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Main
Date: 28 Nov 2006 05:09:32
From: Emanuele D'Arrigo
Subject: Photographic Size of a Star
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Hello everybody,
quoting from wikipedia (Apparent Magnitude article)
"a first magnitude star is about 2.512 times as bright
as a second magnitude star".
Does this effectively means that in a photo, the radius
of a first magnitude star (i.e. in pixels) is 2.512 times
the radius of a second magnitude star?
Can the same be said of the size/lenght of the diffraction
artifacts, those star spikes produced by the struts holding
the secondary mirror?
Thanks for your help!
Manu
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Date: 28 Nov 2006 16:32:06
From: Roger Hamlett
Subject: Re: Photographic Size of a Star
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"Emanuele D'Arrigo" <manu3d@gmail.com > wrote in message
news:1164719372.616451.163810@l12g2000cwl.googlegroups.com...
> Hello everybody,
>
> quoting from wikipedia (Apparent Magnitude article)
> "a first magnitude star is about 2.512 times as bright
> as a second magnitude star".
>
> Does this effectively means that in a photo, the radius
> of a first magnitude star (i.e. in pixels) is 2.512 times
> the radius of a second magnitude star?
>
> Can the same be said of the size/lenght of the diffraction
> artifacts, those star spikes produced by the struts holding
> the secondary mirror?
>
> Thanks for your help!
No.
Stars are effectively 'point' sources (they are so far away, that they
display no measurable 'size'). At the scope, what you see/image, is
stretched by a number of processes. First, diffraction effects in the
scope (the so called 'Airy disk'). Then any movement errors of the mount.
Then before it reaches the scope, by 'wander' from the atmosphere, and
defocus from the same source. All these effects for a given scope/point in
the image field/sky, remain constant, whatever the brightness of the star
involved. The reason they look bigger, is simply that becaue they are
brighter, you see further 'down' the sides of the resulting recorded
image. If you take an image showing a number of stars of different
brightnesses. Say some at 4000 counts 'max', and some others at 24000
counts max, and adjust the viewing intensity range of the image, to run
from the background level to 4000, the brighter stars will appear much
larger. Now make a note of how 'big' the dimmer stars appear, and change
the viewing intensity range to run from the same background level up to
the 24000 count level of the brighter stars. You will find that the images
of the brighter stars, now looks exactly the same size (except for some
experimental error), as the dimmer stars appeared with the other settings.
Imagine that you had a set of cones, all with exactly the same taper on
their sides, but different heights. The diameter of the 'ring' you see if
you cut through them, depends on how far down them you cut. Your 'view' is
like a sheet cutting through the 'cones' of information generated by the
stars.
Unfortunately, the shape of the 'cone', is not straight sided. At the
bottom it flares out, and at the top it flattens, hence the exact
relationship to apparent size, is not nicely linear. However it
approximates to the inverse of the magnitude change itself. So for a given
visualisation range, a star that is say Mag4, will appear about 50% larger
than a star that it Mag6.
Best Wishes
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Date: 28 Nov 2006 14:46:37
From: Chris L Peterson
Subject: Re: Photographic Size of a Star
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On 28 Nov 2006 05:09:32 -0800, "Emanuele D'Arrigo" <manu3d@gmail.com >
wrote:
>Hello everybody,
>
>quoting from wikipedia (Apparent Magnitude article)
>"a first magnitude star is about 2.512 times as bright
>as a second magnitude star".
>
>Does this effectively means that in a photo, the radius
>of a first magnitude star (i.e. in pixels) is 2.512 times
>the radius of a second magnitude star?
No, because you need to consider the PSF of the optical system and the
noise floor of the sensor. But it is true that as stars get brighter,
their photographic size increases.
>Can the same be said of the size/lenght of the diffraction
>artifacts, those star spikes produced by the struts holding
>the secondary mirror?
Approximately. But again you need to consider the sensor noise floor.
Brighter stars always produce brighter (and therefore longer)
diffraction artifacts.
