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FWHM--Try #2

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Rodd Dryfoos avatar
Rodd Dryfoos avatar
Lets start over–you all missed my point.  Let me ask a simple question.  Do you think its possible to achieve as good a FWHM shooting at 2.5 arcsec/pix as you get when shooting at .77 arcsec/pix.

I shoot both (well .77 and 2.46) using the same camera, in the same sky.  When at perfect focus while shooting at .77 arcsec/pix i get a FWHM value of 2.2 arcsec.  When Shooting at 2.46 arcsec/pix using the same camera at perfect focus I get a FWHM value of 4.1

Explain.
John Hayes avatar
John Hayes avatar
Never.  For any given pixel in the image plane, the signal is given by the responsivity of the sensor multiplied by the form of irradiance distribution integrated over the extent of the pixel (in the form of a double integral.)   It's easy to show that the result turns out to be simply the responsivity of the sensor times the area of the sensor times the average irradiance incident on the pixel.  In English, that means that when you use any detector with pixels of finite size, the image will be blurred by the size of the pixels.  It's easy to understand in frequency space simply because a finite sensor looses its ability to modulate a spatial frequency smaller than the size of the pixel so it acts as a bandpass filter.  Removing higher spatial frequency content always makes things blurrier.  You can also think of a system with a geometrically perfect point response with a width of zero.  In that case, only one pixel lights up and one pixel has a FWHM value of the pixel spacing, which is wider than zero.  It works the same way even when the PSF has a finite size.

If you start with any (non-zero) size blur disk in the image plane and sample it with a big and a small pixel, the big pixel will always blur it more in the output than the small pixel.  Hence sampling at 2.46 arc-sec/px will always produce a larger FWHM value than sampling at 2.2 arc-sec/px.

Just understand that there are also disadvantages to oversampling and that you can't reverse the process.  Past a certain point, making the pixels smaller and smaller (past the sampling limit) does not continue to reduce FWHM by any significant amount.

John.
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Rodd Dryfoos avatar
Rodd Dryfoos avatar
John Hayes:
Never.  For any given pixel in the image plane, the signal is given by the responsivity of the sensor multiplied by the form of irradiance distribution integrated over the extent of the pixel (in the form of a double integral.)   It's easy to show that the result turns out to be simply the responsivity of the sensor times the area of the sensor times the average irradiance incident on the pixel.  In English, that means that when you use any detector with pixels of finite size, the image will be blurred by the size of the pixels.  It's easy to understand in frequency space simply because a finite sensor looses its ability to modulate a spatial frequency smaller than the size of the pixel so it acts as a bandpass filter.  Removing higher spatial frequency content always makes things blurrier.  You can also think of a system with a geometrically perfect point response with a width of zero.  In that case, only one pixel lights up and one pixel has a FWHM value of the pixel spacing, which is wider than zero.  It works the same way even when the PSF has a finite size.

If you start with any (non-zero) size blur disk in the image plane and sample it with a big and a small pixel, the big pixel will always blur it more in the output than the small pixel.  Hence sampling at 2.46 arc-sec/px will always produce a larger FWHM value than sampling at 2.2 arc-sec/px.  Just understand that there are also disadvantages to oversampling.  Making the pixels smaller and smaller does not continue to reduce the FWHM.

John.

**I am not trying to go smaller pixels. I am just trying to get a handle on what is a good FWHM for my images.  I am pretty sure the when I shoot at 2.46 4 is a decent fwhm.  But when I shoot at .77 4 is terrible.  I have achieved 1.7 which is my best.  At 2.46 the best I have done is 3.5.  So one can see why I would think the pixel scale had something to do with it
John Hayes avatar
John Hayes avatar
I got a phone call and my editing ability timed out before I could correct the following statement:

If you start with any (non-zero) size blur disk in the image plane and sample it with a big and a small pixel, the big pixel will always blur it more in the output than the small pixel.  Hence sampling at 2.46 arc-sec/px will always produce a larger FWHM value than sampling at 0.77 arc-sec/px.

The time out "feature" on editing is EXTREMELY irritating!  What in the world is that about any way?

