Max magnification - can it be exceeded?

[davekelley]

I understand that the max magnification for my 127mm mak is  calculated at 315x.  Can it be pushed a little higher?  I ask because I have the Nirvanah  16mm and 7mm ep's and really like those and for planets I'd sometimes like a little more power, but the 4mm in the series would yield 375x.  Now I have a tracking scope I wonder if fov is not so critical on planets (no need to keep nudging it along to keep the object in the fov) I wondered if maybe a BST starguider 5mm with 60degs would be a more suitable highest power planetary ep.  I owned a bst years ago and I recall it was a comfortable ep, with fabulous sharpness and contrast on planets, brilliant at the price, I didn't like the relatively narrow fov but with tracking that wouldn't be an issue.  I like Hyperions as well and they do a 5mm but is it worth the extra cost?

    

Cheers guys!

 

Dave

[Cornelius Varley]

12 minutes ago, davekelley said:

I understand that the max magnification for my 127mm mak is  calculated at 315x.  Can it be pushed a little higher?  I ask because I have the Nirvanah  16mm and 7mm ep's and really like those and for planets I'd sometimes like a little more power, but the 4mm in the series would yield 375x.  Now I have a tracking scope I wonder if fov is not so critical on planets (no need to keep nudging it along to keep the object in the fov) I wondered if maybe a BST starguider 5mm with 60degs would be a more suitable highest power planetary ep.  I owned a bst years ago and I recall it was a comfortable ep, with fabulous sharpness and contrast on planets, brilliant at the price, I didn't like the relatively narrow fov but with tracking that wouldn't be an issue.  I like Hyperions as well and they do a 5mm but is it worth the extra cost?

    

Cheers guys!

 

Dave

I think you have made an error in your calculations. The practical maximum magnification is 2x per mm aperture, 127x2=254. 

[johninderby]

Using the actual scope aperture (assuming it’s a Skymax 127j the Teleview eyepiece calcular gives the maxiumum usable magnification as 280x. A 6mm would give 250x and a 5mm would give 300x so the 6mm is the highest mag eyepiece you would find usable and that would be on the moon. For planets a bit less would be better.

Edited December 17, 2019 by johninderby

[NGC 1502]

“Maximum magnifications” are largely theoretical.   So much depends on the state of the atmosphere, the type and quality of the instrument, collimation, cooldown, and what type of object you’re viewing, and probably other things too.....

Obviously the claims of 500x with a very cheap telescope on a wobbly mount are ridiculous......

With all of the telescopes I’ve owned over the years, double / multiple stars take higher magnification than planets.

Ed.

[John]

Most of the time planetary views will be better (ie: sharper and more contrasty) at magnifications somewhat lower than the theoretical maximium for your scope. For Jupiter you may well find that 130x - 150x gives the best views. For Saturn and Mars maybe 150x - 250x. Seeing conditions are the big leveller here plus the nature and needs of the target object, which vary.

Even with my 12 inch scope I rarely use more than 350x and often much less on the planets.

So you can try using as much magnification as you like but the planetary views, although larger in scale, will appear fuzzy and washed out.

 

[vlaiv]

Now this is interesting, I just did the math while trying to confirm old rule - x2 aperture size, and I think that someone messed up calculation long time ago

It is not x2 aperture diameter in mm, but rather aperture in diameter / 2.

Let's go thru all of that together to see if I made a mistake, shall we?

Angular resolution of telescope is 1.22 * lambda / diameter, where lambda is wavelength of light usually taken to be 550nm - green light where human eye is most sensitive, and diameter is taken for our case in mm (we will need this to convert units later) - this gives angular resolution in radians (we will need to convert to arc seconds or similar later)

Angular resolution of human eye is said to be 1 minute of arc on average (I assumed that this is for 20/20 vision but I now found why is this - and it can be more in some cases - but let's go with 1 minute of arc).

