second separation of the pairs is the Dawes limit for a 50mmm scope, to resolve it and see that thin dark line, it takes considerably more than 100x. This is because a Dawes limit split is not well resolved at the focal plane or in the exit pupil.

Jon

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azure1961p
Postmaster

Reged: 01/17/09

Loc: USA
Re: Resolution, magnification and seeing. [Re: Starman1]
#5658724 - 02/02/13 06:49 PM

Given say 120x in two scopes of apertures you mentioned, the larger telescope will provide more detail so long as it isn't overly bright. Irradiation caused by the greater aperture can have those lower power views seem less detailed if only because so much light is crammed into a small area. A neutral density filter does wonders here for low power bright objects through large aperture. The full thrust if the benefits of large aperture higher resolution are typically appreciated at 30x or more.

The low power full resolution magnification needs some clarifiers...

13x per inch is said to have all that can be seen in terms of resolution and its wonderful theory but higher magnification makes it so much better. Doublestars are a great example. Sure there are double stars I can barely detect at 120x as double but enough to just make the call but detecting is one thing, fruitfully observing is another. You don't want to JUST make out a detail ( tho as u kno at times its all we can do) when you can see the SAME detail PLAINER.

There's a whole lot to be said for the comfort and enjoyment of the plainer image had at higher magnifications. A trend among observers often is to see how little magnification is needed to make out a detail. I rarely bother with that. Instead I prefer to find what which makes it most apparent.

Like music -you don't want to just hear it - you want to listen.

Pete

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