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# Back of the envelope calculation for seeing limited magnification

Observing Visual
28 replies to this topic

### #26 TicoWiko

TicoWiko

Vostok 1

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Posted 06 August 2024 - 03:28 AM

I asked a similar question here - basically, how does one come up with the empirical rule that the max useful magnification is ~ 50x - 60x per inch of aperture. The 1 arcmin value for the resolution of the eye suggests values closer to ~ 18x per inch of aperture. The simple answer seems to be that the scotopic resolution is quite a bit lower than 1 arcmin...

If I'm not mistaken that rule relates to a scope's diffraction limit. What I'm asking about here is strictly the imposed atmospheric limit, assuming you're far from your diffraction limit.

### #27 Redbetter

Redbetter

Hubble

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Posted 06 August 2024 - 03:54 AM

I think the problem with your reckoning is that the eye's resolution, the angular measure of the seeing, and the concept of a sharp image are all of them pretty fuzzy concepts.

For what it's worth, I consider my own eye's resolution to be 4 arcminutes. To phrase that more precisely, I can split naked-eye doubles with equal-magnitude components when the components are 4 arcminutes apart, but not when they're much closer than that. Likewise, I can split a telescopic double with 4-arcsecond separation at 60X but not much lower than that.

In my experience most people's resolution is a bit better than mine, but fewer than half of all people can separate the Double Double naked-eye. Its components are 3.5 arcminutes apart. Very few people indeed can split 2-arcminute doubles, and 1 arcminute is an exceedingly optimistic assessment of the human eye's resolution.

Likewise, it's not clear exactly what telescopic seeing of 1 arcsecond means. This is traditionally assessed photographically, but time-exposure photos are more affected by atmospheric smearing than visual observing is, due to the human eye's capability of freezing motion.

And finally, even if an image appears really sharp at 240X, it might appear quite a bit sharper if the seeing was better.

I generally have trouble seeing the Double-Double split anymore naked eye without correction, yet a few nights ago I was commenting on that very problem to another experienced observer and pointed up to it, and realized I was readily seeing it and the PA correctly.  I then coached him through it and he could see it too.  Neither of us were using any correction.  It was a good dark night, and reasonably steady up high, both of which helped.  For reference, when I was describing where the Double-Double was to my son (with sharper eyes than mine, and tons of accommodation) a year or so ago, he became exasperated and finally asked, "you mean the one that is double?"  He was already seeing it that way easily without prompting.  I felt somewhat stupid, but I also remember what it was like to have eyes that sharp...

Splits like this are somewhat dependent on how dark the sky is since the components are not that bright themselves and can easily blur together as a result.   Acuity and correction for distance are major factors.  My acuity varies from night to night anymore.

### #28 Xilman

Xilman

Viking 1

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Posted 06 August 2024 - 04:10 AM

How do you determine whether the seeing is 1" or 2"? I suppose you might have a list of a few hundred even-magnitude doubles, and run down the list from widest to narrowest until you find one you can't split. But by then the time I was done, the Sun would be rising.

Binary search runs in logarithmic time, which is much more efficient than the linear time search you propose.

Take your list of doubles and sort them in order of separation, widest first. If you can't resolve the first (i.e. widest) on the list, game over. Otherwise, select a star half way down the list . If you can resolve that, select one which is half way down from that point, otherwise choose one from your list located half way between the current closest which can be resolved and the current widest which can't. Repeat until you find there are no more stars in your list between the two which are just resolvable and just not resolvable.

Even if you have 256 stars in your list, it only takes 8 observations to find the borderline case.

Edited by Xilman, 06 August 2024 - 04:15 AM.

### #29 Keith Rivich

Keith Rivich

Fly Me to the Moon

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Posted 06 August 2024 - 11:25 AM

Oh, wow, you're going by predictions rather than reality? Good luck!

My experience with seeing predictions is that they're barely better than blind chance.

Here at our dark site there is usually someone imaging that can get us a seeing estimate. Last Friday night we were consistently getting 1.5" where, according to the imager, 2.5" to 3" is the norm.

Visually the seeing jibed with his number, was quite good.

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