Maximum useful magnification of the telescope is magnification that is needed so that resolving power of telescope is matched to resolving power of human eye - any more magnification and you will not see additional detail - all detail that is there by telescope resolving power will be resolved by human eye - you will be able to see it.

magnification * 1.22 * lambda / diameter = 1 minute of arc

Let's see what is magnification based on diameter after we convert to same units

magnification = 60 * diameter * 1000 * pi / (1.22 * 0.55 * 180 * 60 * 60)

- first 60 converts from 1 minute of arc to seconds of arc

- 1000 converts from micrometers to millimeters - matching diameter and wavelength of green 550nm = 0.55um = 0.55 / 1000 mm

- pi converts radians to degrees  ( rad * 180 / pi = deg)

- 180 is other part of converting radians to degrees)

- 60 * 60 - is converting degrees to arc seconds ( 60 arc minutes in degree, 60 arc seconds in arc minute)

magnification = diameter * 3141.5 / (1.22 * 0.55 * 180 * 60) = diameter * 3141.5 / 7246.8 = diameter / 2.3

You can test that I'm right using online airy disk diameter calculators like this one:

http://www.wilmslowastro.com/software/formulae.htm#Airy

For 200mm scope it gives airy disk size of - 1.28" and we need half of that for Rayleigh criteria (airy radius - or distance from center to first minima) = 0.64"

How much times we need to magnify that to make it 60" or 1" that our eye can resolve - 60/0.64" = x93.75

Expressed in diameter of scope (we said it was 200mm) this would be 200 x something = 93.75 -> something is 2.133333

(difference being use of 510 vs 550nm in calculations, but if you put 550 instead you get airy disk size of 1.38" or resolving power of 0.69" or magnification of ~87, or 200 / 87 = 2.298 = 2.3 )

It looks like maximum useful magnification is in fact only about x0.45 diameter and not x2 diameter in millimeters????

 

 

[Rob Sellent]

21 minutes ago, John said:

Seeing conditions are the big leveller

Aye, my own experience is just as @John says. Seeing conditions play a huge role in what is possible on a given night. Add to this the optical quality of the scope and eyepieces, cooling, collimation, the nature of one's own eyes, fatigue, and comfort and we've got quite a cocktail going on. There are also objects which can take magnification well (Saturn, Moon, Globs and some planetaries) and others which are not nearly so obliging (Mars, Galaxies, Sun, many nebulae). 

For general comfort viewing, I'm not a fan of pushing exit pupil beyond 0.6mm. The balance is to look for a crisp, sharp and contrasty image from which beyond you gain very little. Magnification, then, isn't so important in this case but rather the quality of visual experience.

Regardless of the scope I'm using, I typical find myself working between around x50 - x200. Beyond this seems to only happen on exceptional nights of seeing. 

[Rob Sellent]

5 minutes ago, vlaiv said:

It looks like maximum useful magnification is in fact only about x0.45 diameter and not x2 diameter in millimeters????

I'm being dumb, but I don't get this, @vlaiv. I'm not disputing the math - I couldn't nor wouldn't. But I don't get how maximum useful magnification for a given eye is x0.45 the diameter of a scope's lens or mirror in mm. I apologise for calling you up. I've no doubt I've missed something  but it's interesting what you've written and I'd like to understand it

[johninderby]

This article on the subject is worth a read. 👍🏻

https://starizona.com/tutorial/understanding-magnification/

[vlaiv]

12 minutes ago, Rob Sellent said:

I'm being dumb, but I don't get this, @vlaiv. I'm not disputing the math - I couldn't nor wouldn't. But I don't get how maximum useful magnification for a given eye is x0.45 the diameter of a scope's lens or mirror in mm. I apologise for calling you up. I've no doubt I've missed something  but it's interesting what you've written and I'd like to understand it

Sure, no problem, I'll explain in detail reasoning behind all of that and math is written above.

When starting off in astronomy, max useful magnifications was one of those things I read about and adopted. At some point when I started being interested in resolution, both in terms of imaging (planetary and deep exposure) and visual I gathered - either read about or concluded, but I do think I read about it somewhere that maximum useful magnification of the telescope is defined as magnification that matches resolving power of telescope and that of human eye.

Maybe best explained on pair of double stars that have just right separation - first part is telescope and depending on aperture size of telescope (under perfect or non existent atmosphere) following can happen:

You can clearly distinguish two stars given their angular separation, you can just make out that there are two discs and you can't be certain if that is some weird elliptical object or two stars.

