FWHM

andrea tasselli:
They are unrelated. I guess you got this at the wrong end. FWHM is an independent parameter that depends on various factors (such as seeing, aperture size, various optical errors and in general anything that stands in the way of the rays coming to focus) but does NOT depend on how you sample it. The scope of sizing your detector pixel scale is to match your FWHM with the sensor pixel size in order to achieve the optimum sampling (for discussion's sake let's say 3 pixel across). Too little and you cannot reliably reconstruct the original PDF which is needed for a host of post-processing tasks (although there are way to minimise this, see drizzling). Oversample it and you're wasting photons (well, potentially) spreading the butter ever so thinner on the bread, in a manner of speaking.

As for the other question the FWHM is a measure of the seeing, so you can't.

*OK--lets take 3 pixels across.  I shoot at 2.5 arcsec/pix and the FWHM will be 7.5 arcsec  if I shoot at 1 arcsec/pix the FWHM will be 3 arcsec.

How is pixel scale not important?

Also--I got a FWHM of 1.8 arcsec the other night (several between 1.8 and 2)  and I know my sky was not 1.8 arcsec seeing

Kevin Morefield:
Rodd,

I have shot at a lot of difference image scales (0.3 to about 2.0)  What I've found is that when I'm shooting a very large image scale and seeing is maybe a pixel or less I can get a FWHM in pixel counts of 2.0 or a little less than 2.0 on some subs.  I'm not sure that the measures below 2.0 are really meaningful as it should not be possible to correctly define a light wave without two samples, one for the peak and one for the trough of the wave.  So with my FSQ and QHY600 at 1.47" the realistic minimum FWHM is 2 pixels ore about 3.0".  And I see that in practice.

With the long focal length Planewave, I typically see the best FWHM numbers for subs a little below 3 pixels.   2.5 at the absolute lowest and 3 is a more normal great sub.  That's with an image scale of .60.  In this case I think I'm usually running into limitations other than seeing that are keeping my FHWM in arc seconds above 1.5"

John Hayes wrote a great comment on this topic in this thread recently:

https://www.astrobin.com/forum/c/astrophotography/equipment/pixel-scale-advice-appreciated/

Kevin

*So I am not crazy.  As pixel scale increases (goes higher) the FWHM values will rise correspondingly for teh reasons I and you just said.  On a good night shooting at a pixel scale of 2.47 arcsec/pix I can chieve 3.9-4.0 FWHM--which is about 1.6x the pixel scale.  However, when shooting at .77 arcsec/pix, a good FWHM is 2.5 or so ( a factor of 3.2).

So--does that mean that when I am shooting at 2.47 and I get 3 spixels across teh FWHM, the FWHM is almost 7 arcsec--I have always considered anything above 5  at this pixel scale throw aways--should I rethink?

andrea tasselli:

Rodd Dryfoos:

andrea tasselli:
They are unrelated. I guess you got this at the wrong end. FWHM is an independent parameter that depends on various factors (such as seeing, aperture size, various optical errors and in general anything that stands in the way of the rays coming to focus) but does NOT depend on how you sample it. The scope of sizing your detector pixel scale is to match your FWHM with the sensor pixel size in order to achieve the optimum sampling (for discussion's sake let's say 3 pixel across). Too little and you cannot reliably reconstruct the original PDF which is needed for a host of post-processing tasks (although there are way to minimise this, see drizzling). Oversample it and you're wasting photons (well, potentially) spreading the butter ever so thinner on the bread, in a manner of speaking.

As for the other question the FWHM is a measure of the seeing, so you can't.

*OK--lets take 3 pixels across.  I shoot at 2.5 arcsec/pix and the FWHM will be 7.5 arcsec  if I shoot at 1 arcsec/pix the FWHM will be 3 arcsec.

How is pixel scale not important?

