Resolution and the Irrelevance of MTF (1 Viewer)

[Ignatius]

The Dawes' limit is 116/D where D is the aperture of the scope in millimetres.
If the 85 mm objective module of your BTX were diffraction limited it should be able to resolve 1,36"
With a visus of 0,8 you should be able to resolve about 1,25' or 75". The scope resolution however is baseed on line pairs, so you would need a magnification of (2x75)/1.36 or about 110x to see the limitations of your scope.

John

I got 1.4" for the scope (116/85), times its magnification of 30x gave me the the 40.9" for the 85 mm BTX (68.2" for the BTX + TC = 50x) because I look through it at the magnified end, not immediately behind the first lens in the objective. Or does that no come into it?

Does resolution for a give aperture decrease with increasing magnification? Like so:
6 x30 23,2”
8 30,9”
8 x40 23,2”
10 29,0”

And does it decrease with decreasing aperture for a given magnification? Like so:
10 x56 20,7”
50 23,2”
40 29,0”
8 x40 23,2”
30 30,9”
25 37,1”

 

[Tringa45]

There's monochrome resolution, such as with the USAF charts, etc.; and then there is contrast and MTF.

Contrast and MTF in any objective will become important if you try to resolve minute details of low contrast, such as with astronomical observations of Jupiter (which is 47" across at best). That is, this matters when you are reaching towards the resolution limit and spatial frequencies above it.

White light is monochrome?!
Contrast diminishes with increasing line pair frequency so resolution is the ability to show contrast. If contrast is high at moderate to high spacial frequencies it will also be high at lower spacial frequencies.
You can't perform MTF measuremenfs on a binocular or scope because they are afocal instruments and focus is only achieved on the retina of the observer's eye.
MTF measurements could theoretically be performed on some astronomical scopes used for astrophotography but they are then used without an eyepiece and are effectively mere camera objectives.

John

 

[Tringa45]

I got 1.4" for the scope (116/85), times its magnification of 30x gave me the the 40.9" for the 85 mm BTX (68.2" for the BTX + TC = 50x) because I look through it at the magnified end, not immediately behind the first lens in the objective. Or does that no come into it?

Resolution is a measurement of the potential of a scope or binocular objective. It is completely independent of magnification, which is the relationship of objective and eyepiece focal lengths.
If your SUV can deliver 500 PS, you're probably not going to call that up in city driving.

John

 

[Ignatius]

This thread has gone beyond my ability to follow, so before I say something really stupid, I’ll just sit and watch.

In retrospect you have it sorted, good Sir. I should have followed your example.

 

[Yarkho]

White light is monochrome?!
Contrast diminishes with increasing line pair frequency so resolution is the ability to show contrast. If contrast is high at moderate to high spacial frequencies it will also be high at lower spacial frequencies.
You can't perform MTF measuremenfs on a binocular or scope because they are afocal instruments and focus is only achieved on the retina of the observer's eye.
MTF measurements could theoretically be performed on some astronomical scopes used for astrophotography but they are then used without an eyepiece and are effectively mere camera objectives.

John

With white light you are in a high-contrast situation, as you would be with monochrome.

Try resolving something clearly above Dawes' limit, but in low contrast, such as features on Jupiter, that will be a much different matter.

And you can define MTF for any optical system, even the afocal one, where the camera is placed in the place of the eye ('digiscoping').

 

[Tringa45]

With white light you are in a high-contrast situation, as you would be with monochrome.

Please explain!

Try resolving something clearly above Dawes' limit, but in low contrast, such as features on Jupiter, that will be a much different matter.

If the Dawes limit can be exceeded, then only marginally in a high contrast situation, but on a low contrast object you would not get anywhere near it.

And you can define MTF for any optical system, even the afocal one, where the camera is placed in the place of the eye ('digiscoping').

And how would you factor out the deficiencies introduced by the camera lens?

John

 

[Tringa45]

In retrospect you have it sorted, good Sir. I should have followed your example.

I'm only interested in furthering knowledge, much of which I have gained directly or indirectly from this forum, and the more I know, the less I know.
If you're not interested, that's OK with me.

John

 

[Binastro]

The Dawes limit is the limit of separation, visually with good eyesight, of two equal white double stars of sixth magnitude with a six inch good refractor.

This was established by Dawes and other noted astronomers.

Please stop using this term, the Dawes limit, for cases where it doesn't apply.

As to detail on Jupiter, which may involve dots with fair or low contrast, the Dawes limit also is not relevant.

On a white background in good light black dots can be seen several times smaller than the resolution produced by the Dawes limit.

As to the limit on Jupiter this varies.

The visual acuity of a person's eyes is normally measured using a standard Snellen chart at 20ft or 6 metres, using both eyes for binocular acuity.
The visual acuity is usually less with one eye. Each eye varies.

Good binocular eyesight in young persons is usually around 20/15 rather than 20/20, using glasses if necessary. 20/20 is a term often used for very good eyesight, although incorrect.

Regards,
B.

 

[Yarkho]

Please explain!

If the Dawes limit can be exceeded, then only marginally in a high contrast situation, but on a low contrast object you would not get anywhere near it.
And how would you factor out the deficiencies introduced by the camera lens?

John

Oh my, I best not write late in the evenings, as I am clearly not being clear (my bad).

You can produce an USAF-chart analog in any of the monochrome color. That is still a high-contrast situation. Useful for detecting highest spatial frequencies, where you still can resolve the line pairs. But your results may depend on the color used (due to CA).

