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  #21  
Old 12-12-2011, 08:45 PM
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Ok,

http://www.startools.org/download/airy_refractor.tiff

Load this image into PhotoShop (it's important that your program supports 16-bit bit-depth).

You'll see a small star in the middle. This is a computer generated star, with an Airy Disk-like PSF applied.
Now launch a curve manipulation tool and start adjusting the white point down, way down.
Now you'll see how the star grows along the airy disk diffraction pattern as its core gets overexposed (multiplied).

Does this help?
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  #22  
Old 12-12-2011, 08:46 PM
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OK
Time out!
"There will now be a short intermission - ice-cream and sweets are available in the Foyer..."

IVO, I based my wording on this:
http://en.wikipedia.org/wiki/Airy_disk
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  #23  
Old 12-12-2011, 10:27 PM
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Quote:
OK
Time out!
"There will now be a short intermission - ice-cream and sweets are available in the Foyer..."


Mmmm... icecream...

Quote:
IVO, I based my wording on this:
http://en.wikipedia.org/wiki/Airy_disk
I understand.
Your question is; "Why do star images grow?" (with longer exposures).
The answer is; because more energy is distributed according to their diffraction pattern/PSF/Airy Disk.

The wording in the Wikipedia article makes it sound like the Airy Disk is just a finite fuzzy blob around the location of a star. This is not the case (it is a simplification) and it is important to be aware of this in order to answer your question on why stars seem to 'grow'.

For purposes of Gaussian Curve fitting, the fuzzy blob gets pretty close to a Gaussian curve and we can leave it at that. And that's why Full Width Half Maximum measurements can be performed reliably and can be compare amongst eachother. Overexpose the fuzzy blob though and your Gaussian curve's top will be chopped off and/or distorted. This makes it harder to fit a Gaussian curve to and get FWHM results that you can compare with other measurements within the same image.

Now back to your question, "Why do star images grow?" (with longer exposures). You seem confused that stars can grow beyond the central fuzzy blob in the Airy Disk. The reason they can, is because the central fuzzy blob is not the end of the Airy Disk. The Airy disk has no end. Its pattern stretches out far beyond where the CCD sits.

Give the Airy Disk a bright enough star whose light needs spreading and it will saturate more and more CCD wells, further and further away from the central blob. The brighter the star, the further away from the center CCD wells get saturated. True, the central blob will be the first to completely saturate, but it doesn't stop there.

83% of all starlight falls in that central blob. But what if you got so much starlight that that 83% blob gets saturated? The other 17% all of a sudden becomes very important - that's where things start to saturate instead - the star starts to grow beyond the blob. It will take a lot of light to make it grow further and further (growing it just a single pixel will require more and more light) but it can definitely be done with enough photons. And because the spread function covers the whole CCD (and beyond), in theory, a single star can grow across the whole CCD, given enough photons.

I attached a visualisation of the underlying diffraction pattern that belongs to the tiny lonely 1-pixel star from the TIFF file I posted earlier. Diffraction is quite beautiful hey?
Stretch that TIFF far enough in PhotoShop and you'll see that tiny star grow according to this pattern. Try it; the data is really in there.
Note that non-linear stretching the TIFF is not what nature does. Nature just piles one more and more photons. You can do the same by adjusting the whitepoint in Photoshop, allowing pixels to gradually saturate. This is how a photograph gets exposed and how a star grows; the answer to your question.
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  #24  
Old 12-12-2011, 10:51 PM
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Great explanations Ivo
I think I was on the right idea path; just didn't have the theory to back it up.

Great read.
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  #25  
Old 12-12-2011, 11:33 PM
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"Gannet on a stick...Gannet on a stick" - The cinema scene from Monty Python...
IVO...with all your smooth talking you almost had me there
To quote:
True, the central blob will be the first to completely saturate, but it doesn't stop there.