Also--I got a FWHM of 1.8 arcsec the other night (several between 1.8 and 2)  and I know my sky was not 1.8 arcsec seeing

Rodd

Rodd,

You get this backward, I'm afraid. The PSF is there and it may be measured by the Full Width at Half Modulation. Let's suppose your PSF's FWHM (related to your kit in that moment and in that moment only) is 3" and you shoot at 2.5"/px you should get something close to 1.25 FWHM in theory. But because your sampling system does not know anything about what is the actual PSF it will only measure what it can measure within its parameters. Since part of the energy of the PSF lays outside the FWHM circle  it will use that to fit the gaussian function, error or not. It just does. I myself, when severely under sample the seeing I can get FWHM less than 1.5 px, but never 1. Even for a hot pixel. Most of the programs out there will use anything to make a fit. So, by way of under sampling the PSF you throw away the information you need to actually know what is your actual FWHM at all.

*You lost me.  What, exactly, do I have backwards?  The FWHM is measured using pixels.  The software calculates how many pixels the FWHM covers.  Let's say it is 3.  Well, that m,eans if I am shooting with the FSQ 106 and .6x reducer for a pixel sacle of 2.5 arcsec/pix, the FWHM value is 7.5 arcsec.  If I am shooting with the TOA 130 at a pixel sacle of .75 arcsec/pix, the FWHM value will be 2.25 arcsec.

Hi Rodd,

RE:  "Does anybody know how FWHM is related to pixel scale? If one uses Nyquist and chooses 3 pixels across the FWHM, it results in wildly different FWHM values depending on pixel scale.  For example, when I shoot at .77 arcsec/pix,  3 x .77 = 2.31 acrsrec.  But when I shoot at 2.47 arcsec/pix  3 x 2.47 = 7.41 arcsec."

I do think you have gone crazy!  ;-)    Your question and conclusion are backward.   It's a bad sign when you get to a place where FWHM correlates to platescale.   Your 2.47 arcsecs/pix is a good example of this.

In the above statement, when you shoot at .77 arcsec/pixel, you say you want Nyquist samples; thus you implicitly expect seeing of 2.31 arcsecs or more.    If the seeing was less, you toss Nyquist and cannot know what the real seeing was!  When you shoot at 2.47, you are in trouble.   If you really wanted Nyquist, seeing would need to be 7.41 arcsecs.    I doubt you'd be happy with subs taken in 7.4 arcsecs seeing.

FWHM should really only be correlated to the energy profile of the star (which for us amateurs is correlated to seeing).   You definitely don't want it to correlate to your sampling!   When platescale is sufficiently smaller than seeing, you always get an appropriate FWHM/seeing correlation (even though there's oversampling risk).   Typical amateur sites have seeing in the 1.5 to 4 arcsecs (2.5-3.5 avg).  So, having a platescale somewhere between 0.5 to 1.2 will typically get you to Nyquist sampling and resolution as good as seeing will allow.    The only reason to go to bigger platescale is when resolution is sacrificed for FOV.    Taking wide field shots?   Go big.   Shooting planetaries?   Go small.    Platescale and seeing matters, but FWHM should only be a rough metric for seeing, and for that you want the platescale to be Nyquist smaller than seeing.

andrea tasselli:

Rodd Dryfoos:

andrea tasselli:

Rodd Dryfoos:

andrea tasselli:
They are unrelated. I guess you got this at the wrong end. FWHM is an independent parameter that depends on various factors (such as seeing, aperture size, various optical errors and in general anything that stands in the way of the rays coming to focus) but does NOT depend on how you sample it. The scope of sizing your detector pixel scale is to match your FWHM with the sensor pixel size in order to achieve the optimum sampling (for discussion's sake let's say 3 pixel across). Too little and you cannot reliably reconstruct the original PDF which is needed for a host of post-processing tasks (although there are way to minimise this, see drizzling). Oversample it and you're wasting photons (well, potentially) spreading the butter ever so thinner on the bread, in a manner of speaking.

As for the other question the FWHM is a measure of the seeing, so you can't.

