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Old 26-11-2016, 04:35 PM
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Imaging below a diffraction limit

Hi all,

I have been quite successfully using my 4" doublet with a reducer that combined with my camera give me 1.33" per pixel - about the diffraction limit for a 4" telescope. Now when I have a reliable mount, I was wondering if it would make sense to try imaging the native fl- it would mean slowish f/7 and 1.07 arcseconds per pixel, which unfortunately is below theoretical diffraction limit for my 4" telescope.

Does anyone have experience in imaging below the theoretical diffraction limit for their telescope?

Ta
Suavi
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Old 26-11-2016, 04:39 PM
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Someone can correct me if I am wrong but the diffraction limit is the ability to separate two point sources. With the diffraction limit (Dawes) being about 1.15" that means that you can have a pixel scale half of that to reach the diffraction limit.
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Old 26-11-2016, 05:02 PM
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Unless I am doing something wrong, I keep getting diffraction limit about 1.3" for OIII and about 1.6" for Halpha for a 102 mm telescope.

Does it mean I can successfully use half of that for imaging, indicating that a 4" telescope could in theory give a lot of detail with cameras with small pixels?
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Old 26-11-2016, 05:09 PM
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The Dawes limit is an average and not an exactness for each wavelength.
As the angular resolution is the ability to separate two point sources, you need at least half of that to actually resolve it. This is my understanding but happy to be corrected.
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Old 26-11-2016, 05:20 PM
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As the Dawes limit applies to seeing a single point source as just being percieved as two , that you are going to need greater sampling than just half pixel size to acheive diffraction limited imaging - I'm guessing at least 1/3 pixel scale maybe even less .

I know that planetary imagers typically use F# of f20 to F50 so Airy Disc size is 30 to 80 micron to the first minima. Combined with the fact that those imaging cameras usually have pretty small pixels I'm guessing that there is significant oversampling of the Airy Disc going on to extract all possible planetary detail
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Old 26-11-2016, 05:33 PM
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Thank you Colin and Mark.

From what have been written it looks like a 4" telescope when combined with sufficiently small pixels and at a long (slow) fl could in theory capture as much detail as a 16inch telescope in a suburban conditions? Of course well depth would be different and the required length of exposure, but otherwise we could achieve splendid detail with small telescopes, is that right?
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Old 26-11-2016, 05:40 PM
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by the time you add in any sort of atmosphere, you will have stars of at least 2 arcsec FWHM and the atmosphere will dominate. You will need ~3 pixels across for best resolution, so you could use down to about 0.7 arcsec - mind you it will be as slow as a wet week at that resolution and my guess is that ~1 arcsec should be a good compromise.

In the average Australian atmosphere, the resolution of a good 4 inch scope will be almost the same as that of a 20inch RCOS or the AAT. It will just take a looong time to get many photons.
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Old 26-11-2016, 05:46 PM
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It is possible to get really good detail with a small telescope and small pixels, just very difficult to do due to the very small light grasp. A 4" telescope under excellent seeing will out perform a 16" under average seeing BUT a 16" under excellent seeing will out perform a 4" under the same conditions. Under all but the best conditions a 6" telescope resolution wise will forever be limited by seeing conditions.

An 8" has the best resolution that can be achieved on the Earths surface.
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Old 26-11-2016, 06:04 PM
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Thank you Ray and Colin. Therefore a poor man's solution could be a relatively fast 5" telescope combined with a camera with small pixels. For example 650mm FL at F/5 with 3.1 micron pixels (ICX834) would give 0.98 arcseconds per pixel and becasue of its relative lightweight could ride on a portable mount and therefore should not/would not end up in a divorce LOL
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Old 26-11-2016, 06:46 PM
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the problem with a relatively fast 5 inch will be CA. There are only a couple of refractor designs that seem capable of keeping the spot size within the diffraction region over much of the visible spectral region. For narrowband though, it should be a reasonable approach. Better bet might be a 6 inch fast Newtonian with a decent coma corrector.

Last edited by Shiraz; 26-11-2016 at 09:22 PM.
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Old 26-11-2016, 08:17 PM
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Originally Posted by Slawomir View Post
Thank you Ray and Colin. Therefore a poor man's solution could be a relatively fast 5" telescope combined with a camera with small pixels. For example 650mm FL at F/5 with 3.1 micron pixels (ICX834) would give 0.98 arcseconds per pixel and becasue of its relative lightweight could ride on a portable mount and therefore should not/would not end up in a divorce LOL
This just happens to be what I've got
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Old 27-11-2016, 08:41 AM
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the problem with a relatively fast 5 inch will be CA. There are only a couple of refractor designs that seem capable of keeping the spot size within the diffraction region over much of the visible spectral region. For narrowband though, it should be a reasonable approach. Better bet might be a 6 inch fast Newtonian with a decent coma corrector.
Sounds like a good advise Ray. The only four things that at the moment stop me from going the fast Newtonian path are the requirement for an accurate collimation, perfect optical alignment is a must with a fast system, narrowband filters such as 3nm ones become less effective at faster f ratios and to a lesser degree possible CA introduced by the lenses in a coma corrector. I know these things can be overcome but to me it looks like a fast Newtonian can add a few extra challenges to this already challenging hobby of ours

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This just happens to be what I've got
Yes, I have been looking at similar options to your telescope and was wondering whether we possibly trade quality for speed in a refractor (slower refractor having tighter stars across the visible spectrum) and the need for a more frequent refocus with temperature shift with faster refractors.

