## Pixels and resolution

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• I have been working on this article for a while now, since I believe that there is some misinformation out there on the internet. The trouble is how do you
Message 1 of 6 , Jul 30, 2013
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I have been working on this article for a while now, since I believe that there is some misinformation out there on the internet.

The trouble is how do you tackle this without starting a flame war of opinion based argument? Well by stick very closely to the physics of telescopes, CCD Sensors and Astronomy I hope to avoid that outcome. Much of the information here can be looked up directly on the internet or reference books.

One key point is that light, is treated both as a particle and a wave. In fact, many of the technique that we use, such as wavelet sharpening rely on the fact.

http://www.insideastronomy.com/index.php?/topic/1013-pixels-and-resolution-what-really-matters/

I have tried to keep it fun to read, using only the formulas that were required (No calculus)

Regards

Neil.
www.insideastronomy.com
• Hi, Where did you get the formula for seeing? I have always been under the impression that the seeing was FWHM x image-scale in arc sec if FWHM was quantified
Message 2 of 6 , Jul 30, 2013
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Hi,

Where did you get the formula for seeing? I have always been under the impression that the seeing was FWHM x image-scale in arc sec if FWHM was quantified in pixels, not two time that value.

For what it is worth, here is the Wikipedia definition.

http://en.wikipedia.org/wiki/Astronomical_seeing

Here is another reference where FWHM is assumed to be the unit of measure of seeing.

http://www.eso.org/gen-fac/pubs/astclim/papers/lz-thesis/node11.html

George

On Jul 30, 2013, at 5:41 AM, nismo.godzilla wrote:

> I have been working on this article for a while now, since I believe that there is some misinformation out there on the internet.
>
> The trouble is how do you tackle this without starting a flame war of opinion based argument? Well by stick very closely to the physics of telescopes, CCD Sensors and Astronomy I hope to avoid that outcome. Much of the information here can be looked up directly on the internet or reference books.
>
> One key point is that light, is treated both as a particle and a wave. In fact, many of the technique that we use, such as wavelet sharpening rely on the fact.
>
> http://www.insideastronomy.com/index.php?/topic/1013-pixels-and-resolution-what-really-matters/
>
> I have tried to keep it fun to read, using only the formulas that were required (No calculus)
>
> Regards
>
> Neil.
> www.insideastronomy.com
>
>

[Non-text portions of this message have been removed]
• I d like to weigh in on this; seeing is something that I spend a lot of time analyzing and understanding. There are a huge number of misconceptions about
Message 3 of 6 , Jul 30, 2013
• 0 Attachment
I'd like to weigh in on this; seeing is something that I spend a lot of time analyzing and understanding. There are a huge number of misconceptions about seeing wandering around the amateur community.

I believe what you are talking about are what I would refer to as "measurements of seeing." There is quite a range of acceptable ways to measure and report seeing. All of them have _some_ validity.

It depends enormously on whether you are trying to:

* Accurately measure and report the actual seeing conditions of the atmosphere
* The (near) instantaneous net effect of various seeing effects between source and recording medium
* The cumulative effect on an integrated exposure

All three are valid and interesting numbers, but they can be quite different. And it is actually possible to report atmospheric seeing both as a number based on FWHM, and as a structure constant.

And it is also possible to talk about seeing in terms of its causes, which are numerous, various, and of quite different natures at various elevations of the atmosphere, and inside your observatory/instrument.

I could write a book about seeing in light of the above. And perhaps one day I will. I will include a section in the upcoming book that deals with these various aspects.

OK, here's some actual response. :-)

There are two types of seeing numbers that are useful to an imager:

* The _imaged_ FWHM for a given exposure duration (e.g., 15-min exposures). You can track this from image to image, night to night, year to year, and it gives you a consistent value that you can use for relative comparisons. "The seeing is better tonight," or "The seeing was better last year around this time."

* The measured FWHM from a seeing monitor. This is typically based on near-instanteous differences between spatially distinct inputs (two aperture method) or actual width measurements of a star.

The first method is relative - the data is convolved by exposures > about 1/100th of a second. So you are looking at an average of seeing at a huge number of time resolutions.

The second method is expensive - you need a seeing monitor, you can't measure seeing without some kind of reference (two aperture method) or baseline (width measurements from a single aperture). Both methods use statistical combine methods to generate an actual number, by the way. A single reading is not statistically useful. You have to integrate the results to get something useful.

Structure functions/structure constants are much, much more complicated mathematical concepts, but they model and describe seeing much more effectively. As an amateur, the best way to approach this is alluded to above: learn the various ways in which seeing effects are created. (I gave a detailed talk on this at AIC some years ago; if you have that presentation, it contains a lot of useful information along these lines.) I will be talking about seeing again at AIC this fall, with updated information.