*OK--lets take 3 pixels across.  I shoot at 2.5 arcsec/pix and the FWHM will be 7.5 arcsec  if I shoot at 1 arcsec/pix the FWHM will be 3 arcsec.

How is pixel scale not important?

Also--I got a FWHM of 1.8 arcsec the other night (several between 1.8 and 2)  and I know my sky was not 1.8 arcsec seeing

Rodd

Rodd,

You get this backward, I'm afraid. The PSF is there and it may be measured by the Full Width at Half Modulation. Let's suppose your PSF's FWHM (related to your kit in that moment and in that moment only) is 3" and you shoot at 2.5"/px you should get something close to 1.25 FWHM in theory. But because your sampling system does not know anything about what is the actual PSF it will only measure what it can measure within its parameters. Since part of the energy of the PSF lays outside the FWHM circle  it will use that to fit the gaussian function, error or not. It just does. I myself, when severely under sample the seeing I can get FWHM less than 1.5 px, but never 1. Even for a hot pixel. Most of the programs out there will use anything to make a fit. So, by way of under sampling the PSF you throw away the information you need to actually know what is your actual FWHM at all.

*You lost me.  What, exactly, do I have backwards?  The FWHM is measured using pixels.  The software calculates how many pixels the FWHM covers.  Let's say it is 3.  Well, that m,eans if I am shooting with the FSQ 106 and .6x reducer for a pixel sacle of 2.5 arcsec/pix, the FWHM value is 7.5 arcsec.  If I am shooting with the TOA 130 at a pixel sacle of .75 arcsec/pix, the FWHM value will be 2.25 arcsec.

Exactly what you wrote. The FWHM is measured in pixel because that is what you have. It could be grains of sand for all that it cares. It is just a proxy for the PSF which is virtually infinite in extent. The FWHM is a measure of an angular quantity which is the PSF. if you use a 2"/px scale and your PSF has a FWHM of 4" then your *measured* FWHM is 2 px. If you use a 1"/px  scale is 4. Yet its is still 4" in width. no matter what is the scale you use.

**No.  This is how it is,  When I shoot at 2.46 arcsec/pix I achieve a FWHM of 4.5.  When I shoot at .7 arsec/pix I achieve a FWHM of 2.5.  It is the same camera so the same pixels.  What is so backward about that....its reality.   There is no way I can achieve a FWHM of 2.5 when shooting at a pixel scale of 2.46 arcsec/pix.  That would mean less than 1 pixel across the FWHM.

andrea tasselli:

Rodd Dryfoos:

andrea tasselli:

Rodd Dryfoos:

andrea tasselli:
They are unrelated. I guess you got this at the wrong end. FWHM is an independent parameter that depends on various factors (such as seeing, aperture size, various optical errors and in general anything that stands in the way of the rays coming to focus) but does NOT depend on how you sample it. The scope of sizing your detector pixel scale is to match your FWHM with the sensor pixel size in order to achieve the optimum sampling (for discussion's sake let's say 3 pixel across). Too little and you cannot reliably reconstruct the original PDF which is needed for a host of post-processing tasks (although there are way to minimise this, see drizzling). Oversample it and you're wasting photons (well, potentially) spreading the butter ever so thinner on the bread, in a manner of speaking.

As for the other question the FWHM is a measure of the seeing, so you can't.

*OK--lets take 3 pixels across.  I shoot at 2.5 arcsec/pix and the FWHM will be 7.5 arcsec  if I shoot at 1 arcsec/pix the FWHM will be 3 arcsec.

How is pixel scale not important?

Also--I got a FWHM of 1.8 arcsec the other night (several between 1.8 and 2)  and I know my sky was not 1.8 arcsec seeing

Rodd

Rodd,

You get this backward, I'm afraid. The PSF is there and it may be measured by the Full Width at Half Modulation. Let's suppose your PSF's FWHM (related to your kit in that moment and in that moment only) is 3" and you shoot at 2.5"/px you should get something close to 1.25 FWHM in theory. But because your sampling system does not know anything about what is the actual PSF it will only measure what it can measure within its parameters. Since part of the energy of the PSF lays outside the FWHM circle  it will use that to fit the gaussian function, error or not. It just does. I myself, when severely under sample the seeing I can get FWHM less than 1.5 px, but never 1. Even for a hot pixel. Most of the programs out there will use anything to make a fit. So, by way of under sampling the PSF you throw away the information you need to actually know what is your actual FWHM at all.

