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Observing >> Deep Sky Observing

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FirstSight
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Why do brighter stars appear "larger" in scopes? new
      #5280894 - 06/20/12 03:19 PM

At least in the apertures of even larger amateur telescopes, the angle subtended by the diameter of even relatively close stars such as Vega is far too small to be visibly resolved into a disc rather than (in principle) a point of light no larger than the smallest angular resolution the particular instrument is capable of showing. For example, Vega has an equatorial diameter approximately 2.74x that of the sun, and we can ignore for discussion that its polar diameter is more like 2.25x that of the sun due to distortion induced by rapid rotation. The key thing for our purpose is that since Vega is about 25 light-years distant from earth, we can calculate that it visually subtends an arc approximately 1.61x10^-8 degrees or 4.47x10^-12 arc-seconds from the distance of earth. Even assuming I haven't figured the amount of arc-seconds quite accurately, nevertheless the basic point is correct: the visual angle subtended by its diameter at the distance of earth is too small by an enormous factor to resolve into anything approaching the minimal resolution capability of amateur telescopes.

YET, brighter stars such as Vega unmistakably "appear" quite distinctly larger to us than fainter stars in our telescopes, and even to some extent naked eye. I presume that a key part of the explanation is diffraction effects: in a telescopic view is that the brighter the star, the more light flux is available to spill over into diffraction rings further out from the central axis, and the lenses of our own eyes accomplish the equivalent thing naked-eye. This will be true even of an extremely high-quality optic with a high Strehl ratio, although the amount of light leaking into outer diffraction rings will be less than for a poorer-quality optic. Is this an accurate understanding of why brighter stars appear larger, even to the extent of generating a pseudo-disc in the case of the brightest stars?

I understand that in some very large aperture high-quality professional telescopes, it actually is possible to barely resolve the actual disc of a tiny handful of bright stars at very high magnification, Betelgeuse in particular. However, the essential point remains that this accomplishment is vastly beyond the capabilities of any telescope owned by members of the CN community. Correct, and if so, for the reasons I stated? Or am I merely correct as far as it goes, and there's more to it than just that?


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hbanich
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Re: Why do brighter stars appear "larger" in scopes? new [Re: FirstSight]
      #5280946 - 06/20/12 04:09 PM

Hi Chris, I don't really know, but think it has to do with their brightness - with a variable density filter it's possible to dial the brightness of any bright star down for it look just like a fainter and "smaller" star.

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David Knisely
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Re: Why do brighter stars appear "larger" in scopes? new [Re: FirstSight]
      #5280986 - 06/20/12 04:33 PM

There are two effects here. One is the human eye itself. Bright stars tend to "saturate the detector", so their brightness tends to spill over making them appear larger than the point sources they are. That brightness also allows some of the aberrations of the eye to become a lot more noticeable, further enlarging the spot of light which the eye sees. The second is diffraction. Brighter stars will show several diffraction rings around their diffraction disks, and (especially in bad seeing) this can make them appear larger than fainter stars that show either no rings or perhaps only the first one. Clear skies to you.

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Tony Flanders
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Re: Why do brighter stars appear "larger" in scopes? new [Re: David Knisely]
      #5281293 - 06/20/12 08:32 PM

Quote:

There are two effects here. One is the human eye itself. ... The second is diffraction.




At all but the highest magnifications, the human eye is by far the dominant factor. It's much the same reason that bright stars appear bigger in film photos.


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FirstSight
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Re: Why do brighter stars appear "larger" in scopes? [Re: Tony Flanders]
      #5281444 - 06/20/12 10:20 PM

It astounds me that the telescope aboard the Hubble has the necessary fine resolution to at least crudely resolve the disc of Betelgeuse itself, rather than merely being artifacts of diffraction or the intensity load on the sensors. Although Betelgeuse is considerably farther than Vega (about 640 ly, or twenty-five times farther), it is also considerably larger at about 700 million miles in diameter, or about 295 times the diameter of Vega. If you work this out, this means that from Earth, the disc of Betelgeuse subtends an angle roughly on the order of 10x larger than that of Vega, but still on the rough order of 10^-11 arc-seconds. That's some remarkable sensitivity of optical resolution, if I've done my rough calculations at all accurately. By contrast, in our typical better, larger aperture amateur instruments with ideal atmospheric conditions, we're delighted with half arc-second resolution or the order of 5x10^-1 arc seconds (as compared to the order of 10^-11).

Edited by FirstSight (06/23/12 02:28 AM)


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Starman1
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Re: Why do brighter stars appear "larger" in scopes? new [Re: FirstSight]
      #5284333 - 06/22/12 07:07 PM

Example: the crescent moon appears to have a larger diameter than the earthlit part visible immediately adjacent.
The reason: The brain sees brighter as larger.
Reduce the brightness by using a telescope (which reduces the exit pupil and the unit area brightness) and the diameter difference goes away.

The brain interprets brighter stars as larger.
It's been demonstrated in experiments wherein two identically-sized squares, side-by-side, are differentially illuminated. The brain sees the brighter square as larger.

It could partially be related to retinal response, but it's mostly in the brain.


