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Old 12-12-2011, 01:07 AM
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FWHM -Why do star images grow???

Using a CCD camera, each pixel records the photons and displays an ADU - the relationship between them being the gain of the camera.
Every star image produced by a telescope is basically an Airy Disk.
Due to atmospherics etc (ignore guiding errors and aberrations for a moment) a PSF (Point Spread function) curve is seen, basically the same Gaussian shape as the Airy disk but much larger in diameter.
The usual measure of this curve is the FWHM ( the width/diameter of the curve at half the peak intensity)
Still with me?
I do a 3 min exposure.....
The fainter stars appear smaller than the brighter stars ( get's even worse if the star intensity causes saturation...)
Why is this so??
The full extent of the PSF curve doesn't change.
Why doesn't the intensity just build up in each pixel within the PSF curve? Why does it appear to enlarge the PSF curve??
The reasons given say that as the exposure increases the CCD can record "fainter outer regions of the curve" and these show up as an increased diameter.....Sorry, I can't see that!
If ALL the light from the star is within a defined PSF curve and that curve, for a faint star is say 5 pixel diameter, then surely for a brighter star the total size should still be 5 pixel allbeit with a higher peak intensity.
Add 10 x 30 sec star images.....compare the size with a 5min star image????
I'm finding that if the star image is NOT saturated, then the PSF curve remains close to constant...when the star becomes a saturated image it starts to grow outwards ie 5 pixel max profile for a non-saturated star image v's 15-20 pixel for a saturated star!!!
( Ron Wodaski in his "The New CCD Astronomy", p 50-53 demonstrates this issue but gives no reasoning or answer to the possible cause.)
Can anyone add to my confusion?????
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Old 12-12-2011, 01:24 AM
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Old 12-12-2011, 01:28 AM
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OK a possible lead....
Blooming and saturation?
http://learn.hamamatsu.com/articles/...dblooming.html

Interesting...the "overflow" is dumped, not transferred to nearby pixels...
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Old 12-12-2011, 07:11 AM
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Interesting thread. I have seen that effect more pronounced with sensors with a smaller well depth than with cameras with a larger well depth.

I assumed it was a case of oversaturated pixels dumping nearby but I think it is probably more the fact that there is more scatter with brighter stars and the light accumulating in nearby pixels shows that scatter more when its a bright star. Accordingly if you use shorter exposures it will have the effect of tightening up the stars but also at the expense of losing some detail in the faint areas of your image.

CCD chips have a cover slip standardly (Kodak). These can create small halos and reflections. That would add to it. Additionally I don't know how good the antireflection coatings are on these cover slips. On top of that most astro chips have a microlens layer that focuses the light to the side of the pixel that has the higher QE. So you've got a few things going on there.

Its a similar phenomena with blue filters versus other colours. Blue is often more bloated. I have read that this is because blue is more scattered. Seems to work as a theory.

Reading that article you linked it mentions anitblooming is less efficient on one side of the pixel than the other and that various antiblooming methods have different characteristics and efficiencies. The implication there is that perhaps they don't work 100% in every scenario so perhaps there still is some overflow to nearby pixels. It does not clarify that point too much.

Also I wonder if this comes into it:

http://www.paquettefamily.ca/astro/star_study/

In that colours are not registered with the same FWHM usually. Blue being worst. Sensors are often listed with QE for each colour channel and often are not equal in QE. It can vary by 10-20% more or less QE. Could that effect of bloated stars also be they were bright and bluish stars?
Greg.

Last edited by gregbradley; 12-12-2011 at 07:34 AM.
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Old 12-12-2011, 09:11 AM
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maybe an article on this page can help

http://www.stark-labs.com/craig/articles/articles.html
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Old 12-12-2011, 09:15 AM
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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,
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Old 12-12-2011, 03:18 PM
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Are you asking why the increase of the maximum of the FWHM with overexposure?
You could try this one.