Just slowly planning my next "upgrade"...
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Old 27-11-2016, 11:11 AM
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There's some argument for sampling at 3x the possible resolution of the system if you don't want to leave any detail on the table, but like everything it's a trade-off.

Additionally, the diffraction limit isn't really a hard limit and changes depending on which formula you use. Dawes for instance gives you 1.14" for a 4" scope.

Jon Rista (posts on CloudyNights) uses the following formula to estimate FWHM:

FWHM = SQRT(Seeing^2 + Dawes^2 + ImageScale^2 + GuideRMS^2)

I'm going to make some (reasonable) assumptions and say we have typical seeing of 2", and a guiding RMS of 0.4", which means for your current (native FL) system, we get:

FWHM = SQRT(2^2 + 1.14^2 + 1.07^2 + 0.4^2)
FWHM = 2.56992218"

Keeping everything the same except switching to an (unobstructed) 6" aperture you would improve your resolution as follows:

FWHM = SQRT(2^2 + 0.76^2 + 1.07^2 + 0.4^2)
FWHM = 2.42538657"

And for the sake of illustration, were you to continue to use your 4" scope but go for pixels half the current size, you'd be looking at:

FWHM = SQRT(2^2 + 1.14^2 + 0.535^2 + 0.4^2)
FWHM = 2.39704506"

As you can see, the diffraction limit is not a hard wall, and you actually get (admittedly marginal) increase in resolution by going for even smaller pixels.

My 2c is that a 4" is fine for you, especially given that you primarily shoot nebulae.
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Old 27-11-2016, 04:46 PM
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Thank you Lee for explaining it so plainly and for your advice

I must agree that no matter in what direction I look, I always end up with a conclusion that an upgrade would make a solid dent in my savings and any improvements won't be radical. Perhaps in a few years, IF we move to a darker location and I would like to try RGB imaging, then I could possibly look for something better.

Let's hope that this dark storm lurking in the west will go past Brisbane quickly and we will get a few hours of clear skies tonight...
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Old 27-11-2016, 06:46 PM
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Here here!
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Old 27-11-2016, 09:44 PM
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Hi Suavi,

I don't think it's worth trying for small image scales with a refractor. Unless you have a fairly exotic (i.e. expensive) design you won't be getting diffraction limited performance over more than a small area at the centre of the field. Even then, coupled with a small pixel size camera the combination will be slow. Might as well bite the bullet and go for a larger Newt or CDK if that's what you want.

Cheers,
Rick.
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Old 28-11-2016, 09:42 AM
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Interesting discussion. I'm assuming there must be some wavelength factor in the FWHM...although I'd expect tighter stars from shorter wavelengths...

The other night from our little back yard in Brissie I was taking some Ha and OIII subs of the Tarantula. Seeing must have been decent, as happens occasionally. Plugging them into above formula suggests I should be seeing 2.7 arc second stars. PixInsight's subframe selector measured my best of the night at 1.9 and the mean of 2.3 over ~100 subs.
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Old 28-11-2016, 09:56 AM
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Hi Suavi,

I don't think it's worth trying for small image scales with a refractor. Unless you have a fairly exotic (i.e. expensive) design you won't be getting diffraction limited performance over more than a small area at the centre of the field. Even then, coupled with a small pixel size camera the combination will be slow. Might as well bite the bullet and go for a larger Newt or CDK if that's what you want.

Cheers,
Rick.
Thank you for your reply Rick. It is certainly a fascinating topic and I am happily learning more about different telescope designs. I need to read more on how to properly interpret spot diagrams. Here is an interesting read on OPD (Optical Path Difference) diagrams: http://www.cfftelescopes.eu/OPD.html


Quote:
Originally Posted by Camelopardalis View Post
Interesting discussion. I'm assuming there must be some wavelength factor in the FWHM...although I'd expect tighter stars from shorter wavelengths...

The other night from our little back yard in Brissie I was taking some Ha and OIII subs of the Tarantula. Seeing must have been decent, as happens occasionally. Plugging them into above formula suggests I should be seeing 2.7 arc second stars. PixInsight's subframe selector measured my best of the night at 1.9 and the mean of 2.3 over ~100 subs.
Great result Dunk Recently I was getting around 1.7 Half Flux Radius for the NGC1763 in Ha which I think is not too bad neither.
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Old 28-11-2016, 09:59 AM
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It needs to be pointed out that it depends what you are trying to image . If you are doing planetary imaging then there is benefit from a greater degree of oversampling or density of pixels as you are going to pick up better random moments of excellent seeing in very short exposures and weed them out for stacking. You would have far less chance of capturing the finest moments when you are doing 5 min plus subs.
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Old 28-11-2016, 10:15 AM
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Thank you for your reply Rick. It is certainly a fascinating topic and I am happily learning more about different telescope designs. I need to read more on how to properly interpret spot diagrams. Here is an interesting read on OPD (Optical Path Difference) diagrams: http://www.cfftelescopes.eu/OPD.html
Hi Suavi,

I have a copy of Telescopes, Eyepieces and Astrographs: Design, Analysis and Performance of Modern Astronomical Optics if you'd like to borrow it. It's a very interesting read. They are big on ray fan plots as well as spot diagrams.

http://www.willbell.com/TM/Telescope...trographs.html

Cheers,
Rick.
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