This separation is related to size of airy disk and is equal to its radius - from max value to first minimum. This is also called Rayleigh criterion for telescope resolution (visual).

Next part in the equation is to match that image which is really tiny if there is no magnification - for usual amateur apertures this criteria gives about 1" resolution (or distance between stars that can be resolved) - that is too small angular separation to be seen by naked eye without magnification.

In fact, according to "eye science" - visual acuity of average human is about 1' - one arc minute, you can read up on this topic here:

https://en.wikipedia.org/wiki/Visual_acuity

But for simple explanation - on eye exam if you have 20/20 vision (considered average / regular for healthy human) this letter:

is 5 arc minutes in size, so in order to know it is E letter - you need to be able to distinguish features of 1/5 in size or 1 arc minute (otherwise you could think it is some other letter as you would not be able to see gaps or little bar or wiggles - each of them is 1/5 in size compared to whole letter - which is sort of matrix of 5x5 elements)

Now if you can magnify two stars enough so that separation between them visually is 1 arc minute, then you should be able to see them as two stars.

In order to magnify something that is close to 1 arc seconds to size of 1 arc minute - you need magnification of x60 (1 arc minute is 60 times larger than one arc second).

For actual math, you can see my earlier post, but bottom line is - I was under impression that x2 is calculated by matching resolving power of the telescope and resolving power of human eye with some magnification, but once I actually tried to do math in response to this thread - it turned out that factor is not x2 but rather x1/2 - so I figured that maybe it was originally miscalculated - it can be easily mistaken as 1/value if you are not careful what multiplies and what divides in math above.

One more important thing to note is that you can use higher magnifications but you will not see additional detail - all the detail that telescope can resolve - so can you at this magnification (threshold magnification), and at higher magnification things will be larger but no additional detail will be seen. This is why it is called maximum practical magnification - like with sampling - you can oversample but you will get larger blurrier image without additional detail.

 

[Paul M]

2 hours ago, Rob Sellent said:

Regardless of the scope I'm using, I typical find myself working between around x50 - x200. Beyond this seems to only happen on exceptional nights of seeing. 

Ditto.

My 10" newt can be pushed to x300 in favorable conditions on a suitable target but x200 is a sweet spot for my eyes on the planets.

While I admire (without fully understanding) Vlaiv's mathematical sojourn above, I think environmental factors and optical quality far outweigh theoretical considerations... for most of us, anyway!

[johninderby]

That’s why a zoom eyepiece is so useful. Find the right mag then switch to a regular eyepiece once you know what the seeing will allow. 

[vlaiv]

I'm not sure that I was understood properly - above I'm implying that maximum useful magnification is not x2 aperture in millimeters but rather something like x0.45 aperture in millimeters.

Take for example 8" scope - you should be able to see all there is to see at something like x90 power and going above that will not show you more detail. Now, I did not make this up - I just followed the logic that lead to x2 aperture in millimeters - and just got different number instead - that is why I said that my math should be checked.

In any case this deserves to be checked at eyepiece as we all know that seeing allows us to go to x150 or there about on most occasions. Question is - can you see a feature on x150 mag that you can't see on x90 mag (a small crater on the moon, or detail in planetary atmosphere or separation between double stars at the edge of resolving power).

I'm not implying that it will not be "easier" to see the same on higher mag - I'm just saying that in theory you should be able to see it on lower magnification as well.

[John]

I was using 280x to observe Neptune with my ED120 refractor a few nights back at an outreach event. I wanted enough magnification to show a clear disk to the punters and it was appreciated. The undriven, alt-azimuth mount that I was using made tracking at this magnfication challenging but we managed and the speed with which Neptune scooted across the field of view prompted some good discussion about the rotation of the Earth

Even at that power, Neptunes 2.5 arc second disk was very small indeed - definitely not "star like" though as all observers noted. And most thought it a pale blue colour as well, especially the younger observers.

Though a large planet, Neptune is over 4 billion km away.