_________________________________________________
Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com
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Date: 28 Nov 2006 06:35:17
From: AustinMN
Subject: Re: Photographic Size of a Star
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Emanuele D'Arrigo wrote:
> Hello everybody,
>
> quoting from wikipedia (Apparent Magnitude article)
> "a first magnitude star is about 2.512 times as bright
> as a second magnitude star".
>
> Does this effectively means that in a photo, the radius
> of a first magnitude star (i.e. in pixels) is 2.512 times
> the radius of a second magnitude star?
No. It could be that the radii are the same size, but the 1st
magnitude star is exposed 2.512 times as bright (or the 2nd magnitude
star is that much dimmer), or it could mean the 1st magnitude star is
2.512 times as overexposed (i.e. they look the same).
If the magnitude did equiate to the size of the circle, I would not
expect the radius to be 2.512 times the size, I would expect the circle
to have 2.512 times the area, which is quite a bit less than 2.512
times the radius.
> Can the same be said of the size/lenght of the diffraction
> artifacts, those star spikes produced by the struts holding
> the secondary mirror?
No. The diffraction spikes are all the same length. It's just that
with brighter stars, they are easier to see. The effect may be that
the spikes appear 2.512 times as long, but not necessarily.
Austin
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Date: 28 Nov 2006 15:16:26
From: Chris L Peterson
Subject: Re: Photographic Size of a Star
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On 28 Nov 2006 06:35:17 -0800, "AustinMN" <tacooper260@hotmail.com >
wrote:
>No. It could be that the radii are the same size, but the 1st
>magnitude star is exposed 2.512 times as bright (or the 2nd magnitude
>star is that much dimmer), or it could mean the 1st magnitude star is
>2.512 times as overexposed (i.e. they look the same).
The stellar profile typically has an approximately Gaussian profile. The
apparent diameter is determined by the intersection of that profile with
the noise floor of the detector. As the star brightness increases from
the limit of visibility, you initially see a rapid increase in apparent
diameter. Then, over a range of increase you see a steady, but smaller
increase in the apparent diameter. Above a certain brightness, the
apparent diameter again increases rapidly with increasing brightness.
>No. The diffraction spikes are all the same length.
Yes, theoretically the spikes are infinitely long. In practice, of
course, they are limited by the fact that only a finite number of
photons (or a finite amount of energy) creates each stellar image. The
length of the diffraction spike above the noise floor will increase with
brightness- approximately scaling with intensity, I believe.
_________________________________________________
Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com
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Date: 28 Nov 2006 21:07:05
From: Ioannis
Subject: Re: Photographic Size of a Star
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"Chris L Peterson" <clp@alumni.caltech.edu > wrote in message
news:r2kom25p3s42jvpq1dplc1r64bvhggksqu@4ax.com...
[snip]
> The stellar profile typically has an approximately Gaussian profile. The
> apparent diameter is determined by the intersection of that profile with
> the noise floor of the detector. As the star brightness increases from
> the limit of visibility, you initially see a rapid increase in apparent
> diameter. Then, over a range of increase you see a steady, but smaller
> increase in the apparent diameter. Above a certain brightness, the
> apparent diameter again increases rapidly with increasing brightness.
[snip]
Chris,
On a related topic: do you or anyone else know WHY we have an increase of
apparent diameter on photo and digital plates for brighter stars in the first
place?
What exactly causes the circular saturation, i.e. the increase in diameter in
photos? Is it stray light, scintilation, or is it a property of the detector
to saturate sideways, always?
I know that overexposure in normal photos tends to saturate sideways, covering
the boundries with excess light, but why does it happen on point sources?
Assuming of course the scope is properly focused as to produce pin-point
images!
Thanks,
> Chris L Peterson
--
Ioannis
-------
The best way to predict reality, is to know exactly what you DON'T want.
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Date: 28 Nov 2006 19:25:56
From: Chris L Peterson
Subject: Re: Photographic Size of a Star
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On Tue, 28 Nov 2006 21:07:05 +0200, "Ioannis" <morpheus@olympus.mons >
wrote:
>Chris,
>
>On a related topic: do you or anyone else know WHY we have an increase of
>apparent diameter on photo and digital plates for brighter stars in the first
>place?