John
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Bradley Watson avatar
Bradley Watson avatar
Hey Rodd, I think this is a tough one sometimes to explain. I read the previous thread too.

See below formula. You can see the 4 components that are affecting FWHM, one of those is image scale, so if this goes up then FWHM will too, so it’s relative to the image system.
FWHM = SQRT(Seeing^2 + Dawes^2 + GuideRMS^2 + ImageScale^2)

There is a good discussion on cloudy nights as I was struggling to understand this a while back and sometimes technical jargon and long sentences just confuse everything. I think the formula says enough by itself.

https://www.cloudynights.com/topic/557308-explain-to-me-what-is-fwhm/

Hope this helps

CS
Brad
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John Hayes avatar
John Hayes avatar
Rodd Dryfoos:
**I am not trying to go smaller pixels. I am just trying to get a handle on what is a good FWHM for my images.  I am pretty sure the when I shoot at 2.46 4 is a decent fwhm.  But when I shoot at .77 4 is terrible.  I have achieved 1.7 which is my best.  At 2.46 the best I have done is 3.5.  So one can see why I would think the pixel scale had something to do with it

I believe that I just explained that pixel scale does indeed have something to do with it and your numbers confirm that.  If you are sampling at 2.46 "/pix, you can never achieve a FWHM less than 2.46".  And if the blur function is larger than a delta function with a width on the order of 1", you'll measure a width in the range of 3.46" so it sounds like you are doing pretty well.
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Rodd Dryfoos avatar
Rodd Dryfoos avatar
John Hayes:
I got a phone call and my editing ability timed out before I could correct the following statement:

If you start with any (non-zero) size blur disk in the image plane and sample it with a big and a small pixel, the big pixel will always blur it more in the output than the small pixel.  Hence sampling at 2.46 arc-sec/px will always produce a larger FWHM value than sampling at 0.77 arc-sec/px.

The time out "feature" on editing is EXTREMELY irritating!  What in the world is that about any way?

John

I was not aware of it.  To be clear, in my example the sampling rate is changed due to focal length changes. The pixels remain the same. I use the same camera on both scopes.  Does what you stay still hold true?
Rodd Dryfoos avatar
Rodd Dryfoos avatar
John Hayes:
Rodd Dryfoos:
**I am not trying to go smaller pixels. I am just trying to get a handle on what is a good FWHM for my images.  I am pretty sure the when I shoot at 2.46 4 is a decent fwhm.  But when I shoot at .77 4 is terrible.  I have achieved 1.7 which is my best.  At 2.46 the best I have done is 3.5.  So one can see why I would think the pixel scale had something to do with it

I believe that I just explained that pixel scale does indeed have something to do with it and your numbers confirm that.  If you are sampling at 2.46 "/pix, you can never achieve a FWHM less than 2.46".  And if the blur function is larger than a delta function with a width on the order of 1", you'll measure a width in the range of 3.46" so it sounds like you are doing pretty well.

*I am mixing up threads. I was called crazy for thinking pixel scale and fwhm were related in the other thread.
Rodd Dryfoos avatar
Rodd Dryfoos avatar
Bradley Watson:
Hey Rodd, I think this is a tough one sometimes to explain. I read the previous thread too.

See below formula. You can see the 4 components that are affecting FWHM, one of those is image scale, so if this goes up then FWHM will too, so it’s relative to the image system.
FWHM = SQRT(Seeing^2 + Dawes^2 + GuideRMS^2 + ImageScale^2)

There is a good discussion on cloudy nights as I was struggling to understand this a while back and sometimes technical jargon and long sentences just confuse everything. I think the formula says enough by itself.

https://www.cloudynights.com/topic/557308-explain-to-me-what-is-fwhm/

Hope this helps

CS
Brad

*Thanks Brad.  I’ll have a read.  Nice to know I am not crazy though!😰
Salvatore Iovene avatar
Salvatore Iovene avatar
John Hayes:
The time out "feature" on editing is EXTREMELY irritating!  What in the world is that about any way?


