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Tommohawk

DSO resolution - effect of aperture?

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Yet another probably daft question - from the seemingly inexhaustible supply...

Having just read another thread on fast Newts vs Refractors, I got to wondering what effect  - if any -aperture has on resolution. With slow planetary scopes/set-ups, aperture is all.

But how small can you go with a refractor before aperture affects resolution? Is it simply the case that when reducing aperture, and maintaining the F ratio, the FOV increases ( or image size reduces)  such that resolution isnt an issue?

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It actually does have an effect. Not major one, but it's present.

I'll just run thru the principles of it as I understand them. I'll make couple of assumptions that in general case for typical long exposure astro photography hold.

Resolution is mainly dominated by seeing, but that is not whole story, more accurate description would be - resolution depends on PSF - point spread function, or Gaussian bell shape of a star - something that we characterize with FWHM. PSF depends on three components, each that can be approximated with Gaussian shape (neither is exactly gaussian, but two asymptotically tend to that shape with longer exposure, whilst one can be approximated by it really good). One is of course seeing PSF, other is mount tracking PSF (if tracking imprecision is such that it's random in nature - like guiding error without major problems to deform stars out of circular shape) and third is Airy disc. These three components kind of "multiply" to give final result (precise operation is convolution which is spatial equivalent of frequency domain multiplication). For certain setup, we can assume that two of those components are more or less the same. Third component - Airy disk size is dependent on aperture. So larger scope will have smaller FWHM (under same seeing and same tracking error) but it is not a linear dependence.  With small apertures difference can be quite big, but as soon as seeing becomes dominant factor, differences fall off rapidly.

All of this is expressed in angular values, but when you take into account focal length and pixel size, you will get different FWHM values for different setups. If you measure FWHM on image in pixels and convert that into arcsecs, you will end up with "tighter" stars with larger telescope. This of course translates into resolution (of course there are other factors like sampling rate - but we will take "ideal" case, not oversampled, not undersampled, but just right :D ).

For example it's not uncommon for PHD to report FWHM of  5"-7" or even 10" in bad seeing on my 60mm guide scope, while images I produce with main scope have much lower FWHM.

 

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Great question. My feeling is that it has to do with your sky conditions. Large aperture scopes will be able to show smaller details, but if you have an average atmosphere between you and the object, like most of us (not being on top of a South American mountain or in space), it soon becomes meaningless with increasing aperture. It may be that a 10" newtonean at f/5 will give you slighly more detail than a 5" refractor at f/5 for the same amount of data on a very good night, but I doubt that a 16" scope would add much more. The. you also need a camera that have enough pixels to pick up any additional resolution.

Very exited to hear what the experts think about this!

Edit:  I see that I replied at the same second as vlaiv that clearly had a more scientific take on it.

Edited by gorann
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There are formulae to calculate FWHM given following:

1. airy size disk (depends on wavelength of light and aperture size)

2. Seeing FWHM

3. Tracking error

For example in 2" seeing with 0.5" RMS tracking error at 510nm:

50mm scope gives 5.26"

80mm scope gives 4.478"

200mm scope gives 3.7"

400mm scope gives 3.44"

These are all FWHM values of star profile. Also for values of 2" and 1" RMS tracking error my guider of 60mm should produce ~6.1" (this is pretty much consistent with my PHD reported values).

Edit:

I just attached spreadsheet with calculation (OpenOffice type) for anyone interested

FWHMCalc.ods

Edited by vlaiv
Added spreadsheet ...
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There's a ha

On 14/03/2017 at 20:56, Tommohawk said:

what effect  - if any -aperture has on resolution. With slow planetary scopes/set-ups, aperture is all.

 

The simple formula we were taught in Physics for Dawes Limit is:

R=134/D

were R is the maximum resolving power in arc seconds and D is the telesope aperture in mm.

Thus a 300mm Newtonian is 0.446 arc seconds resolution and an 80mm refractor is 1.675 arc seconds.

There's a good explaination on Damian Peach's website

http://www.damianpeach.com/simulation.htm

Damian uses a C14 SCT, not an 80mm refractor...............

Edited by laser_jock99

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So vlav, is the conclusion that you can go on increasing the aperture until you reach 2" (which would be a meter aperture or so I guess)?