>
>What exactly causes the circular saturation, i.e. the increase in diameter in
>photos? Is it stray light, scintilation, or is it a property of the detector
>to saturate sideways, always?
>
>I know that overexposure in normal photos tends to saturate sideways, covering
>the boundries with excess light, but why does it happen on point sources?
>
>Assuming of course the scope is properly focused as to produce pin-point
>images!
Because telescopes _don't_ produce pinpoint images. Diffraction,
tracking errors, optical aberrations, and atmospheric effects all act to
increase the size of the stellar profile. Even with perfect optics under
perfect conditions, a circular aperture produces an image described by a
Bessel function (the Airy disk and surrounding rings). As the star gets
brighter, you'll see farther out on the central disk (the star image
will appear larger), and eventually you'll see more and more rings.
In real life, the profile of a star is approximately Gaussian (because
of the factors listed above). That means it has an infinite diameter.
What you will actually see is the part of the profile that is above the
noise floor. Aim a scope at a very bright star and take a long exposure,
and the resulting star can be hundreds of pixels across.
_________________________________________________
Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com
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Date: 28 Nov 2006 21:55:16
From: Ioannis
Subject: Re: Photographic Size of a Star
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"Chris L Peterson" <clp@alumni.caltech.edu > wrote in message
news:jm2pm2hfjbb8qt3qrllikea7b5bf04pkp9@4ax.com...
[snip]
> Because telescopes _don't_ produce pinpoint images. Diffraction,
> tracking errors, optical aberrations, and atmospheric effects all act to
> increase the size of the stellar profile. Even with perfect optics under
> perfect conditions, a circular aperture produces an image described by a
> Bessel function (the Airy disk and surrounding rings). As the star gets
> brighter, you'll see farther out on the central disk (the star image
> will appear larger), and eventually you'll see more and more rings.
But the Airy disk and the diffraction rings are visible with high
magnifications relative to aperture, aren't they? For example, on my Tasco,
I'd need to go at least up as far up as 140x to start discerning the Bessel
profile of very bright stars.
I seem to remember that higher apertures need higher magnifications to show
Airy disks and rings, at least visibly.
Why do we get such a profile even with low magnifications relative to aperture
or with photos where the notion of magnification doesn't even apply, such as
by prime focus imaging? For example, the least magnification needed to see
diffraction rings on a 20-inch scope must be quite high. I don't know HOW
high, but usually photographers take photos using prime focus. And the star
images STILL saturate circularly.
If memory serves right, Schmidt cameras don't even have any magnification (I
may be wrong here). They STILL produce disks for star images though.
Perhaps even with photos at prime focus, the Bessel profile is visible through
the extreme sensitivity of the scope/camera and would otherwise not show
visibly?
Thanks,
[snip]
> Chris L Peterson
--
Ioannis
-------
The best way to predict reality, is to know exactly what you DON'T want.
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Date: 28 Nov 2006 20:35:33
From: Chris L Peterson
Subject: Re: Photographic Size of a Star
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On Tue, 28 Nov 2006 21:55:16 +0200, "Ioannis" <morpheus@olympus.mons >
wrote:
>But the Airy disk and the diffraction rings are visible with high
>magnifications relative to aperture, aren't they?
You need to distinguish between visible at the eyepiece and visible on
an image. Unless the image time is very short- less than a few seconds
under good seeing, and perhaps tens of milliseconds under average
seeing- the PSF ends up being a convolution of the various aberrating
effects, mainly atmospheric motion. When you watch a star at high
magnification, you normally see the Airy pattern dancing around, both in
position and shape. Imagine what you get if you make a long exposure of
that- it isn't going to look like a central disk and outer rings. It is
going to look like a Gaussian.
>Why do we get such a profile even with low magnifications relative to aperture
>or with photos where the notion of magnification doesn't even apply, such as
>by prime focus imaging?
While "magnification" is largely meaningless when imaging, it has an
analog called image scale. Unless you are grossly undersampled (that is,
even bright stars will fit on a single pixel) you will always see the
stellar profile with a diameter that is some function of brightness.
>Perhaps even with photos at prime focus, the Bessel profile is visible through
>the extreme sensitivity of the scope/camera and would otherwise not show
>visibly?
