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Star brightness and Airy disks

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#1 derangedhermit

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Posted 25 January 2013 - 08:31 PM

I guess I thought in the past that the Airy disks of brighter stars were actually larger than those of dimmer stars. But tonight I think that makes no sense.

For centuries, in naked eye observing, the appearance of stars is such that people thought they were looking at actual diameters, and that brighter stars are bigger. Then that turned out to be false, I think, and all stars would appear as point sources without diffraction effects.

I think I have been holding onto the old view, and just translating it to Airy disk size. But I now think is correct is that we see more rings of the diffraction pattern for brighter stars, since everything is brighter, and that gives the appearance of greater diameter - yet the actual size of the disk and ring structure is the same size for all stars.

Is this latter view correct?

#2 Jon Isaacs

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Posted 25 January 2013 - 09:13 PM

I think I have been holding onto the old view, and just translating it to Airy disk size. But I now think is correct is that we see more rings of the diffraction pattern for brighter stars, since everything is brighter, and that gives the appearance of greater diameter - yet the actual size of the disk and ring structure is the same size for all stars.



The question you ask is a very good, one I have asked a number of times:

Why do brighter stars appear larger than faint stars? Consider Rigel, the companion is a tiny dot, the primary is big and bright. Pairs with lesser differences show this as well. Castor consists of two stars, magnitudes 1.58 and 2.97, the dimmer star clearly appears smaller to my eye than the primary.

I hope Glenn Ledrew can comment, I am sure he has a better understanding that I do. In any event I think there are several causes, the airy disk can be approximated with a Gaussian function, the central disk is not a sharp cutoff but rather somewhat gradual so a larger star is brighter further out.

A second factor is that a star like Rigel it is so bright that the scattered light is bright enough that you really never see the Airy disk.

And finally, there is the response of the eye, the eye is not a perfect sensor, a bright point affects the sensing cells around it, I believe they call this irradiation.

Cameras also show bright stars are larger but most cameras do not resolve the Airy disks.

Jon

#3 Asbytec

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Posted 25 January 2013 - 10:52 PM

One point, it's not the Airy disc we see as larger or smaller. That is fixed by the nature of the aperture (diameter, obstruction and aberration.) I believe the bright central disc changes apparent size because it's intensity is less, we see less of the PSF. On Dim stars the PSF just barely peeks above the visible threshold, while on brighter stars we can see more of it's radius. The rings may appear tighter, but really they are set by diffraction, too, at a fixed radius. As Jon mentioned, the eye response is complicated. Irradiance (or illuminance) causes the eye to act accordingly, including pupil size, modes of vision, contrast response, etc.

#4 derangedhermit

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Posted 25 January 2013 - 11:28 PM

Asbytec, that's what I think I'm stating. The Airy disk remains the same size regardless of the brightness of the star. Its size is dependent only on the optical system. What makes bright stars seem larger is the additional light outside the Airy disc. It drops off at the same rate regardless of the star's brightness (again, using the same instrument, including the naked eye), and what makes the bright star appear larger is that additional light at some distance from the center is enough for us to see, whereas at the same angular distance, the light from the dim star cannot. The pattern itself is the same size, regardless of stellar brightness, it's the brightness that changes.

A wikipedia graph of a generic PSF shows that the light from a psf is not uniform even in the center "hump". I had assumed the Airy disc was of uniform brightness. If it is of uniform brightness, then the dimmest stars we can see will have a uniform cutoff where we either see an Airy disk (and nothing else) or not. If the central area is not of uniform brightness, and tapers off, then the cutoff will be where we see some central portion of the disk (although in this case I am disinclined to continue to call it a disk), the outer edges being too dim to see.

#5 Asbytec

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Posted 25 January 2013 - 11:38 PM

Well, yes, the central disc can appear uniformly bright especially with brighter stars. But that is an eye response to bright stars. Even the first ring can appear brighter than it really is. The central disc brightness is not uniform.

In fact, splitting very close, equal magnitude pairs, say 7 Tau for example, one can see the edges of the central discs fall off in brightness. This is what provides the contrast needed for the Dawes split. It's more apparent with dimmer stars.

http://www.telescope..._resolution.htm

#6 kansas skies

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Posted 26 January 2013 - 09:44 AM

I would imagine that atmospheric scattering of light comes into play here as well. It makes you wonder how different the stars would look (both naked-eye and through a telescope) from the depths of space?

Bill

#7 REC

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Posted 27 January 2013 - 10:18 AM

I always wondered that myself? I once met an Astronaut what the stars looked like in space and he said that I wouldn't recognize any of the constellations as we see it from Earth as there are so many more stars visible in space you could read a book by it's light. Must be some sight with a small scope looking up from say the Moon:)

Bob

#8 Seldom

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Posted 27 January 2013 - 12:02 PM

Cameras also show bright stars are larger but most cameras do not resolve the Airy disks.

There's a Meade LX850 advertisement on the back of the March 2013 S&T. It compares a photo taken by the LX850 (12") with one taken by the Hubble (94"). Bright stars look larger on both, but the stars in the Hubble photo (Ring Nebula?) are significantly smaller than those of the LX850, and the ratios of the sizes on the LX850 appear to be greater than the ratios of sizes on the Hubble. I suspect the difference is just increased resolution from the 94" aperture. Do bright stars appear larger on really large aperture observatory scopes?

#9 Tom Polakis

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Posted 27 January 2013 - 01:35 PM

Good Cloudynights thread on this subject from 2009, particularly Ed Zarenski's comments half way down.

Cloudynights thread

#10 kansas skies

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Posted 27 January 2013 - 01:52 PM

This really is an interesting topic for discussion. I remember years ago being amazed at how bright stars seemed dimmer through the eyepiece. Of course, the dimmer stars got much brighter, which was more what I would have expected. I also remember being a little disoriented when viewing a dark sky from high in the mountains (without optical aid), the constellations didn't quite look the same. My point here is that even though these examples differ, the effect was similar.

Bill

#11 Qwickdraw

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Posted 27 January 2013 - 05:52 PM

I have to wonder if also mind tricks can come into play. Is our mind accustomed to brighter objects being closer hence bigger? An optical illusion of sorts could possibly exaggerate any real differences.

#12 kansas skies

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Posted 27 January 2013 - 11:06 PM

I did a little more research after taking more time to study all of these excellent comments and I think I now understand. After seeing the PSF of the Airy disk as mentioned above, it all made sense. :tonofbricks:

Bill






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