The bottom line is that seeing is the accumulated wavefront distortions from light passing through various refractive indices during its travel through the atmosphere. Imagine that the incoming light wavefront is a plane; as it goes through the atmosphere, it gets tilted overall (AO units from SBIG and others correct this and only this effect), and distorted in various more complex ways. In effect, the various levels of the atmosphere present different types of lenses which mess up your image wavefront, and it is constantly changing and evolving. Seeing measures an integrated slice of these effects over a specified timescale.

(I've used a Shack-Hartmann device to view these distortions, and, honestly, one wonders how we can image though this atmosphere of ours at all!)

Examples of two very different height-dependent effects:

* The jet stream will move existing refractive conditions past your aperture. The faster it moves, the more different optical effects is moves over your aperture, and the greater the potential impact on seeing. (If the jet stream is slow, then very short exposures can be taken with virtually no jetstream input; this is why planetary imagers are always concerned about the speed and location of the jetstream.)

* Rising plumes of warmer air in your observatory can refract incoming light, so finding ways to deal with them is critical to improving your seeing. (Yep; there are actually ways to improve your seeing; it's not all in the upper atmosphere! In fact, the closer the source of a seeing effect is to your camera, the greater the impact is will have due to angular resolution issues.)

I could go on. Way, way on. But maybe this will help a little in understanding seeing. I've got to get back to writing!

On Jul 30, 2013, at 10:13 AM, george hall <george2003@...> wrote:

> Hi,
>
> Where did you get the formula for seeing? I have always been under the impression that the seeing was FWHM x image-scale in arc sec if FWHM was quantified in pixels, not two time that value.
>
> For what it is worth, here is the Wikipedia definition.
>
> http://en.wikipedia.org/wiki/Astronomical_seeing
>
> Here is another reference where FWHM is assumed to be the unit of measure of seeing.
>
> http://www.eso.org/gen-fac/pubs/astclim/papers/lz-thesis/node11.html
>
> George
>
> On Jul 30, 2013, at 5:41 AM, nismo.godzilla wrote:
>
>> I have been working on this article for a while now, since I believe that there is some misinformation out there on the internet.
>>
>> The trouble is how do you tackle this without starting a flame war of opinion based argument? Well by stick very closely to the physics of telescopes, CCD Sensors and Astronomy I hope to avoid that outcome. Much of the information here can be looked up directly on the internet or reference books.
>>
>> One key point is that light, is treated both as a particle and a wave. In fact, many of the technique that we use, such as wavelet sharpening rely on the fact.
>>
>> http://www.insideastronomy.com/index.php?/topic/1013-pixels-and-resolution-what-really-matters/
>>
>> I have tried to keep it fun to read, using only the formulas that were required (No calculus)
>>
>> Regards
>>
>> Neil.
>> www.insideastronomy.com
>>
>>
>
>
>
> [Non-text portions of this message have been removed]
>
>
>
> ------------------------------------
>
>
>
>
• Hi Neil. Although the document is certainly understandable, I think it has a couple of problem areas. As an earlier respondent said, 2*FWHM is not a familiar
Message 4 of 6 , Jul 31, 2013
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Hi Neil. Although the document is certainly understandable, I think it
has a couple of problem areas. As an earlier respondent said, 2*FWHM is
not a familiar metric for seeing, nor does it seem to have much
relevance to the underlying math. FWHM is a useful metric for the width
of a Gaussian fit on a stellar profile and as such it tells us something
about the size of the Airy disk. It is *not* the value for sigma in the
Gaussian equation, so there is no reason to multiply it by 2. In fact,
it is equal to 2.35*sigma for a Gaussian curve. Here's a graphical
interpretation:
http://ned.ipac.caltech.edu/level5/Leo/Stats2_3.html
<http://ned.ipac.caltech.edu/level5/Leo/Stats2_3.html>

Also the common simplification of Nyquist as a "2x" rule of thumb is not
accurate in imaging, something that's been covered in many of the
forums. For example, see:
http://www.stanmooreastro.com/pixel_size.htm
<http://www.stanmooreastro.com/pixel_size.htm>

If you doubt the math for some reason - don't know why you would - you
can also find some actual photographic experiments posted on the Web
that clearly show resolution loss with only 2x sampling. The math
works. :-)