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2 hours ago, gorann said:

So vlav, is the conclusion that you can go on increasing the aperture until you reach 2" (which would be a meter aperture or so I guess)?

I think you can keep increasing aperture and fwhm will asymptotically approach guide error + seeing fwhm, but never quite reach it. Also this approximation is suited for long exposure where seeing averages out. Short exposure / lucky imaging is somewhat different. In that case seeing is a bit harder to model, since effects depend on aperture as well - bigger scope - larger volume of air it looks thru - more chance of disturbance.

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From experience aperture does matter but DS imaging introduces variables not present in planetary. Long esposures are very susceptible to seeing, which will often be the limting factor on resolution.

Just talking about refractors, and refractors working within the limits of the seeing, the biggest thing you'll notice is star size and star count. Small refractors will produce fewer and bigger stars in the image. Larger refractors will produce the opposite, smaller stars and significantly more of them. I see this regularly when using TEC140 data to enhance key areas of wider field Tak 106 images. We can safely say that both instruments are of very high otical quality.

Once you introduce a change in optical type you are not comparing apples with apples any more. SCT stars, for some reason, are relatively large and soft compared with refractor stars but nebular resolution can be excellent. Reflectors with spider vanes can produce tiny stars enlarged by the effects of the vanes. Etc etc.

Olly

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Just to throw in something else or a different perspective- larger than 12inch telescopes particularly will resolve atmospheric movement in what I believe are called cells of air which can affect resolution and I suppose are part of what we are referring to as seeing . This is particularly obvious on some nights when observing with different aperture sizes - but I guess as has already been said, you can only exploit big apertures to good effect if seeing allows this . I guess as above, sometimes long exposures will average out episodes of turbulent air and you will lose reolution that you might keep with a shorter shot. I get a bit obsessed by my guiding graphs which are usually sub 1 arc second - which may not really matter as where I live the seeing is seldom better than this!- Tony

Edited by tony210

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I think this also depends on whether the question is being asked from a theoretical or a practical perspective.

If we are talking about a diffraction limited optical system then there is a very simple and linear relationship between aperture and resolution, given by the Dawes limit. In practice, diffraction limited optics don't exist (central obstruction, complete impossibility of a "thin lens", regardless of nonsense advertising bumph) and the optical system as a whole also has seeing etc to contend with. Even if we disregard the pixel scale of the camera (another limiting factor), under most conditions (especially in the UK) the seeing conditions will pose a limit on what can be achieved, and there is limited value in pushing aperture (in and of itself, disregarding speed) much further. A 200mm scope has a theoretical resolution of about half an arcsecond, which is well beyond what the seeing in the UK usually permits.

 

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I agree - the main advantage for imaging, of slightly larger than 8 inch scopes in my opinion, is that you can take much shorter subs and get more data quickly- but mounting them and guiding them is much more tricky- Tony

Edited by tony210

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Thanks for all the helpful responses. I guess I was interested partly from the theoretical, but mostly from the practical viewpoint, particularly when comparing refractors with reflectors.

A couple of thoughts.

Firstly it must be more difficult to control the surfacing of a larger lens/mirror, so presumably larger lenses/mirrors are more prone to manufacturing inaccuracies - any theoretical benefit of the larger aperture may be therefore be lost. This may be why small refractors seem to perform so well compared to say a Newtonian. That said, most Newts in common use (like mine) are probably budget versions - better grade mirrors would presumably get a better result. Also, with most typical Newts you are probably slightly faster which must bring its own potential inaccuracies in collimation etc. 

It must also depend to some extent on the subject - smaller faint targets will want a longer FL without being slower. That's not so easy/cheap to achieve with a refractor compared to a Newt/SCT

So is the summary:

Wide(r)field use a refractor - it can be quite fast and low mag means resolution isnt an issue.

Small targets use a Newt or SCT - the aperture will have to larger to avoid being too slow, in which case resolution isn't an issue.

???

Edited by Tommohawk

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5 hours ago, billyharris72 said:

I think this also depends on whether the question is being asked from a theoretical or a practical perspective.

I suspect this is a key statement. All surfaces are assumed to be "ideal" and "perfect", Reality is otherwise. Even a good lens is spherical and that is not the ideal shape, similar on a mirror - if I recall the centre of a mirror is "parabolised" so that mweans the edges are spherical. And it is generally the outer sections that perform the worst. So a bigger aperture would mean more "bad" profiles involved with the instrument.