Detecting and measuring faint point sources with a CCD
"Herbert Raab"
http://www.astrometrica.at/papers/PointSources.pdf
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Old 12-12-2011, 04:23 PM
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Quote:
Originally Posted by Merlin66 View Post
Using a CCD camera, each pixel records the photons and displays an ADU - the relationship between them being the gain of the camera.
Every star image produced by a telescope is basically an Airy Disk.
Due to atmospherics etc (ignore guiding errors and aberrations for a moment) a PSF (Point Spread function) curve is seen, basically the same Gaussian shape as the Airy disk but much larger in diameter.
The Airy disk does not look like a Gaussian distribution. It looks like a disk with rings around it that get ever fainter. The PSF of a single point light will affect all pixels on your CCD. E.g. the light of a point light is spread all over your image and thus will build up all over your image given a long enough exposure.
The PSF is created by diffraction and has nothing to do a priori with atmospheric turbulence. You will still see an airy disk even outside the earth's atmosphere.
The atmospheric turbulence indeed smears the disk out a little randomly over time (because it moves randomly). This random movement indeed approximates a Gaussian distribution as exposure time increases.

Does that help?
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Old 12-12-2011, 05:06 PM
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Leinad - good find!
The assumption is the PSF is maintained for all unsaturated star images...that's what I'm finding...doesn't address saturated stars?

Maybe the attached write-up will give some ideas of my data/ thoughts...
In the meantime - an analogy...
Point a laser beam at a piece of graph paper on the wall (-CCD/pixels).
The beam illuminates a patch 2 x 2 squares centred on point "A" ( - Airy disk)
After five minutes, the laser still illuminates only the 2 x 2 sq, and the intensity recorded at point "A" will have increased.
There will be no illumination recorded outside the 2 x 2 square.....
More realistically:
Same laser but supported by a shakey table, still centered on point "A" but can wobble around and illuminate up to a patch 10 x 10 squares (-Seeing conditions)
After five minutes, point "A" will still record the peak illumination and the spread will not exceed 10 x 10 squares.....

Why then would a star image appear to spread to say 20 x 20 squares??????

Other than sensor reflections etc - the feeling seems to be that the image saturation will cause the 7% residual light in the "1st Airy ring" to contribute to the image size. This doesn't seem to match....
(BTW with the Hubble...if there's no atmospherics to "smear" the Airy disk --why do brighter stars still look larger?? )
Attached Files
File Type: doc FWHM_01.doc (125.5 KB, 12 views)
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Old 12-12-2011, 05:24 PM
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Quote:
Originally Posted by Merlin66 View Post
the feeling seems to be that the image saturation will cause the 7% residual light in the "1st Airy ring" to contribute to the image size.
And that's exactly the case.
Quote:
This doesn't seem to match....
With what exactly? The size of the Airy disk and the spacing of its rings depend on your aperture and focal length (and CCD resolution of course).
Quote:
(BTW with the Hubble...if there's no atmospherics to "smear" the Airy disk --why do brighter stars still look larger?? )
That's because Airy disks have nothing whatsoever to do with atmospherics- diffraction is the main cause of your stars not being neat points! All telescopes will necessarily have to diffract the light, even the Hubble.

EDIT: I think your analogy is flawed as a laser beam is not a focused beam of light. All photons travel in parallel and have not been diffracted yet, thus showing no Airy disk on the paper. Also you seem to assume there is just one (or two) rings around the primary Airy disk. In fact there are many and they extend for the full surface area of the aperture.

Last edited by irwjager; 12-12-2011 at 05:37 PM.
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Old 12-12-2011, 05:31 PM
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IVO,
You need to read the document I attached to the last message...
I take into account the f ratio and the camera pixel size in the calculations...
The enlarged saturated star images appear to exceed the diameter of the Airy rings..

Re Hubble - this would then infer that the brightest star image recorded will always been no larger than the extended Airy disk...is that really the case???
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Old 12-12-2011, 05:51 PM
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Quote:
Originally Posted by Merlin66 View Post
IVO,
You need to read the document I attached to the last message...
I take into account the f ratio and the camera pixel size in the calculations...
The enlarged saturated star images appear to exceed the diameter of the Airy rings..
There is no diameter of the Airy rings. These rings extend throughout the image - e.g. all wells on the CCD (or film) get a tiny bit of light.

EDIT: I see in your document you define the 'Airy disk diameter' as 2.44 x Lambda x f ratio. This formula is an approximation of the position of the first minimum, but many, many minima (and rings) follow. The disk that you define only contains 83.3% of all the light, with the rest being spread out over an increasingly large area away from the star, concentrated in further rings. Expose this area long enough and it will start showing up, gradually 'growing' the stars until the whole image saturates.