Cheers,

Bruce

--- In ccd-newastro@yahoogroups.com, "nismo.godzilla"
--- In ccd-newastro@yahoogroups.com, "nismo.godzilla" wrote:
>
> I have been working on this article for a while now, since I believe
that there is some misinformation out there on the internet.
>
> The trouble is how do you tackle this without starting a flame war of
opinion based argument? Well by stick very closely to the physics of
telescopes, CCD Sensors and Astronomy I hope to avoid that outcome. Much
of the information here can be looked up directly on the internet or
reference books.
>
> One key point is that light, is treated both as a particle and a wave.
In fact, many of the technique that we use, such as wavelet sharpening
rely on the fact.
>
>
http://www.insideastronomy.com/index.php?/topic/1013-pixels-and-resoluti\
on-what-really-matters/
>
> I have tried to keep it fun to read, using only the formulas that were
required (No calculus)
>
> Regards
>
>
> Neil.
> www.insideastronomy.com
>

[Non-text portions of this message have been removed]
• Hi George, There are several references on the internet, some more complicated than other to follow. Hence for this article I have chosen the simplest version.
Message 5 of 6 , Aug 5, 2013
• 0 Attachment
Hi George,

There are several references on the internet, some more complicated than other to follow. Hence for this article I have chosen the simplest version. If I can find it back I'll provide a link to the information etc...

Regards

Neil
www.insideastronomy.com

--- In ccd-newastro@yahoogroups.com, george hall <george2003@...> wrote:
>
> Hi,
>
> Where did you get the formula for seeing? I have always been under the impression that the seeing was FWHM x image-scale in arc sec if FWHM was quantified in pixels, not two time that value.
>
> For what it is worth, here is the Wikipedia definition.
>
> http://en.wikipedia.org/wiki/Astronomical_seeing
>
> Here is another reference where FWHM is assumed to be the unit of measure of seeing.
>
> http://www.eso.org/gen-fac/pubs/astclim/papers/lz-thesis/node11.html
>
> George
>
> On Jul 30, 2013, at 5:41 AM, nismo.godzilla wrote:
>
> > I have been working on this article for a while now, since I believe that there is some misinformation out there on the internet.
> >
> > The trouble is how do you tackle this without starting a flame war of opinion based argument? Well by stick very closely to the physics of telescopes, CCD Sensors and Astronomy I hope to avoid that outcome. Much of the information here can be looked up directly on the internet or reference books.
> >
> > One key point is that light, is treated both as a particle and a wave. In fact, many of the technique that we use, such as wavelet sharpening rely on the fact.
> >
> > http://www.insideastronomy.com/index.php?/topic/1013-pixels-and-resolution-what-really-matters/
> >
> > I have tried to keep it fun to read, using only the formulas that were required (No calculus)
> >
> > Regards
> >
> > Neil.
> > www.insideastronomy.com
> >
> >
>
>
>
> [Non-text portions of this message have been removed]
>
• Thanks Ron for your input. I have tried to keep this article simple so that everyone can hopefully follow it and the conclusion that I draw, just like your
Message 6 of 6 , Aug 5, 2013
• 0 Attachment

I have tried to keep this article simple so that everyone can hopefully follow it and the conclusion that I draw, just like your first book! :-)

Regarding the mathematics of seeing, it doesn't really matter too much how you measure, so long as you do not use a saturated star of course. The central limit theorem ensures that you will always have a normal distribution.

I agree that you do need to be consistent when using statistical methods to measure any effect.

The two main issues that I wanted to dispel are the pixel size and the idea that the Nyquist theorem doesn't apply because its only for sound waves argument.

Again, main of the advanced statistical techniques that we use in astronomy rely heavily on the fact that light can be treated just as consistently as a wave.

Finally, for most of us in Northern Europe, where I image, the limiting fact is the weather, not the optics, not the mount and definitely not the ccd camera that we use.

Preventing heat retention around or near to your observatory is always a good idea and often overlooked!