83% of all starlight falls in that central blob. But what if you got so much starlight that that 83% blob gets saturated? The other 17% all of a sudden becomes very important - that's where things start to saturate instead - the star starts to grow beyond the blob.
Humour me for a moment...
Let's call the "Blob" (which contains 83% of all the starlight) an Airy Disk, and the ongoing (decreasing) waves of light surrounding it an "Airy Pattern" In this Airy Pattern there are definite brighter/ darker rings which decrease in intensity ( #1 = 8% of the total, #2 = 3% etc etc)
By definition the image of the Airy disk for any star (not just the faint ones or the bright ones - every star, big or small) extends -
Airy disk = 1.342 x focal ratio
For a f7.5 scope this gives a size of 10 micron.
Outside this disk there's a brief gap (first dark diffraction ring) before the 1st ring....
( When you observe a star at high magnification you can always see the diffraction/ Airy disk - it never changes size between stars)

The peak intensity (for a non-saturated star image) increases with exposure..ie Brighter (or more exposed stars) have a higher intensity peak than fainter (less exposed stars)
So, if we had a peak of say 10000ADU for a bright star, the Airy disk diameter would be a constant and the sum of all the pixels in the disk would represent 83% of the total energy/photon count. Let's say the total ADU count within the Airy disk is 300,000ADU - then only 29,000 ADU would be spread into the 1st ring, and 10,800 ADU in the larger 2nd ring. Thats a very large decrease in intensity (ADU/pixel)!!!

So, back to my conclusions...
1. The Airy disk for every unsaturated star is constant
2. The peak intensity increases with brightness/ exposure.
3. You have to fill the whole Airy disk before the lower intensity of the Airy Pattern begins to contribute to the increasing area of the star image.

I couldn't get your computer generated image to show a distribution similar to that of a real star...

"Part 3 - the story so far...Mary, the dark haired divorcee ran of with Guy, the one with the bushy eyebrows......."
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  #26  
Old 13-12-2011, 01:56 AM
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/gone to get more popcorn.
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  #27  
Old 13-12-2011, 02:23 AM
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Hmmm
reading up to understand this "ever expanding star"....
I think the issue is that I'm hung up on the Airy Disk as being the manifestation of the size of the star image....and the Airy pattern of ever decreasing rings as being so low in relative intensity relative to the "core" that even if they were over-over exposed they would never reach the intensity values of the Airy disk, and would, therefore, only contribute the the "wings" of the image and not the "flat topped" over exposed, saturated area seen in and around the Airy disk..
Be gentle with me.......
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  #28  
Old 13-12-2011, 07:19 AM
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Quote:
Originally Posted by RickS View Post
I think there are a number of different factors involved here but saturation alone is enough to explain a degree of bloat on bright stars. When the top of a star profile starts to get truncated by reaching full well depth the FWHM will increase. A diagram would help to make this clear but I don't have time to draw one right now...

Cheers,
Rick.
I think so Rick.

A simple experiment would be to take 2 exposures of a bright star field. One is short, say 20 seconds, the other is 10 minutes and measure the FWHM's of the same stars in each. That would reveal the short image has tighter stars I am predicting.

Greg.
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  #29  
Old 13-12-2011, 08:13 AM
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Quote:
Originally Posted by Merlin66 View Post
Hmmm
reading up to understand this "ever expanding star"....
I think the issue is that I'm hung up on the Airy Disk as being the manifestation of the size of the star image....
It appears so. I don't know what else to say to persuade you otherwise. How exactly do you come to that conclusion in the face of what is on Wikipedia and what I explained and demonstrated?
Quote:
and the Airy pattern of ever decreasing rings as being so low in relative intensity relative to the "core" that even if they were over-over exposed they would never reach the intensity values of the Airy disk, and would, therefore, only contribute the the "wings" of the image and not the "flat topped" over exposed, saturated area seen in and around the Airy disk..
The latter is just not true.

If George Bidell Airy was able to distinguish the second ring with his puny human eyes, what do you think a long exposure would show?

