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Interpreting FWHM

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#1 Peter Zbib

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Posted 25 May 2020 - 07:21 PM

Hi

 

To fine tune the "Bahtinov obtained focus" of my telescope (or the "Canon Live view x 10 focus"), I start Backyard EOS, pick a visible star in BEOS Live View. Backyard EOS then gives me its FWHM value. I adjust focusing to minimize the BEOS calculated FWHM of the star.

 

How should I interpret this value ?

 

Intuitively, it seems to me that if I always use the same setup (same camera+ same scope), the FWHM of a fixed star is correlated to seeing. When I get 2.7 or 2.8, seeing is good. When it is 3.0 or worse 3.1, seeing is bad (always same star, same place). Correct ?

 

Also: is the FWHM dependent on the scope technology *newtonian, refractor, etc) ?

 

Also: for a family of identically architectured scopes but different focal lengths, would the FWHM be constant ? Eg, (assuming that the Esprit 120Ed and 150ED are architecturally identical inside), if I had 2 setups, next to each other, one with eg a Canon 6d and Esprit 120 and the other with a Canon 6d and Esprit 150, would the FWHM be the same

 

In short, what is FWHM dependent on ????

 

These are far from being critical questions. But after using the Esprit 80ED with a Canon T3i then 6D, I recently started using a Rokinon 135mm lens with my Canon 6D.

 

The FWHM is used to get was from 2.8 to 3.2 (different stars, same bad location). I am now going to a better location, darker site. I tried the Rokinon twice. In both cases, the FWHM of my chosen star for focusing was around 2.3 through 2.5. So that left me wondering: was the decrease due to the change in lenses or to the change of location.

 

Head scratching. Perhaps, certainly, useless but I have no idea how to tackle the problem. If you have a reference to recommend, that would be neat

 

TIA

 

P

 



#2 HockeyGuy

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Posted 25 May 2020 - 08:51 PM

You got it! The larger the FWHM, the larger the airy disk, therefore the seeing is worse. FWHM stands for Full-Width at Half-Maximum. In the case of an airy disk, when the seeing is poor the airy disk will be smeared out over more pixels, and its maximum amplitude is decreased, so the FWHM will be larger. It's kind of like compressing a Gaussian probability distribution from above (or changing it's standard deviation) so it becomes shallower and wider:

 

fig_gaussian_distribution_1.png

 

We typically talk about FWHM in terms of arc-seconds. Excluding seeing, you can estimate the nominal FWHM for a given system using the formula for the angular diffraction limit:

 

FWHM ~= 206265 * lambda / D

 

where lambda is the wavelength of light (typically between 350 and 750 nm) and D is the aperture of the telescope. The constant 206265 is there to convert angles from radians to arc-seconds.

 

I don't think Backyard EOS has any knowledge of the telescope specs, so I assume it reports FWHM in pixels? In this case, using a camera with a different pixel pitch should change the FWHM reported on Backyard EOS, as larger pixel pitch will yield lower FWHM in terms of pixels and vise-versa.

 

Using a lens with a different diameter will also affect the FWHM. All things being equal, larger diameter scopes will yield smaller FWHM. If I understood your post correctly, I think this is the opposite of what you witnessed: you found a lower FWHM using the Rokinon (I believe smaller D) under better skies than the 80mm Esprit (larger D)? So you must have been seeing-limited at your former site! If you try using both scopes on the same star, same seeing conditions, you'll find that the larger diameter scope yields lower FWHM. Oh, and the FWHM will also vary depending on the altitude of the star (how much atmosphere you're looking through).

 

Here is a pretty good resource for more information on diffraction and angular resolution: https://www.telescop..._resolution.htm


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#3 Peter Zbib

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Posted 25 May 2020 - 10:06 PM

Thanks a lot for your answer.

 

Now that I read your post it struck me that Bracken's book discusses airy disks. I did read that book five or six years ago (cant remember when it was published) but not using this info in my sort of AP (iei elementary) it disappeared in the meanders of my memory :-)

 

But you did a perfect job at reminding me of the physics behind it (the formula and its consequences eg the focal length or the telescope/lens type have nothing to do with the FWHM but the aperture sure does). When I read the book, I did not link this formula to anything practical (and I remember asking myself why it was presented....)