Quote:
Re Hubble - this would then infer that the brightest star image recorded will always been no larger than the extended Airy disk...is that really the case???
Not sure what you're saying here, but rest assured that an incredibly bright star, which would be incredibly far away (e.g. for all intents and purposes a point light) can easily swamp Hubble's CCD wells with a long enough exposure.

Last edited by irwjager; 12-12-2011 at 06:07 PM.
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Old 12-12-2011, 06:01 PM
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IVO,
Sorry,
what I'm trying to say is that even if you add the contribution of the light from the 1st and 2nd rings ( total star energy = 94%) the apparent saturated star image still seems to exceed the linear diameter of the rings....
The background shot noise level will be sqrt max intensity, which I'm sure would exceed the residual star energy...so no additional signal to expand the image???
I probably need to use the photometry aperture feature (AA5) to better determine how the summed ADU count in each star image changes. This should be linear (for non- saturated images) - but what about a saturated image?
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Old 12-12-2011, 06:33 PM
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Quote:
Originally Posted by Merlin66 View Post
IVO,
Sorry,
what I'm trying to say is that even if you add the contribution of the light from the 1st and 2nd rings ( total star energy = 94%) the apparent saturated star image still seems to exceed the linear diameter of the rings....
Ok, what sort of excess energy/starlight are you observing?
Quote:
The background shot noise level will be sqrt max intensity, which I'm sure would exceed the residual star energy...so no additional signal to expand the image???
You be must taking really short exposures for the shot noise to drown out the Airy disk! There are many examples of a diffracted Alnitak overwhelming the Horse Head nebula for instance (http://www.iceinspace.com.au/forum/s...ad.php?t=83886), even though Alnitak was never even projected on the CCD (its light still made it through the aperture of the scope).
Quote:
I probably need to use the photometry aperture feature (AA5) to better determine how the summed ADU count in each star image changes. This should be linear (for non- saturated images) - but what about a saturated image?
You hit the nail on the head - the way your CCD deals with saturation of its wells varies wildly. But it is, alas, almost never truly linear. Saturation is dealt with in various way by the anti-blooming circuits of your CCD (if any). Fitting a Gaussian curve to a saturated star is therefore not very reliable.
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Old 12-12-2011, 06:37 PM
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I think I see where you're getting. but confused by your analogy's.
This was also interesting.. diffraction. Wouldn't saturation cause the PSF maximum to be larger than the airy disk over x time due to the diffraction. got me glued to the screen now.
I don't know how this incorporates into your Hubble comparisons though..

http://www.willbell.com/aip/haip2_chap_1.pdf
Pg 29 - Section 1.5.4
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Old 12-12-2011, 06:54 PM
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Leinad,
That's the nub of the problem - at least for me...
If the PSF of the Airy Disk contains ALL the energy/ photons available from the star, then the maximum size of the star image can NEVER exceed this size....hence my laser pointer analogy.... there's never any illumination beyond a 10 x 10 box...so whatever the exposure the size should always be less than 10 x 10.

If you look at the profile data say for Star#1 and Star #2 (one is saturated the other is well exposed). The "max" diameter recorded for #1 is 20 pixel and for #2, 12 pixel, and the FWHM is 6 pixel v's 3.5 pixel.
Why, when the brighter star is over-exposed more does the "size" increase by 166%....Aah...the longer exposure collects the light from the outer reaches of the PSF curve...Hmmmm don't think so....

IVO,
The second comment you refer to - wasn't the Airy disk being drowned out, but the light in the extreme "wings" ie that last 6% of total energy being drowned in the background noise....
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Old 12-12-2011, 07:35 PM
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After going over your document; I see what you're addressing now... even more interesting.

/seated with popcorn.


Quote:
Originally Posted by Merlin66 View Post
Leinad,
That's the nub of the problem - at least for me...
If the PSF of the Airy Disk contains ALL the energy/ photons available from the star, then the maximum size of the star image can NEVER exceed this size....hence my laser pointer analogy.... there's never any illumination beyond a 10 x 10 box...so whatever the exposure the size should always be less than 10 x 10.

If you look at the profile data say for Star#1 and Star #2 (one is saturated the other is well exposed). The "max" diameter recorded for #1 is 20 pixel and for #2, 12 pixel, and the FWHM is 6 pixel v's 3.5 pixel.
Why, when the brighter star is over-exposed more does the "size" increase by 166%....Aah...the longer exposure collects the light from the outer reaches of the PSF curve...Hmmmm don't think so....