One last example of where you're going wrong;
Let's say my annual income is $100.000 (my CCD well depth) and I'd like to get a loan of $1000 (photons to disperse, aka star brightness). My bank offers a rate of 17% (percentage of photons dispersed outside the central fuzzy blob, or the PSF for the non-central fuzzy blob).
I'd be paying $170 per year - peanuts! It is easily serviceable with a $100.000 income and hardly noticeable when compared to my income (it's just 0.17% of my income).
By your logic I could just as easy take out a loan of $100.000.000. You seem to think the 'interest rate' (PSF) somehow is an absolute value, whereas it is a multiplication factor. Pick a high enough loan (star brightness) and it *will* start to matter. In the example of a $100.000.000 loan, I'd be paying $17.000.000 interest. I would need 170.000% my annual income (170 CCD wells) just to service the interest!
You're arguing the bump from 0.17% to 170,000% of my income isn't noticeable.

I really don't know what else to say or do. I've attached results of the TIFF multiplied by 800%, 3200%, 32000% and 320000%, just to show you it *does* grow, even though you can't see the light being spread at low energy levels.

FYI, the the initial PSF (i.e. the star in the TIFF) was obtained by creating a circular aperture (e.g. a white circle with a diameter of the 256 pixels) and then performing a forward Fourier transform and taking the magnitudes of the resulting complex numbers. Just like the math in the Wikipedia article.
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  #30  
Old 13-12-2011, 08:26 AM
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It would be the same if you were photographing the sun, with a normal SLR CCD camera and a 50mm lens ( not that it is recommended )
You might use a shutter speed of 1/64000th of a second and get a bright round circle, but use 1/2000th of a second and get your whole frame over saturated.
The only difference between the sun and the stars is the time it takes to expose them.
If you want to do a simple experiment. (not with the Sun ) get your SLR mount it on a tripod set up a LED (point Source light) in a dark room and expose it at different shutter speeds. You will see the exact same effect as what is being discussed.

Unfortunately for astronomers there are huge contrast ratios between the stars and faint fuzzy objects. So Airy disks, bloated stars what ever you want to call them, will be an issue. As CCD technology advances I am sure someone will come up with adaptive pixels, where the user could control the amount of saturation for individual pixels. It would be like the old darkroom technique of dodging and burning but on a far more advanced level.

Cheers
Phil
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  #31  
Old 13-12-2011, 08:35 AM
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Quote:
Originally Posted by CDKPhil View Post
It would be the same if you were photographing the sun, with a normal SLR CCD camera and a 50mm lens ( not that it is recommended )
You might use a shutter speed of 1/64000th of a second and get a bright round circle, but use 1/2000th of a second and get your whole frame over saturated.
The only difference between the sun and the stars is the time it takes to expose them.
If you want to do a simple experiment. (not with the Sun ) get your SLR mount it on a tripod set up a LED (point Source light) in a dark room and expose it at different shutter speeds. You will see the exact same effect as what is being discussed.
Yes!
Quote:
Unfortunately for astronomers there are huge contrast ratios between the stars and faint fuzzy objects. So Airy disks, bloated stars what ever you want to call them, will be an issue. As CCD technology advances I am sure someone will come up with adaptive pixels, where the user could control the amount of saturation for individual pixels. It would be like the old darkroom technique of dodging and burning but on a far more advanced level.
That'd be great. And there are indeed some techniques we can use in the interim. SkyViking (Rolf Wahl Olson) used one such technique to cancel out much of Beta Pictoris diffraction, revealing the dust disc.
Another one is using Deconvolution (and knowing the exact PSF) but that only works on non-saturated stars. The future is a type of video astronomy where many short exposures are stacked to create a very high bit-depth image with a huge dynamic range (and no overexposed pixels). The only thing holding us back right now is the various types of noise that become worse (such as read noise) when using many frames.
There also the good-old HDR compositing trick we could use today (as used for M42 for example), but alas there is no catch-all formula for smoothly blending the various frames.
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  #32  
Old 13-12-2011, 08:37 AM
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FWHM is commonly used as a measure of focusing and choosing stars for stacking.