 

And yes, what I noticed on the field was contrary to what I intuitively expected and that was started my head scratching ( but only after I processed my image :-) )

 

The Esprit 80ED is F/5. I image with the Rokinon at F2.8. So to get a much lower FWHM value with the Rokinon does show that seeing was MUCH worse on my old site

 

Thanks again. This was a perfectly timed reminder of the basics. This time, I wont forget it !

 

smile.gif

 

P

 

BTW: Backyard EOS does not seem to need / use the telescope info. But it does need the camera model although I presume this is just for computer related technical reasons (using the correct driver).



#4 HockeyGuy

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Posted 26 May 2020 - 01:23 AM

You're very welcome! You were definitely on the right track, just needed a tiny boost to piece it all together laugh.gif I forget the basics sometimes myself, and there's no shame in that. When I attempt to explain concepts to others, I find it helps me remember them, so this was mutually beneficial heh.

 

I look forward to seeing your images at the new site!

 

Cheers,



#5 sharkmelley

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Posted 26 May 2020 - 07:33 AM

 

The FWHM is used to get was from 2.8 to 3.2 (different stars, same bad location). I am now going to a better location, darker site. I tried the Rokinon twice. In both cases, the FWHM of my chosen star for focusing was around 2.3 through 2.5. So that left me wondering: was the decrease due to the change in lenses or to the change of location.

 

It's because of a change of lenses.

 

If I understand you correctly, you were getting FWHM of around 3.0 pixels with the Canon 6D on the Esprit 80.  Pixels of 6.5microns with focal length 400mm gives an imaging scale of 3.3 arcsec/pixel, so the FWHM is 10arcsec.

You were getting FWHM of 2.4 pixels with the Canon 6D and Rokinon 135mm.  This gives an imaging scale of 9.9 arcsec/pixel, so the FWHM is 24arcsec.

 

The FWHM figures of 10arcsec and 24arcsec are both much higher than typical seeing conditions so the seeing has almost nothing to do with the difference.

 

Mark


Edited by sharkmelley, 26 May 2020 - 07:39 AM.


#6 Peter Zbib

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Posted 26 May 2020 - 07:59 AM

Wow. Hum. This is going to cause some head scratching.

You got good points but your message is incomplete in the sense that you dont explain what I observed

Given that the Esprit is F/5 and I image at F/2.8 with the Rokinon, the diffraction law implies that difference is going to be even large than 10 vs 24.

????

Next task: find a calm spot in my day to think about this

#7 sharkmelley

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Posted 26 May 2020 - 08:36 AM

Given that the Esprit is F/5 and I image at F/2.8 with the Rokinon, the diffraction law implies that difference is going to be even large than 10 vs 24.
 

The diffraction law has very little to do with it.  The diameter of the diffraction limited Airy disc is 2.44*wavelength*f_ratio.  For the Esprit at f/5 and Rokinon at f/2.8 that gives spot sizes of 6.1 microns and 3.2 microns respectively for green light at 500nm.  Both are less the pixel pitch of your Canon 6D.  In any case you can't believe that the Esprit and especially the Rokinon give diffraction limited optics when used wide open. 

 

I admit that I'm not explaining what you observed.  On the other hand, certain explanations can be ruled out.

 

Mark


Edited by sharkmelley, 26 May 2020 - 08:47 AM.


#8 Peter Zbib

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Posted 28 May 2020 - 06:27 AM

Still at a loss to understand. Worse, sometimes I have a feeling I agree to two contradictory explanations/points of view.confused1.gif

 

Mark's conversion from pixels to arc second does show that the difference betwwen the 2 values (Esprit vs Rokinon) is +- 14 arc seconds. And just about everybody agrees that the seeing variations are "in the lower single digit arc-second values". So attributing the thing to the difference in seeing seems impossible

 

P

 

PS: I have noticed that some people refer to their "usual FWHM" as some sort of absolute measure of seeing. Like "In my FWHM 2.2 sky, etc...." ....



