Are Deep Sky objects and portability mutually exclusive?

[acey]

"Aperture still wins under light polluted conditions, though I agree that more is visible in a smaller scope under dark skies than a large scope under light polluted ones."

magic612 - you agree with my conclusions but not my reasons. I disagree with your reasons.

It's covered very well in Roger Clark's Visual Astronomy Of The Deep Sky (it's Clark who makes the comment - with which we agree - that a 4" in the country beats a 16" in the city). For extended objects, contrast is constant with respect to magnification, but contrast threshold varies according to object size and background: Clark used the data gathered by Blackwell in his famous wartime study of human contrast perception. So a faint fuzzy becomes visible once magnified to a big enough size, even though its actual contrast doesn't change. Larger aperture means you get a brighter image for any given magnification, compared to a smaller scope at same magnification, regardless of focal ratio.

For the significance of exit pupil, let the magnification of a scope be k times its lowest useable magnification. Then exit pupil = ep/k where ep is the diameter of the eye pupil (a fact that is independent of focal ratio). Suppose you have an eye pupil size 7mm and can tolerate an exit pupil size down to 0.5mm. Then you can let k go up to 14. If your scope aperture is 70mm then your lowest power is x10 and your top will be 14x10=140; if your aperture is 280mm then your lowest power is x40 and you can go up to 14x40 = 560. If you've got a galaxy whose size and contrast require a magnification of x300 then you've got a chance of seeing it with the larger scope, but not the smaller. (This of course says nothing about seeing conditions or image degradation due to optical limitations, which further constrain upper magnification in practice).

The most conspicuous DSOs don't require anything like that sort of magnification to become visible: some are naked eye and all the Messiers need no more than about x20, assuming the sky is dark enough. So portability and DSO visibility are not mutually exclusive, though obviously the Messiers look more interesting with higher magnifications, requiring larger apertures and potentially bulkier instruments. Fainter NGC objects do in many cases require powers over x150 in order to become visible, a fact easily demonstrated by the use of a zoom eyepiece.

I do the vast majority of my galaxy viewing with a 12" f4.9 at a magnification of x250, exit pupil 1.2mm.

[ismangil]

Since Clarke's book is no longer in print and second hand copies are close to three digits, I've found a reference to the next best thing: a document from ASSA that quotes extensively from Clarke on this issue http://www.assabfn.co.za/activities/deepsky/deepsky_observers_companion_assa.pdf

Just in case anybody want to know more on the relationship between aperture, magnification, and eye contrast perception :-)

-- Perry Ismangil

[magic612]

So a faint fuzzy becomes visible once magnified to a big enough size, even though its actual contrast doesn't change. Larger aperture means you get a brighter image for any given magnification, compared to a smaller scope at same magnification, regardless of focal ratio.

But isn't it true that at the higher magnifications, the sky background effectively darkens? My point was that the contrast of the object is effectively increased (though it remains constant relatively speaking) - in other words, it easier for the human eye to spot a grey faint fuzzy on a black background than a grey faint fuzzy on a grey background. The increase in aperture allows for the magnification boost, preserving image brightness while simultaneously darkening the sky background.

You said it much more articulately, and with good math (not one of my strong points, I will concede!). Maybe I'm not making sense, but I do understand what you are saying.

[hunterknox]

I do love the design of the Sumarian optics dobsonians, which fold down to a suitcase size box + trusses. Pricey though.

[umadog]

It is pricey, but it works. It's expensive compared to mass-produced but it's not expensive compared to other custom builders. It allows you to go observing with a good-sized aperture in situations where you otherwise could not. A big bonus. I have one and like it a lot.

[acey]

But isn't it true that at the higher magnifications, the sky background effectively darkens? My point was that the contrast of the object is effectively increased (though it remains constant relatively speaking) - in other words, it easier for the human eye to spot a grey faint fuzzy on a black background than a grey faint fuzzy on a grey background. The increase in aperture allows for the magnification boost, preserving image brightness while simultaneously darkening the sky background.

Key point is to distinguish between contrast (a physical parameter which doesn't change) and contrast threshold (a psycophysical parameter dependent on target size and background brightness).

Call the surface brightness of the sky Bsky, and the increment surface brightness (i.e. the object you're trying to see) Bobj. Define contrast C = Bobj/Bsky. Now magnify by m: sky and increment surface brightnesses are both divided by m^2. Hence we have new contrast = (Bobj/m^2)/(Bsky/m^2) = Bobj/Bsky = C, unchanged. So, as you say, contrast is not changed by magnification.

Next consider the threshold contrast, which we can think of as the lowest value of contrast that the eye perceives (in practice it's really defined as the value at which there's a 50% probability of detection). Experiments show that for a uniform circular target and a given observer, the threshold depends on two things: background surface brightness and target size.

Upshot is that at low light levels an object needs to be bigger in order to be visible. This is familiar experience: small print we can read in daylight becomes illegible in twilight, where we would need a magnifying glass to read it.

Now consider a galaxy of angular area A which has a certain contrast C against a sky of surface brightness Bsky. Let's say this value of C is below the threshold of visibility. If we magnify it, C is unchanged, but A and Bsky change, and we may reach a point where the object looks big enough, and the background dark enough, for the threshold to fall below C. Then the target becomes visible.

Clark has a webpage outlining his work.

Clarkvision.com: OMVA in Visual Astronomy of the Deep Sky