Best regards

Neil
www.insideastronomy.com

--- In ccd-newastro@yahoogroups.com, Ron Wodaski <yahoo@...> wrote:
>
> I'd like to weigh in on this; seeing is something that I spend a lot of time analyzing and understanding. There are a huge number of misconceptions about seeing wandering around the amateur community.
>
> I believe what you are talking about are what I would refer to as "measurements of seeing." There is quite a range of acceptable ways to measure and report seeing. All of them have _some_ validity.
>
> It depends enormously on whether you are trying to:
>
> * Accurately measure and report the actual seeing conditions of the atmosphere
> * The (near) instantaneous net effect of various seeing effects between source and recording medium
> * The cumulative effect on an integrated exposure
>
> All three are valid and interesting numbers, but they can be quite different. And it is actually possible to report atmospheric seeing both as a number based on FWHM, and as a structure constant.
>
> And it is also possible to talk about seeing in terms of its causes, which are numerous, various, and of quite different natures at various elevations of the atmosphere, and inside your observatory/instrument.
>
> I could write a book about seeing in light of the above. And perhaps one day I will. I will include a section in the upcoming book that deals with these various aspects.
>
> OK, here's some actual response. :-)
>
> There are two types of seeing numbers that are useful to an imager:
>
> * The _imaged_ FWHM for a given exposure duration (e.g., 15-min exposures). You can track this from image to image, night to night, year to year, and it gives you a consistent value that you can use for relative comparisons. "The seeing is better tonight," or "The seeing was better last year around this time."
>
> * The measured FWHM from a seeing monitor. This is typically based on near-instanteous differences between spatially distinct inputs (two aperture method) or actual width measurements of a star.
>
> The first method is relative - the data is convolved by exposures > about 1/100th of a second. So you are looking at an average of seeing at a huge number of time resolutions.
>
> The second method is expensive - you need a seeing monitor, you can't measure seeing without some kind of reference (two aperture method) or baseline (width measurements from a single aperture). Both methods use statistical combine methods to generate an actual number, by the way. A single reading is not statistically useful. You have to integrate the results to get something useful.
>
> Structure functions/structure constants are much, much more complicated mathematical concepts, but they model and describe seeing much more effectively. As an amateur, the best way to approach this is alluded to above: learn the various ways in which seeing effects are created. (I gave a detailed talk on this at AIC some years ago; if you have that presentation, it contains a lot of useful information along these lines.) I will be talking about seeing again at AIC this fall, with updated information.
>
> The bottom line is that seeing is the accumulated wavefront distortions from light passing through various refractive indices during its travel through the atmosphere. Imagine that the incoming light wavefront is a plane; as it goes through the atmosphere, it gets tilted overall (AO units from SBIG and others correct this and only this effect), and distorted in various more complex ways. In effect, the various levels of the atmosphere present different types of lenses which mess up your image wavefront, and it is constantly changing and evolving. Seeing measures an integrated slice of these effects over a specified timescale.
>
> (I've used a Shack-Hartmann device to view these distortions, and, honestly, one wonders how we can image though this atmosphere of ours at all!)
>
> Examples of two very different height-dependent effects:
>
> * The jet stream will move existing refractive conditions past your aperture. The faster it moves, the more different optical effects is moves over your aperture, and the greater the potential impact on seeing. (If the jet stream is slow, then very short exposures can be taken with virtually no jetstream input; this is why planetary imagers are always concerned about the speed and location of the jetstream.)
>
> * Rising plumes of warmer air in your observatory can refract incoming light, so finding ways to deal with them is critical to improving your seeing. (Yep; there are actually ways to improve your seeing; it's not all in the upper atmosphere! In fact, the closer the source of a seeing effect is to your camera, the greater the impact is will have due to angular resolution issues.)
>
> I could go on. Way, way on. But maybe this will help a little in understanding seeing. I've got to get back to writing!
>
>
>
>
> On Jul 30, 2013, at 10:13 AM, george hall <george2003@...> wrote:
>
> > Hi,
> >
> > Where did you get the formula for seeing? I have always been under the impression that the seeing was FWHM x image-scale in arc sec if FWHM was quantified in pixels, not two time that value.
> >
> > For what it is worth, here is the Wikipedia definition.
> >
> > http://en.wikipedia.org/wiki/Astronomical_seeing
> >
> > Here is another reference where FWHM is assumed to be the unit of measure of seeing.
> >
> > http://www.eso.org/gen-fac/pubs/astclim/papers/lz-thesis/node11.html
> >
> > George
> >
> > On Jul 30, 2013, at 5:41 AM, nismo.godzilla wrote:
> >
> >> I have been working on this article for a while now, since I believe that there is some misinformation out there on the internet.
> >>
> >> The trouble is how do you tackle this without starting a flame war of opinion based argument? Well by stick very closely to the physics of telescopes, CCD Sensors and Astronomy I hope to avoid that outcome. Much of the information here can be looked up directly on the internet or reference books.
> >>
> >> One key point is that light, is treated both as a particle and a wave. In fact, many of the technique that we use, such as wavelet sharpening rely on the fact.
> >>
> >> http://www.insideastronomy.com/index.php?/topic/1013-pixels-and-resolution-what-really-matters/
> >>
> >> I have tried to keep it fun to read, using only the formulas that were required (No calculus)
> >>
> >> Regards
> >>
> >> Neil.
> >> www.insideastronomy.com
> >>
> >>
> >
> >
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
> > ------------------------------------
> >
> >
> >
> >
>
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