Certainly, with a short exposure. When I collimate my scope I use a
video camera, and the diffraction pattern is very obvious on the image.
But never with a long exposure.
_________________________________________________
Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com
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Date: 28 Nov 2006 08:25:20
From: William C. Keel
Subject: Re: Photographic Size of a Star
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Emanuele D'Arrigo <manu3d@gmail.com > wrote:
> Hello everybody,
> quoting from wikipedia (Apparent Magnitude article)
> "a first magnitude star is about 2.512 times as bright
> as a second magnitude star".
> Does this effectively means that in a photo, the radius
> of a first magnitude star (i.e. in pixels) is 2.512 times
> the radius of a second magnitude star?
> Can the same be said of the size/lenght of the diffraction
> artifacts, those star spikes produced by the struts holding
> the secondary mirror?
> Thanks for your help!
> Manu
No to both questions. The size in an image (photographic or not)
is equivalent to slicing the point-response of the optical system at
different intensity levels, so the relation betwen diameter at
some brightness in the image and a star's magnitude depends on
the properties of the telescope and atmosphere. Doing absolute
brightness measurements from photographs was always a delicate and
tedious business, made dramatically easier by digital detectors.
(There are better ways to use photographs to measure magnitudes
as long as there are some independently measured reference
stars in the picture).
Bill Keel
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Date: 28 Nov 2006 11:51:39
From: atasselli@hotmail.com
Subject: Re: Photographic Size of a Star
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Chris L Peterson wrote:
> On Tue, 28 Nov 2006 21:07:05 +0200, "Ioannis" <morpheus@olympus.mons>
> wrote:
>
> >Chris,
> >
> >On a related topic: do you or anyone else know WHY we have an increase of
> >apparent diameter on photo and digital plates for brighter stars in the first
> >place?
> >
> >What exactly causes the circular saturation, i.e. the increase in diameter in
> >photos? Is it stray light, scintilation, or is it a property of the detector
> >to saturate sideways, always?
> >
> >I know that overexposure in normal photos tends to saturate sideways, covering
> >the boundries with excess light, but why does it happen on point sources?
> >
> >Assuming of course the scope is properly focused as to produce pin-point
> >images!
>
> Because telescopes _don't_ produce pinpoint images. Diffraction,
> tracking errors, optical aberrations, and atmospheric effects all act to
> increase the size of the stellar profile. Even with perfect optics under
> perfect conditions, a circular aperture produces an image described by a
> Bessel function (the Airy disk and surrounding rings). As the star gets
> brighter, you'll see farther out on the central disk (the star image
> will appear larger), and eventually you'll see more and more rings.
>
> In real life, the profile of a star is approximately Gaussian (because
> of the factors listed above). That means it has an infinite diameter.
> What you will actually see is the part of the profile that is above the
> noise floor. Aim a scope at a very bright star and take a long exposure,
> and the resulting star can be hundreds of pixels across.
>
Actually, in real life we can see the Airy profile and the diffraction
pattern extends to infinity, exactly as a gaussian. IOW, it is not a
matter of a specific PSF but rather that the PSF extends to infinity,
with infinitely decreasing intensity.
Andrea T.
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Date: 28 Nov 2006 20:04:39
From: Chris L Peterson
Subject: Re: Photographic Size of a Star
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On 28 Nov 2006 11:51:39 -0800, "atasselli@hotmail.com"
<atasselli@hotmail.com > wrote:
>Actually, in real life we can see the Airy profile and the diffraction
>pattern extends to infinity, exactly as a gaussian. IOW, it is not a
>matter of a specific PSF but rather that the PSF extends to infinity,
>with infinitely decreasing intensity.
It is rare to see the diffraction profile in images. You can capture it,
of course, with a deliberate fast exposure, but that isn't typical of
the vast majority of images. Once the exposure time is longer than a few
seconds, you lose the diffraction pattern to atmospheric turbulence, and
your purely Bessel PSF becomes approximately Gaussian. In either case,
of course, the size of the function is infinite, with the apparent
diameter determined by the noise floor.
_________________________________________________
Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com
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