Gotcha, will extend it to 24 hours. I think I added because of people throwing the stone and hiding the hand, in the past, but I understand that it's not worth annoying people who want to legitimately edit a question. Next time you have feedback like this make sure to contact me directly: feedback is the best way to improve AstroBin!
Doug Summers avatar
Doug Summers avatar
Hi John,

Not to beat a dead horse here, but I think it's confusion to allow folks (who don't fully appreciate what FWHM is) to think that FWHM has something to do with platescale.   I get what you're saying and it's true, but folks can easily be confused by the resolution of a measuring tool vs what the true metric means/is.   That's where I think Rodd went somewhat astray.      While we fully agree that sampling resolution affects the measurement, I hope we agree that FWHM should not be thought of as dependent on the measurement device.   To accomodate this would just be confusion IMO.    Cheers,  Doug
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Rodd Dryfoos avatar
Rodd Dryfoos avatar
Doug Summers:
Hi John,

Not to beat a dead horse here, but I think it's confusion to allow folks (who don't fully appreciate what FWHM is) to think that FWHM has something to do with platescale.   I get what you're saying and it's true, but folks can easily be confused by the resolution of a measuring tool vs what the true metric means/is.   That's where I think Rodd went somewhat astray.      While we fully agree that sampling resolution affects the measurement, I hope we agree that FWHM should not be thought of as dependent on the measurement device.   To accomodate this would just be confusion IMO.    Cheers,  Doug

*I am not theorizing. I am simply trying to achieve good fwhm. And understanding that I can’t active as good fwhm when I shoot at lower resolution is what I needed to confirm. So I can stop focusing and refocusing and just collect some data.
Doug Summers avatar
Doug Summers avatar
If what you mean is you're trying to "measure" FWHM accurately, then we've made progress.    Cheers,   Doug
John Hayes avatar
John Hayes avatar
Doug Summers:
Hi John,

Not to beat a dead horse here, but I think it's confusion to allow folks (who don't fully appreciate what FWHM is) to think that FWHM has something to do with platescale.   I get what you're saying and it's true, but folks can easily be confused by the resolution of a measuring tool vs what the true metric means/is.   That's where I think Rodd went somewhat astray.      While we fully agree that sampling resolution affects the measurement, I hope we agree that FWHM should not be thought of as dependent on the measurement device.   To accomodate this would just be confusion IMO.    Cheers,  Doug

Doug,
I guess that I don't know what you mean by "the resolution of the measuring tool vs what the true metric means/is."  The optical system produces an irradiance distribution in the focal plane and we measure a time average of that distribution with a sensor array.  When you measure the FWHM of the measured PSF, you get a value that is impacted by the size of the pixels.  That's just the way it works--and it's the number that you are after because it relates directly back to the smallest detail that you can detect in an image.  Remember that the optical system itself is a bandpass filter that also impacts the FWHM.  Since the atmosphere, telescope and sensor are all incoherently coupled, it's valid to simply multiply the MTFs for each to find determine the system response.  (Remember that the inverse transform of the MTF is simply the PSF.)   So, if we aren't after the FWHM of the PSF of the whole system (optics+atmosphere+sensor), what is the "true metric" of FWHM?

John
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Rodd Dryfoos avatar
Rodd Dryfoos avatar
Doug Summers:
If what you mean is you're trying to "measure" FWHM accurately, then we've made progress.    Cheers,   Doug

*not precisely.  I assume the software measures it accurately. I am trying to achieve good fwhm for a given system. Step 1 was to confirm that different systems (specifically for me systems of different pixel scale using the same pixels) will yield different fwhm values.  Step 2 was determining what these values might be.  I needed to know if a fwhm of 4 or 4.5 ( even 5) arcsec was decent for my Fsq at f3/asi 1600 system. That way I can stop trying so hard to achieve  an unrealistic fwhm
Doug Summers avatar
Doug Summers avatar
Hi John,

After reading and rethinking on your latest post, I acknowledge you have the correct perspective and I am more wrong than right.   It's been a while since I needed to think this deeply about FWHM.    For others who may be more confused than John is, I found the following link helpful to refresh my memory on imaging resolution:

http://www.roentdek.com/info/OnResolution.pdf

Cheers,  Doug
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