However, if you produce an USAF-chart analog not in monochrome (or black and white) but in say, similar shades of gray, you will be in a low-contrast situation, and the result may be much different. This would simulate the Jupiter situation, or in a birding situation, resolving small-scale shades of color say at edges of a bird's feathers. (The other day I was trying to distinguish a common chiffchaff from some other, much rarer species, based on whether the edges of its feathers are greenish or grayish, and I had no such luck with binoculars.)

Sorry to write "above Dawes' limit", I can see how this is understood as resolution larger than that permitted by diffraction; I meant low-contrast detail of size larger than the resolution limit; that is, of size which ought to be resolved by good optics if it were high-contrast.

Binastro correctly points out that Dawes' limit does not apply to many binocular situations (unless, say, one observes double stars from a tripod).

Regarding visibility of black dots several times smaller than the Dawes' limit, this is also correct, but here we need to distinguish visibility from detectability of unresolved features (where contrast again plays a role).

And as regards MTF... you can define MTF for any optical system, or its part, no? The camera industry does this for complex lenses anyway.

 

[Tringa45]

The Dawes limit is the limit of separation, visually with good eyesight, of two equal white double stars of sixth magnitude with a six inch good refractor.
This was established by Dawes and other noted astronomers.
Please stop using this term, the Dawes limit, for cases where it doesn't apply.

The Dawes' limit is a description of the potential resolution of a telescope in relation to its aperture.
It's not hewn in stone but is a very good approximation of a scope's quality even when used with a well-illuminated 1951 USAF chart.
IIRC Henry might have measured around 110/D on his Astro Physics telescope, but no way is any scope going to manage 90/D.
The resolution of many astronomical scopes is quoted in specifications according to Dawes.

The visual acuity of a person's eyes is normally measured using a standard Snellen chart at 20ft or 6 metres, using both eyes for binocular acuity.
The visual acuity is usually less with one eye. Each eye varies.

We are discussing telescope resolution not visual acuity, though admittedly a certain minimum of the latter is necessary to determine the former.
Personally, I would now need around 1,5D magnification to see the resolution limit but at 2/3 mm exit pupil floaters start to intrude.

Regards,
John

 

[Tringa45]

You can produce an USAF-chart analog in any of the monochrome color. That is still a high-contrast situation. Useful for detecting highest spatial frequencies, where you still can resolve the line pairs. But your results may depend on the color used (due to CA).

The 1951 USAF chart is black on white or a positive or negative transparency!

And as regards MTF... you can define MTF for any optical system, or its part, no? The camera industry does this for complex lenses anyway.

No, MTF measurements express the contrast at the image plane of specific tangential and sagittal line pair frequencies from centre to edge.
With a binocular or telescope the image plane is your own retina (or the virtual image between objective and eyepiece to which you have no access).

Binastro correctly points out that Dawes' limit does not apply to many binocular situations (unless, say, one observes double stars from a tripod).

Even though most commercially available binoculars fail to get near the Dawes' limit you can still measure their central resolution, which is often way beyond the capabilities of the user's eyes.
As an example the Dawes' limit for my 56mm Swarobski SLC would be 2,1" and I measured 2,9".
To do so however, I had to boost the magnification with a second 8x binocular behind it for a total of 64x.

John

 

[Yarkho]

I wrote not about the 1951 USAF chart, but about an USAF chart analog, which you can (?) easily imagine.

Regarding MTF... please understand there is a difference between a defined physical property and some (re-scaled) measurements the lens manufacturers provide.

 

[agus_m]

With a binocular or telescope the image plane is your own retina (or the virtual image between objective and eyepiece to which you have no access).

With the use of a high quality lens you could focus the image that comes out of the bino onto a sensor. Assuming you know the MTF of the lens itself, you could perhaps infer the MTF of the bino from the MTF of the combination bino + lens. I guess that the main component of the function at high frequencies would be from the binocular since it comes before the lens. It is also possible to compare different binoculars while keeping the same lens for consistency. I haven't tried this but I don't see why this method wouldn't work if done properly.

 

[Tringa45]

I wrote not about the 1951 USAF chart, but about an USAF chart analog, which you can (?) easily imagine.

Regarding MTF... please understand there is a difference between a defined physical property and some (re-scaled) measurements the lens manufacturers provide.

I have repeated myself once or twice but it seemms you have made no effort to uderstand my original post or subsequent answers.
I'm open to informed criticism but not to trolling.

 

[Tringa45]

With the use of a high quality lens you could focus the image that comes out of the bino onto a sensor. Assuming you know the MTF of the lens itself, you could perhaps infer the MTF of the bino from the MTF of the combination bino + lens. I guess that the main component of the function at high frequencies would be from the binocular since it comes before the lens. It is also possible to compare different binoculars while keeping the same lens for consistency. I haven't tried this but I don't see why this method wouldn't work if done properly.

This imaginary camera is wild speculation and what could it possibly achieve that a resolution measurement cannot?
A FoV >60° and small aperture (exit pupil) would result in it having poor resolution and edge MTF.
You can't interpolate with what has already been lost!

 

[Yarkho]

I have repeated myself once or twice but it seemms you have made no effort to uderstand my original post or subsequent answers.
I'm open to informed criticism but not to trolling.

Okay since gloves are now off, I too will be blunt: I have re-read your original post for a third time now and as a physicist and astronomer I have to tell you for a third time (or so) that your take on the matter it is at best simplistic.