[vlaiv]

I tried to find source of x2 per mm of aperture rule, and was not able to find it - I was able to find similar derivation and it also gives lower value:

http://www.rocketmime.com/astronomy/Telescope/MaximumMagnification.html

It starts by assuming that you need 2 arc minutes of separation between the stars - giving this logic:

while I used Rayleigh criteria and visual acuity of 1 arc minute. Reality is probably somewhere in between (neither everyone has 20/20 vision, but mind you, you are using telescope and far/nearsightedness don't count for sharpness - if you need glasses because of that you can say that you have 20/20 or better with telescope - unless you have astigmatism or such) - one needs between 1' or 2' for Rayleigh criteria.

In any case, above website concludes:

or in another words - maximum useful magnification is x1 aperture in mm (twice larger than my above value because they used 2 arc minutes instead of 1 arc minute for derivation).

Btw, I have no idea so far where x2 rule originated from, and wikipedia says:

with emphasis on "citation needed" part, or:

This means that even wiki reckons it's "hearsay"

[vlaiv]

I just found another interesting text on human eye resolution - so I'll just paste a link to it with citing few important bits and then I'll stop spamming this topic further

https://www.quora.com/At-what-screen-resolution-is-the-human-eye-incapable-of-detecting-an-increase-in-resolution

Quote

Most people are capable of appreciating resolution far beyond that however. A large majority of people have visual acuity sharper than 20:20 after corrective lenses.

and this:

Quote

In the image above, even if you can only barely resolve the lines from each other, you will still be able to see that the lines on the bottom are shifted slightly to the right relative to the lines on top. Humans can detect the position of line segments down to above 0.1 arc minutes, more than 10X finer than the resolution of the eye.

 

[lenscap]

Vlaiv, I have skimmed through the "Magnification" section of this  source

and it seems  that the 2D figure is reached by assuming 4 arc min as a resolution limit for the eye, not the 1 arc min in your first analysis, which accounts for the difference between the 2D & D/2 results.

So I suppose the question is, what is a practical, realistic resolution limit for a typical, dark-adapted eye observing a double star through an appropriate telescope exit pupil.

 

[Merlin66]

The resolution of the human eye is usually stated as 2 arc min. Fantastic eyesight (few and far between) can get down to around 1.5 arc min.

The Dawes Limit for visual observing (generally double stars) depends on the ability to discern the low contrast peaks of the star PSF maxima.

A good test is to determine the minimum magnification to resolve double stars....

I managed to resolve the Double double in Lyra at x49 (Genesis, 10.5mm TV plossl). The separation is 2.3/ 2.6 arc sec , giving 1.88 arc min for the eye resolution.

 

 

Edited December 17, 2019 by Merlin66

[vlaiv]

15 minutes ago, lenscap said:

Vlaiv, I have skimmed through the "Magnification" section of this  source

and it seems  that the 2D figure is reached by assuming 4 arc min as a resolution limit for the eye, not the 1 arc min in your first analysis, which accounts for the difference between the 2D & D/2 results.

So I suppose the question is, what is a practical, realistic resolution limit for a typical, dark-adapted eye observing a double star through an appropriate telescope exit pupil.

 

Well worth a read for all interested.

2 minutes ago, Merlin66 said:

The resolution of the human eye is usually stated as 2 arc min. Fantastic eyesight (few and far between) can get down to around 1.5 arc min.

The Dawes Limit for visual observing (generally double stars) depends on the ability to discern the low contrast peaks of the star PSF maxima.

A good test is to determine the minimum magnification to resolve double stars....

I managed to resolve the Double double in Lyra at x49 (Genesis, 10.5mm TV plossl). The separation is 2.3/ 2.6 arc sec , giving 1.88 arc min for the eye resolution.

 

 

If you read above quoted link you will see that often quoted angular resolution of human eye of 1 arc minute (or 2 arc minutes for line pair) is not representative of human eye resolution at telescope eye piece.

In fact 1 arc minute resolution is limit made by pupil size at daytime - using same 1.22 * lambda / D formula - for example 200mm telescope has Rayleigh criteria of ~0.64" and 2mm pupil in daytime will have x100 larger airy disk - so resolution is then 64" or 1' 4" - or about 1 arc minute.

