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azure1961p
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: Asbytec]
      #5531929 - 11/21/12 10:46 AM

Yeah he got major respect for that one LOL. Apparently it wasn't just a passing remark of fakery at Aldrin but the guy really made a persistent point of ragging on the guy. Again kudos in my book"!

Pete


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Asbytec
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: azure1961p]
      #5533106 - 11/21/12 11:02 PM

You know, when we resolve stars, we're really not resolving one from the other. Especially with evenly bright pairs that do not vary in contrast from one another, there is no resolution of one from the other by definition. We're really resolving each component star from the blackness of space where the contrast does exists.

So, maybe you do not need a dark space between them to call resolution. An elongation has just enough black space around it to show a close companion. Maybe the companion does not need black space all the way around it, just enough to set it apart from the primary. But, that's because we know diffraction patterns are circular.

Imagine two white, square cards on a black background. Push them together and you cannot tell whether there is one rectangle, two squares, or even 4 triangles. It looks like one rectangle, but could be any number of unresolved shapes. But, if we know they are squares, then there is only one resolution as to what we're seeing: two squares side by side.

In fact, we could push them to overlap to such an extent as long as it was not square we could detect the presence of at least two squares or even 35 unresolved squares tightly packed. But, such an appearance would show more than one white square must exist in the image. But we know this because the white barely rectangular shaped are set against a contrasting backdrop, not from one another.


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azure1961p
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: Asbytec]
      #5544338 - 11/28/12 06:20 PM

I see where you are going and it would seem interpttation is a kind of resolution in and of itself. Its not but shifting the emphasis could make it seem such. Rayleigh is concrete and Dawes is an arbitrary agreement of a resolved state of merged patterns for the sake of a common threshold or benchmark by which to classify a specific split per an apertures Res. he could have equally said " well its the Dawes limit the moment elongation is seen at all". in pactice this was probably far to taxing to perform reliably given real world seeing and optical imperfections. Backing off a bit and having the first pinch reveal I guess seemed less an Olympic achievement and more reliable a feature to repeatedly gauge with certain measure. Thomas Jensen elongated. 50 Dawes with an 80mm which is a commendable feat but probably not repeatabley certain as the notch. All that to say I think where they drew the line empericaly was alltigood end even if a "limit" could've been pushed further. Of ourselves Norme the ratio to apertures never change even tho it could look like an optic was stretching.

I'm still not settled on either Abbe or Sparrow as they seem go break down the finer you cut the wire. I RESPECT them but I've got issues. Then again what lines of law emperical measure or established Rayleigh doesn't challenge its own definition upon close enough examination ? move a hundreth past the Rayleigh for an 80mm - who would ever know but by the measure it was breeched.

Pete

Edited by azure1961p (11/28/12 06:35 PM)


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Asbytec
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: azure1961p]
      #5544553 - 11/28/12 09:06 PM

Sure, Raleigh is concrete in that it defines the Airy disc under specific conditions such as the wavelength and aperture. It's still possible not to technically resolve, being a clean dark space, between two brighter stars. At some point, the spurious discs will over lap with no detectable contrast.


Dawes was more empirical based on observation. But, they still define resolution and placing a definition or conditions on resolution is key. If we define it differently, we can "resolve" stars far closer together.

By the way, I discovered it's impossible to resole unequal pairs using the Aldrin limit. When they are that close together, the brighter spurious disc completely overwhelms the companion. It can only be split at the limiting magnitude or by elongation of an equally bright companion. But, the line pairs should be visible under the best conditions and if the spurious discs are literally pin points. And in some sense, that should be the limit except for some difficult to measure change in the Airy pattern as two stars are literally on top of one another.

But, oh well, 72 Peg was not as difficult as I had imagined based on Sparrow's limit. Cool! Still not sure what you have against Abbe limit. Maybe it's some practical limit.


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azure1961p
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: Asbytec]
      #5545034 - 11/29/12 07:17 AM

You know what it is, Dawes has a specific look that's easier than Abbe. I think its easier to call a Dawes than an Abbe in the field. Yeah so in a real way with reservations a limit is what you make it. I guess that was my point condensed into a sentence.

Pete


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fred1871
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: azure1961p]
      #5546050 - 11/29/12 07:09 PM

Quote:

You know what it is, Dawes has a specific look that's easier than Abbe. I think its easier to call a Dawes than an Abbe in the field. Yeah so in a real way with reservations a limit is what you make it. I guess that was my point condensed into a sentence.

Pete





Ummm... do we have a number for the Abbe limit, as transferred from microscopy to telescope use?

Or any idea what the double star image would look like at the Abbe Limit, if it is applicable?


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Asbytec
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: fred1871]
      #5546129 - 11/29/12 07:43 PM

"The formula for microscopes is 0.5l/NA which translates to 113/D = resolution "arc for telescopes (4.46/D inches), putting it between the Dawes and Sparrow limits."

http://www.cityastronomy.com/rez-mag-contrast.htm

If the Sparrow limit is applicable on terms of being the point of zero contrast, the Abbe limit could apply to observing doubles. Its lower than Dawes 5% contrast between spurious discs, but higher than zero presumably between two 6th mag stars. In this case, I suppose the doubles would simply appear elongated to the eye.


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fred1871
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: Asbytec]
      #5546515 - 11/30/12 12:32 AM

I suspect your description of it tells us why it hasn't been used in astronomy - it really doesn't tell us anything new, compared to the better known limits.

It may well be useful in microscopy, where things observed are perhaps more like planets than double stars.


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Asbytec
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: fred1871]
      #5546554 - 11/30/12 01:15 AM

Yea, I dunno, but it's application is probably better suited for Microscopy. Resolving fine details within cells at the diffraction limit, etc. They tend to measure distance rather than angular separation. The Abbe limit equation is better suited for giving distance in terms of wavelengths of light, though it can be converted to angular measurement.

As Pete says, there really is no hard floor limit, depending on how you define resolution. I never thought a 6" could show stars below Dawes, but it can reach to Sparrow (107/Dmm) and below. Seeing elongation at 0.5" arc was amazing (in sub arc second seeing, of course.)


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Asbytec
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: Asbytec]
      #5561230 - 12/08/12 05:19 PM Attachment (38 downloads)

Some thoughts on Raleigh and MTF on extended objects.

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azure1961p
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Re: Abbe Dawes and Sparrow - The Azure Limit new [Re: Asbytec]
      #5561256 - 12/08/12 05:43 PM

I see where your going and thanks for the illustration. I for one want to experiment on Io and Ganymede with CO.

Thanks again I'm seeing how the darker value is less crowded by smaller central airy discs due to co .

This has some compelling possibilities.

Pete


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