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gnowellsct
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Re: Why do brighter stars appear "larger" in scopes? new [Re: David Knisely]
      #5284661 - 06/23/12 12:14 AM

Quote:

The second is diffraction. Brighter stars will show several diffraction rings around their diffraction disks, and (especially in bad seeing) this can make them appear larger than fainter stars that show either no rings or perhaps only the first one.




The diffraction, I think, is the main thing. At any given moment the light (and its diffraction) is not really at a specific coordinate but dancing around that spot in a pattern which is the point spread function. In other words the star is at a specific point in the sky but because of the non-stop variations in the atmosphere the probability of the light being in any one space can be defined loosely as "very high probability" in the center and lower probability as you get farther out. A very bright star like Sirius has so much energy that the dancing beam looks like a blob. It would be easier to observe out in space.
From wiki:
Quote:


The images of the individual object-plane impulse functions are called point spread functions, reflecting the fact that a mathematical point of light in the object plane is spread out to form a finite area in the image plane (in some branches of mathematics and physics, these might be referred to as Green's functions or impulse response functions).




A reverse way of looking at the problem is what happens when the star is very very faint. At the limits of the scope's detection ability, very faint stars in mediocre seeing will wink in and wink out. When they light is too spread out the star can't be detected and disappears. When the light is more concentrated at the heart of the point spread function the star reappears.

By using a bigger aperture you can capture more of the energy that is there, so the star that winks in and out in a six inch aperture won't wink in and out in a fifteen inch.

On a not so great night at medium powers faint stars will look like little dots. They don't show as pinpoints because they are not, in fact, pinpoints.

Greg N

p.s. I'm not sure why we need to bring the human eye into it. The PSF would register as a statistical distribution of photons around a center point never mind whether an eye is looking at it or not. It looks bigger because it IS bigger (i.e. the seeing disk): even blind beings using instruments to record incoming celestial light would get PSFs that varied in size and corresponded to stars that we would call brighter or dimmer, and they would also likely note that the same stars appeared to be "bigger" when the atmosphere wasn't steady. In fact, if they were truly congenitally blind the varying size of the PSF would be one of their ways to "understand" brightness. The eye is seeing something real.


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Tony Flanders
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Re: Why do brighter stars appear "larger" in scopes? new [Re: gnowellsct]
      #5284819 - 06/23/12 05:09 AM

Quote:


The diffraction, I think, is the main thing.




It depends on the magnification. At 1X, to the naked eye, the diffraction pattern is far below the resolving power of the human eye.

Bright stars do look bigger than faint stars to the naked eye and in a wide-angle photo taken on film. But not in a wide-angle photo taken with a DSLR -- to the sorrow of many would-be wide-angle night-sky photographers.

That seems like conclusive proof that it's the sensor rather diffraction that's the main issue.


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Jon Isaacs
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Re: Why do brighter stars appear "larger" in scopes? new [Re: Tony Flanders]
      #5284873 - 06/23/12 07:58 AM

This is an interesting question, I have done some experiments that have led me to believe that as Tony and David have said, it is mostly the eye and the saturation of the retina.

One set of experiments I did was use my 80mm F/7 refractor at about 17x on gamma Arietis, a nice double at about 8 arc-seconds. At 17x, the pair was resolved but poorly but I could not resolve the disks, the stars were large, much larger than the disks.

Rather than increasing the magnification, I masked the aperture to reduce the brightness. What happened was that as the exit pupil was reduced from the initial 5mm the stars became smaller and the pair more perfectly formed. At somewhere around 2mm the disks began to become visible.

Increasing the magnification showed that the image at the focal plane was of the highest quality, the reason for the improved image quality could have been that the objective was not performing well and by masking it, the image was improved but that not the case.

In this range, I am quite sure it is the eye's response that makes brighter objects look bigger.

At high magnifications, it must be a combination of effects as sometimes one can see the airy disk structure of a very bright star. Still, the eye's response would seem to play a major role.

Jon


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gnowellsct
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Re: Why do brighter stars appear "larger" in scopes? new [Re: Jon Isaacs]
      #5285639 - 06/23/12 05:14 PM

I hadn't thought of the 1x issue. Angular resolution of the naked eye is about 1 to 2 arc minutes, I read. So PSF can't be the only issue.

GN


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Starman1
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Re: Why do brighter stars appear "larger" in scopes? new [Re: gnowellsct]
      #5285663 - 06/23/12 05:28 PM

I still think it's in how the brain interprets the image from the eye.
If it was bleed over to adjacent retinal cells, I think it would be seen in many circumstances where bright targets are seen.
On the other hand, if the brain interprets a stronger signal as larger, it makes sense that we see a brighter square adjacent to an equally-sized dimmer square as larger.
It's definitely an example of "trompe l'oeil".


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Tony Flanders
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Re: Why do brighter stars appear "larger" in scopes? new [Re: Starman1]
      #5288372 - 06/25/12 12:24 PM

Quote:

I still think it's in how the brain interprets the image from the eye.




When I say "sensor," I mean the entire eye-brain system, not the retina per se.

Remember, the eye does not take still photos like a CCD camera, and any attempt to explain it in those terms is doomed to failure.

The eye in constant motion, scanning back and forth across the image. So the image of a point source always falls on multiple retinal cells. What the optical system actually detects is changes in intensity, not intensity per se.


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