*You lost me.  What, exactly, do I have backwards?  The FWHM is measured using pixels.  The software calculates how many pixels the FWHM covers.  Let's say it is 3.  Well, that m,eans if I am shooting with the FSQ 106 and .6x reducer for a pixel sacle of 2.5 arcsec/pix, the FWHM value is 7.5 arcsec.  If I am shooting with the TOA 130 at a pixel sacle of .75 arcsec/pix, the FWHM value will be 2.25 arcsec.

Exactly what you wrote. The FWHM is measured in pixel because that is what you have. It could be grains of sand for all that it cares. It is just a proxy for the PSF which is virtually infinite in extent. The FWHM is a measure of an angular quantity which is the PSF. if you use a 2"/px scale and your PSF has a FWHM of 4" then your *measured* FWHM is 2 px. If you use a 1"/px  scale is 4. Yet its is still 4" in width. no matter what is the scale you use.

The question is what is a good FWHM.  There is no way I can achieve as good a FWHM shooting at 2.5 arcsec/pix as I can shooting at .77 arcsec/pix.  Do you think it can be done.  If not--then pixel scale effects FWHM

Doug Summers:
It seems you are looking to answer a question you haven't quite formed well with a different question asked about the wrong variable.    All of us amateurs desire to know what the seeing is on a given night.   Professional observatories have Differential Image Motion Monitors (DIMM) that can tell what the seeing is.   There has been some work done on defocused stars to help determine what the seeing is, but this hasn't been quite fully developed yet.   There are some amateur grade seeing monitors out there too (but $$).

So to your question:   A good FWHM (measurement) is one that is well correlated to seeing (not sampling).   Your 0.77 arcsec/pixel camera is always going to be a better FWHM measuring tool than your 2.5 arcsec/pix setup, especially when the seeing is better than 7.5 (which is probably going to be pretty much always).   It won't be particularly good for measuring seeing below 2.3 though.     Unfortunately, you can't use FWHM to get anything but a rough feel for seeing, and for that you would need to use your 0.77 setup, not the 2.5.

**no, we are just talking about different things, really.  But you answered my question, as did John Hayes in the thread FWHm#2.  He said in answer to my question of whether one can achieve as good a fwhm at 2.56 arcsec/pixel as you can at .77 arcsec/pixel.  His response....”Never”.  So I am not so crazy after all.

Doug Summers:
Hi Rodd,   maybe an analogy is appropriate here.   If I was trying to weigh a 1 pound brick with two scales, one which had a resolution of 2 pounds, and the other with a resolution of 5 pounds, in no case would the brick weigh 0, 2 or 5 pounds!    The brick weighs 1 pound, and unless you weigh with a device of resolution less than 1 pound, you can't know what the brick actually weighs.

FWHM is like this.   It is a value that measures full width (arcsecs) at 1/2 peak intensity in the PSF.    To think of FWHM in terms of the measuring device's resolution is to think about it incorrectly.   In that regard, I jokingly accepted this thought as "crazy".   Sorry if this offended.   CS,   Doug

*but your way of thinking is not helpful to one trying to determine if a fwhm value is good.  How do I know 4.5 for the fsq is good when I get 2.5 with Th TOA.  So thank you, now I know the answer. I’ll take crazy any day over being correct if it gives me the answer. You can think about it correctly and I will Be merrily on my way.  And I submit, that fwhm (or to be correct, the value one gets when measuring fwhm) is influenced by pixel scale. If you deny That, perhaps you belong in the straight jacket next to me