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# In the name of resolution...

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### #1 Hajfimannen

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Posted 19 July 2019 - 05:02 PM

I come across some expressions I would appreciate help to understand:

Is the Resolving Power of a Telescope the same as its Diffraction Limit?

And what about Dawes limit? Is that a valid number when looking at stars?

### #2 denny-o

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Posted 19 July 2019 - 05:45 PM

http://www.telescope...-telescopes.htm

https://www.telescop..._resolution.htm

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### #3 Asbytec

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Posted 19 July 2019 - 06:12 PM

The resolving power of a telescope is usually defined, by diffraction, to be the Rayleigh limit at 138.4/Dmm or about 1.4" arc for a 102mm aperture. But, resolution is  a complicated thing. Rayleigh describes a condition where two point sources can be clearly delineated from one another due to the formation of two distinct diffraction artifacts (and not to be confused with the diffraction limit). However, the scope can often see other detail, especially on extended objects, smaller than that. Cassini division is a classic example, as are tiny craters on the moon which do not apply to the Rayleigh limit. In these cases, it's all about contrast. If the scope can deliver an image with sufficient contrast, the object should be 'resolved'.

Yes, Dawes is a valid number when looking at stars. It's an empirical resolution limit between two point sources (stars) where contrast between the two Airy discs falls to 5% and is given by 116/Dmm. At this separation, there is enough contrast to dilettante two separate Airy discs thus resolving the double star. Both Rayleigh and Dawes are really special cases of resolution involving two equal doubles of the same given brightness. Neither apply to what can be observed on extended objects. When seeing conditions permit, we can often 'resolve' high contrast features on bright extended objects, like the moon, at less than Rayleigh and Dawes.

The diffraction limit, really, is a statement of how good the optics are. It means, the scope is good enough where normal diffraction of the aperture is the dominate feature and any aberration is likely indistinguishable from normal diffraction. It's kind of a measure of image quality where, below which, the image becomes "decidedly prejudicial" (somewhat controversial) meaning it's not quite as good as a better than diffraction limited image. The common criterion often referred to, also not without controversy as to what it means, is the Rayleigh criterion of no more that 1/4 wavefront deviation presumably of primary spherical aberration and a resulting Strehl ratio of 0.8. Thus a Strehl of 0.8 or 0.82 is considered diffraction limited across most definitions. The other definitions, including for chromatic aberration, can be found here: https://www.telescop...et/effects1.htm

Edited by Asbytec, 19 July 2019 - 06:49 PM.

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### #4 TOMDEY

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Posted 19 July 2019 - 06:17 PM

All those criteria are in the same ballpark... Resolution is also sort of a gray area... As you approach the theoretical resolution limit of your scope, the contrast throughput just gets lower and lower... until you can no longer reliably discriminate the fine structure of the object (nominally, a double star with equal components). And Rayleigh, Dawes, Sparrow just put slightly different limits on what they expect a skilled observer will detect, under ideal conditions.

Therefore... just don't sweat it. Any one of those is about where your ability, with your scope --- will poop out. And then, only a bigger, good scope, under great conditions... will improve things.

All the theoretical analysis, equations, etc. are indeed very interesting... but e.g. Rayleigh's 1.22 λ/D is a good, somewhat conservative rule of thumb!    Tom

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### #5 Asbytec

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Posted 19 July 2019 - 06:43 PM

...but e.g. Rayleigh's 1.22 λ/D is a good, somewhat conservative rule of thumb!    Tom

The interesting thing is Rayleigh is derived from the properties of diffraction. It's kind of a diffraction limit in itself, and not to be confused with the diffraction limit (which is really a criterion rather than a limit), eh?

I appreciate the definition of resolution being where our scopes will "poop out".

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### #6 TOMDEY

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Posted 19 July 2019 - 09:04 PM

The interesting thing is Rayleigh is derived from the properties of diffraction. It's kind of a diffraction limit in itself, and not to be confused with the diffraction limit (which is really a criterion rather than a limit), eh?

I appreciate the definition of resolution being where our scopes will "poop out".

Hi, Asbytec; yes, indeed!

I resisted unnecessarily launching into the Bessel Sync Functions, etc., as originally derived by Airy... [J1(x)/x]2 and all that wonderful stuff. Rayleigh, Dawes and Sparrow can be cutely related to the incoherent displaced summation of those (individually/coherently-derived) functions. It turns out that CodeV can do that coherent → incoherent stuff, down in the sub-sub menus, with whatever aberrations are going on within the system. These special cases being free of all geometric and chromatic aberrations. Interesting to compare a designed or measured system (including design aberrations and measured as-built  residuals, central obstruction, etc.) ... with the ideals. That's where I found that ultra-high Strehl is not really that big a driver.