IVO,
The second comment you refer to - wasn't the Airy disk being drowned out, but the light in the extreme "wings" ie that last 6% of total energy being drowned in the background noise....

Last edited by leinad; 12-12-2011 at 07:46 PM.
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Old 12-12-2011, 07:36 PM
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I'm slowly getting there (I think!)
Conclusions/ Comments
  • For unsaturated star images, the maximum size of the star is similar to the Airy disk in diameter.
  • The FWHM of the star image is reasonably constant.
  • As the star image saturates, the “flat top” extends out to the diameter of the Airy disk.
  • Also, for saturated star images the “wings” include additional energy from the outer rings, and can extend, in linear diameter, to and slightly beyond the dimensions of the 1st Airy ring.
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Old 12-12-2011, 07:51 PM
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Quote:
Originally Posted by Merlin66 View Post
Leinad,
That's the nub of the problem - at least for me...
If the PSF of the Airy Disk contains ALL the energy/ photons available from the star, then the maximum size of the star image can NEVER exceed this size....hence my laser pointer analogy.... there's never any illumination beyond a 10 x 10 box...so whatever the exposure the size should always be less than 10 x 10.
The Airy Disk *is* a Point Spread Function. It describes how a single point of light (a star) is spread over (in this case) the CCD when it is shone through a circular opening (in this case the aperture of a telescope).
The sum of all the energy 'scattered' throughout the image by the PSF is indeed equal to the amount of energy received from the point light. Again, the PSF, in this case the Airy Disk, spreads the energy out over a huge area.

You seem to be confused by the 'maximum size of a star'? In a perfect world every star in your image would be a point light. But we run into two problems;
  1. Your CCD wells saturate. They start clipping the signal and can't register a star that's brighter than 'maximum brightness', nor can your computer display display such a brightness. Therefore the signal is capped to 'pure white'. The star itself may in fact be much brighter than that but we can't record that, nor can we display that, so we cap it to the maximum brightness we can represent with our system(s).
  2. The starlight is necessarily diffracted by the aperture of your telescope. This leads to the light being spread over a larger area than just a single point.
Now, combining the two 'problems', more starlight can be captured by your wells because the starlight is spread by the PSF over a larger area, hitting more CCD wells. No longer is the point concentrated into a single well, instead it is spread over all the wells in your CCD. Some may still saturate and be completely white, but others may not.


Again, your laser pointer analogy is flawed as the laser light is not diffracted.
Quote:
If you look at the profile data say for Star#1 and Star #2 (one is saturated the other is well exposed). The "max" diameter recorded for #1 is 20 pixel and for #2, 12 pixel, and the FWHM is 6 pixel v's 3.5 pixel.
Why, when the brighter star is over-exposed more does the "size" increase by 166%....Aah...the longer exposure collects the light from the outer reaches of the PSF curve...Hmmmm don't think so....
Again, Gaussian Curve fitting to overexposed stars and then comparing FWHM readings is next to meaningless.
Quote:
IVO,
The second comment you refer to - wasn't the Airy disk being drowned out, but the light in the extreme "wings" ie that last 6% of total energy being drowned in the background noise....
I understand that, but you can't 'drown out' a PSF. It is merely a function by which you multiply the energy of a star. There are very bright stars (ex. Alnitak) which, when you multiply them by your scope's PSF will readily show up (and ruin your image) even though their core is way off the CCD.
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Old 12-12-2011, 08:32 PM
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Quote:
Originally Posted by Merlin66 View Post
  • For unsaturated star images, the maximum size of the star is similar to the Airy disk in diameter.
False. The Airy Disk does not have a diameter. It is a pattern, patterns don't have diameters. You could, however, say that 83% of all starlight of the imaged star should be contained within the area that extends from the center to the first minimum.
Quote:
  • The FWHM of the star image is reasonably constant.
False. The FWHM is dependent on how well you can fit a Gaussian curve to a star. You will be able to fit a Gaussian curve less well to saturated stars, depending on the response of the CCD you're using. It is also neigh impossible to fit a gaussian curve to undersampled images.
Quote:
  • As the star image saturates, the “flat top” extends out to the diameter of the Airy disk.

False. It can extend way beyond the first minimum.
Quote:
  • Also, for saturated star images the “wings” include additional energy from the outer rings, and can extend, in linear diameter, to and slightly beyond the dimensions of the 1st Airy ring.
False. They extend throughout the whole image.
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