Simple way to look on it is just about everything draws the image created by an optical system as flat, it isn't, the image plane is curved. Until you start to add additional optical components to counter this.

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No, the edges of a mirror are not spherical, at least if the maker knows what he's doing. A parabolic mirror will be figured right to the edge. Also some of the best lenses will be hand aspherised to eliminate that source of spherical aberration, see especially CFF refractors.

As I recall, "diffraction limited" usually equates to lambda/4, or a Strehl value of 0.84, whereas the best lenses will go above 0.96, or even 0.98. These are measured values, not "advertising puff"

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Well, I aim to be looking into this fairly soon. I have a second Mesu 200 mount coming and this should be capable of reliably guiding at or just below an arcsec per pixel. I will then be able to compare, at similar pixel scales, a 10 inch SCT and a TEC 140 apo, each working with pixel sizes giving about 1"PP.

I see no point in theorizing about the outcome. The best thing to do is to try them both.

Olly

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17 hours ago, ollypenrice said:

Well, I aim to be looking into this fairly soon. I have a second Mesu 200 mount coming and this should be capable of reliably guiding at or just below an arcsec per pixel. I will then be able to compare, at similar pixel scales, a 10 inch SCT and a TEC 140 apo, each working with pixel sizes giving about 1"PP.

I see no point in theorizing about the outcome. The best thing to do is to try them both.

Olly

Sounds like a plan! will be interested to see the results.

PS a second Mesu 200? ..... lucky you! :icon_biggrin:

Edited by Tommohawk

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1 hour ago, Tommohawk said:

Sounds like a plan! will be interested to see the results.

PS a second Mesu 200? ..... lucky you! :icon_biggrin:

I do this for a living, don't forget. (What a great excuse that always is...)

:icon_mrgreen:lly

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On March 15, 2017 at 09:54, Tommohawk said:

Thanks for all the helpful responses. I guess I was interested partly from the theoretical, but mostly from the practical viewpoint, particularly when comparing refractors with reflectors.

 

This is purely a practical comparison but gets to the point. The first LRGB image is a crop of a wider field around M106 taken with a 90mm f/7 APO refractor. It was rescaled to match that of the 2nd image which is a mixed focal length shot using luminance from a 10" f/10 SCT, superimposed on the refractor image. They were taken with the same CCD on successive evenings under similar sky and seeing conditions.

 

Derek

image.jpg

image.jpg

Edited by schmeah
Wording clarification
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The theoretical effect of aperture upon resolution was explained to me thus.

Wavefronts defract when they meet any 'edge' .  This diffraction causes interference patterns to form within any image formed by this light.  The lower the amount of interference and strength of these interference patterns, the more detail we can see in an image.

A lens or mirror of infinite size has no edge and would have potentially infinite resolution.  In the real world, an 8" refractor has a lower amount of edge per unit area of light collecting surface than a 4" refractor, and thus has higher resolution.  Similarly, an 8" refractor has less edge than an 8" Newtonian because the central obstruction in the Newtonian adds more edge and hence lowers resolution.

This is a key reason why we can't see artefacts of the Apollo landings from Earth-based telescopes. They just aren't big enough to provide high enough resolution.

In the real world, local and atmospheric seeing conditions, collimation, and the optical quality of the lens/mirror, also have significant effects upon resolution.

 

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On 22/03/2017 at 02:15, schmeah said:

This is purely a practical comparison but gets to the point. The first LRGB image is a crop of a wider field around M106 taken with a 90mm f/7 APO refractor. It was rescaled to match that of the 2nd image which is a mixed focal length shot using luminance from a 10" f/10 SCT, superimposed on the refractor image. They were taken with the same CCD on successive evenings under similar sky and seeing conditions.

erek

 

Thats a useful comparison - it seem to suggest that there is greater detail and presumably better resolution with the 10" SCT. Is that your conclusion too?

But you could say that the reason the resolution is not so good from the first shot is that its had the image scale stretched. In other words, larger diameter scopes may give better resolution simply because they have a longer focal length more appropriate to smaller subjects. Does that make sense?

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