I love the theory… but try to avoid it except when needed.

PS: When doing that... I had the epiphany that aperture is a peripheral obstruction!  And it is that which ultimately limits the resolution... defines the limit... for that scope. And, in that sense... the most ideal telescope would have --- infinite aperture!

[At this juncture --- we shoot the engineers and get on with production.]    Tom

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### #7 CounterWeight

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Posted 19 July 2019 - 10:05 PM

Great posts all.

I'd just add that the interplay of aperture / focal length (and focal ratio) / and eyepiece theory (exit pupil at a magnification {or ep focal length}) are good to get a handle on in an "in general" sense.  It works the same way for all optics and that is useful.  It is east to graph using a spreadsheet program, I use OpenOffice as it's free.  Am attaching one I made for one of my scopes as example.

Often mentioned here is the importance of the glass melt used or Fluorite, lens figuring, coatings, imperfections, scatter, and lens cell.  If in the reflector forum same things as applied to the mirrors.  There is an issue that all equal apertures and focal length are not equal issue here where the tire hits the road where it all counts. So it is who made the aperture.

Keeping in mind the specific 'airmass' you are viewing through will be most likely the main limiting factor and will impact different objects differently as does light pollution. A lot of discussion of what type object or objects it might matter on and how, but resolution is all the story.

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### #8 Asbytec

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Posted 19 July 2019 - 11:01 PM

I love the theory… but try to avoid it except when needed.

I think "poop out" describes resolution quite nicely.

Peripheral obstruction and negative aperture...all interesting stuff, but just go see where our scope poops out. We'll be pleasantly amazed with what we can see when things go right. It's fascinating to know the Airy disc itself is a limit to resolution, but an extended object the same size of the Airy disc can show features. That's pretty tiny.

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### #9 Stephen Kennedy

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Posted 19 July 2019 - 11:26 PM

If you want to actually learn how to derive the equation TOMDEY mentioned, get a copy of "Fundamental Astronomy" by Karttunen et al; and go to go to the last section of the chapter on Observation and Instrumentation where it is explained in detail.  This is a University level textbook for Astronomy and Physics majors so it requires a sound background in Calculus.

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### #10 Hajfimannen

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Posted 20 July 2019 - 05:31 AM

Thanks all.

One of the biggest challenges when entering a new field is not only to understand the different concepts. But also to figure out which one to focus on.

I have my eyes set on the SW Esprit 100ED. It has a Limiting Stellar Magnitude of 12.5.

Does LSM have a fixed relationship with the Strehle ratio?

### #11 Jon Isaacs

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Posted 20 July 2019 - 06:04 AM

Thanks all.

One of the biggest challenges when entering a new field is not only to understand the different concepts. But also to figure out which one to focus on.

I have my eyes set on the SW Esprit 100ED. It has a Limiting Stellar Magnitude of 12.5.

Does LSM have a fixed relationship with the Strehle ratio?

Limiting Stellar Magnitude is just a rough approximation and it's based entirely on aperture.  Of all the specifications, it is the vaguest.  What you will actually see depends on you as an observer as well as the conditions.

As an observer, your skill is very important.  A long time observer will see significantly more than someone starting out. Your level of dark adaptation is critical.  Under dark skies, this means 30 minutes with no extraneous lights.

The conditions are critical.  How bright are your skies.  The darker the skies, the fainter the stars one can see. How steady are the skies..

Jon

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### #12 Hajfimannen

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Posted 20 July 2019 - 06:16 AM

I'd say sky conditions is probably the restricting factor in my case. Not so much when it comes to LP. I'm in bortle 4. And living by the sea, some of the constellations are to my west, meaning open oceans.

But the costal location also means moist air and cloud infested skies from time to time.

I'd assume my seeing is 3 FWHM at its best. Adding an Atik 460 EX mono would give me an image scale of 1.7. So roughly half of the limiting factor.

I'm I adding the right numbers so far?

### #13 Rutilus

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Posted 20 July 2019 - 06:33 AM

Thanks all.

One of the biggest challenges when entering a new field is not only to understand the different concepts. But also to figure out which one to focus on.

I have my eyes set on the SW Esprit 100ED. It has a Limiting Stellar Magnitude of 12.5.

Does LSM have a fixed relationship with the Strehle ratio?

Like what Jon said, it's just an approximation. More depends upon the observers eyesight and seeing conditions.

For example in my local sky condition I can see stars down to magnitude 4.5 with the un-aided eye.

With the 4 inch refractors I have used from my location (Takahashi, Lzos, sky-watcher and even cheap

sky-watcher Achromat)  I have been able to see stars from magnitude 13.7 - 14.0.

People with better seeing conditions have reported on this forum seeing stars fainter than magnitude 14.0

with a 4 inch scope.

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