Is the real point in that FWHM becomes unreliable once the central pixels come close to saturation?

Once you have a circle of saturated pixels FWHM has to be at least twice the diameter of the circle of saturated pixels.

So the moral of the story would appear to me - and to Craig Stark from the Nebulosity doco - do not use saturated stars to do any sort of measurement of focus, or alignment for stacking.
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  #33  
Old 13-12-2011, 08:52 AM
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Here is an animated gif of 7, 15, 30, 60, 120 and 240 seconds exposures with the last being a HDR. 6MB

http://d1355990.i49.quadrahosting.co...1_11/hdr01.gif

Below are the images that made up the gif. The cluster is the Jewel Box.

Bert
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  #34  
Old 13-12-2011, 09:36 AM
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Quote:
Originally Posted by mithrandir View Post
FWHM is commonly used as a measure of focusing and choosing stars for stacking.

Is the real point in that FWHM becomes unreliable once the central pixels come close to saturation?
Comparing FWHM between different stars/frames becomes unreliable. Gaussian curve fitting (of which the FW at HM is a by product) can still be used to help with determining sub-pixel accurate location though (as used for stacking purposes) because in that case you're just interested in the location of the predicted peak of the Gaussian curve, not its width or the magnitude at its maximum.

Quote:
Once you have a circle of saturated pixels FWHM has to be at least twice the diameter of the circle of saturated pixels.

So the moral of the story would appear to me - and to Craig Stark from the Nebulosity doco - do not use saturated stars to do any sort of measurement of focus, or alignment for stacking.
I don't see anything wrong with using them for stacking/alignment, but Craig may have reasons I'm not aware of?
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  #35  
Old 13-12-2011, 03:43 PM
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http://www.lbto.org/LBT%20Website%20...e%20optics.htm
Go down to the bottom of the page....
1. Due to the nature of light a pinpoint star produces an Airy disk, surrounded by a Airy Pattern.
2. All stars great and small produce the same linear diameter Airy disk for the same f ratio ie a 50mm f5 and a 500mm f5 produce the same sized Airy disk.

The limitations are not due to the Airy disk but the receptors ability to resolve and record the disk ( and the outlying pattern)
When you analyse a short exposure image, the star is still the Airy disk in diameter but with a much lower peak intensity. (See Star #4)
A brighter star (or more exposed star) has the same Airy disk diameter but a higher peak intensity (See Star #2)
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  #36  
Old 13-12-2011, 04:40 PM
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Quote:
Originally Posted by Merlin66 View Post
http://www.lbto.org/LBT%20Website%20...e%20optics.htm
Go down to the bottom of the page....
1. Due to the nature of light a pinpoint star produces an Airy disk, surrounded by a Airy Pattern.
It's called diffraction. Light itself doesn't do anything by itself - it requires to encounter an aperture.
Quote:
2. All stars great and small produce the same linear diameter Airy disk for the same f ratio ie a 50mm f5 and a 500mm f5 produce the same sized Airy disk.
Stars don't produce an Airy disk, the Airy disk (re)produces the stars. The Airy Disk is a point spread function. A function light has to go through before it appears on the imaging plane.
Quote:
The limitations are not due to the Airy disk but the receptors ability to resolve and record the disk ( and the outlying pattern)
When you analyse a short exposure image, the star is still the Airy disk in diameter but with a much lower peak intensity. (See Star #4)
A brighter star (or more exposed star) has the same Airy disk diameter but a higher peak intensity (See Star #2)
Until you overexpose and the first few rings fill up (if you can even dissolve the rings at your particular magnification).

Like I said, I don't know what else I can say or do to explain better to you why stars seem to grow. You seem to have drawn your own (erroneous) conclusions, yet wonder why they don't fit reality. I think it's time I give up.

All the best,
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