#9 sharkmelley

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Posted 28 May 2020 - 07:26 AM

Still at a loss to understand. Worse, sometimes I have a feeling I agree to two contradictory explanations/points of view.confused1.gif

 

I think the main effect is probably the difference in quality of the optics.

 

Remember also that assuming your focusing is accurate, the measured FWHM in your DSLR images is a combination of many different factors:

  • Seeing
  • Guiding errors
  • Optical quality of the lens/telescope
  • Bayer matrix interpolation of the colour sensor

Mark


Edited by sharkmelley, 28 May 2020 - 08:08 AM.


#10 Peter Zbib

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Posted 28 May 2020 - 04:30 PM

Could well be.

 

The Esprit 80ED has lower quality optics (Dawes & Rayleigh) compared to its siblings. I tried to find the same info for the Rokinon. Failure (bad search arguments ?). I dont think "regular" lenses are measured by their manufacturers for astro performance.

 

Anyway, I am comparing the FWHM computed by Backyard EOS for the 2 setups. Guiding & Bayer matrix manipulation have nothing to do with this value

 

So that leaves me with : Optical quality (per se as well as optical quality of the architecture (refractor vs newtonian vs reflector etc) & Seeing.

 

Seeing being ruled out as it is a "smaller factor" (1 digit arc seconds), that leaves me with one possibility : the Rokinon is of much better quality than the Esprit 80 (it' smaybe much simpler to produce higher quality if you have a smaller focal length ?)

 

Thanks !

 

P
 



#11 sharkmelley

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Posted 29 May 2020 - 01:53 AM

Anyway, I am comparing the FWHM computed by Backyard EOS for the 2 setups. Guiding & Bayer matrix manipulation have nothing to do with this value

 

I beg to differ. 

 

FWHM will be affected by debayering (or you may prefer the term demosaicing).  Suppose for instance you had incredible optics and good seeing which meant the star illuminated a single pixel on the sensor.  That pixel would be the red, green or blue.  The image created during the debayering would spread that light to neighbouring pixels by interpolation, therefore increasing the FWHM.

 

In my list above of factors that affect the FWHM I forgot one other important factor - the anti-alias filter.  Your Canon 6D has an anti-alias filter which deliberately blurs the incoming light to spread it across adjacent sensor pixels.  This is before the debayering spreads the light still further when creating an image from that sensor data.

 

If you are really interested in the raw FWHM you need to use a mono sensor with pixels small enough to adequately sample the star's profile.

 

Mark


Edited by sharkmelley, 29 May 2020 - 02:03 AM.


#12 Peter Zbib

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Posted 29 May 2020 - 12:07 PM

=== I beg to differ.

 

No need to beg. This is just fine. Disagreeing is an essential part of learning. Personnally I never learn better than when someone corrects a mistake I made.

 

=== FWHM will be affected by debayering

 

Never said it was not affected. But I have a "feeling" that the camera and the software being the same in both set ups, the impact would be about the same for the Rokinon and the Esprit.

 

i.e. the increase in FWHM (due to debayering) would be similar (or at least close) in both cases.

 

The best FWHM values I got where 2.2 and 2.8, that's about a 25% difference which is quite a lot.

 

Would you think that without debayering the FWHM would be much closer or inverted with the Esprit getting a better/lower FWHM value ?

 

========

 

This idea carries over to the A-A filter

 

======== If you are really interested in the raw FWHM you need to use a mono sensor with pixels small enough to adequately sample the star's profile. ====

 

Nopes. I think I have the wisdom of accepting that my results are far from getting an APOD or being very "liked" on Astrobin. Until I get a fixed observatory, I wont go the mono sensor way however sweet the mono sirens song is. I have met a few people that transport Paramount mounts, great Taks and super FF SBIG  along with 17 if not 21 inch screens and a power supply good enough for a week in the wilds, on the field ! They fill up their SUVs.

 

Not my cup of tea :-)  I absolutely need to enjoy looking at the sky. AP is a side occupation :-)))

 

Thanks !

 

P




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