With eye pupil being larger (dimmer light) - eye aberrations start messing around and blurring the image.

When at eyepiece - telescope corrects for eye aberration in two ways - first eye pupil is no longer aperture stop and it does not cause blur. Diopter is corrected by focusing and any aberrations due to shape of eye ball are reduced by smaller exit pupil. Resolution is dictated then by physical "sampling" - spacing of cells on retina - which are about 2um and for human eye and with 22mm of focal length we have about 18"/px (or third of arc minute "per pixel" so real resolution is a bit less than 1' if you need 2-3 "pixels" to sample point source).

One thing is clear - Maximum useful magnification is misnomer and should read something "Minimum resolving magnification". Higher magnifications will still show you same level of detail and at some point due to dimming start messing with contrast, which can again lead to detail loss since human eye has "static" contrast ratio of 100:1 and can only see certain number of shades - so decreasing brightness will lead to some shades that we can distinguish become indistinguishable. I guess that would be hard to quantify exactly.

 

[michael.h.f.wilkinson]

As I understand it the optimal magnification is given by the aperture of the scope in mm, and doubling it does not necessarily reveal more detail, but might make detail easier to spot, and doesn't clearly show fuzzy edges. Much depends on visual acuity, however, and the contrast on the object in question. The moon and Mars take quite a bit more magnification than Saturn or Jupiter.

[Merlin66]

Well worth re-reading Sidgwick's " Amateur Astronomers Handbook" , Section 2, Telescope Function: Resolution, p37-50.

He gives many examples of visual observations and experienced visual astronomer's experiences.

 

[joe aguiar]

The 2x the aperture formula is just a guild line.

Some night u cant go as high depending on sky conditions other times u can go alot more like 50x to 100x power more.

I say go as high untill it get blurry then if it does back down till image clear.

Joejaguar 

[jetstream]

@vlaiv is it possible that resolving stars splits differ from resolving objects such as planets with regard to the MTF for the latter? I find Peachs obervations to be true from my own observing.

from Peach

 

"Understanding Resolution and Contrast

Two points it is important to understand is the resolution a telescope can provide, and how the contrast of the objects we are imaging affects is related to what can be recorded. Its often seen quoted in the Dawes or Rayleigh criterion for a given aperture. Dawes criterion refers to the separation of double stars of equal brightness in unobstructed apertures. The value can given given by the following simple formula:

115/Aperture (mm.) For example, a 254mm aperture telescope has a dawes limit of 0.45" arc seconds. The dawes limit is really of little use the Planetary observer, as it applies to stellar images. Planetary detail behaves quite differently, and the resolution that can be achieved is directly related to the contrast of the objects we are looking at. A great example that can be used from modern images is Saturn's very fine Encke division in ring A. The narrow gap has an actual width of just 325km - which converts to an apparent angular width at the ring ansae of just 0.05" arc seconds - well below the Dawes criterion of even at 50cm telescope. In `fact, the division can be recorded in a 20cm telescope under excellent seeing, exceeding the Dawes limit by a factor of 11 times!. How is this possible?.

As mentioned above, contrast of the features we are looking at is critical to how fine the detail is that we can record. The Planets are extended objects, and the Dawes or Rayleigh criterion does not apply here as these limits refers to point sources of equal brightness on a black background. In fact it is possible for the limit to be exceeded anywhere up to around ten times on the Moon and Planets depending on the contrast of the detail being observed/imaged."

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

Edited December 18, 2019 by jetstream

[vlaiv]

3 hours ago, jetstream said:

@vlaiv is it possible that resolving stars splits differ from resolving objects such as planets with regard to the MTF for the latter? I find Peachs obervations to be true from my own observing.

from Peach

 

"Understanding Resolution and Contrast

Two points it is important to understand is the resolution a telescope can provide, and how the contrast of the objects we are imaging affects is related to what can be recorded. Its often seen quoted in the Dawes or Rayleigh criterion for a given aperture. Dawes criterion refers to the separation of double stars of equal brightness in unobstructed apertures. The value can given given by the following simple formula:

115/Aperture (mm.) For example, a 254mm aperture telescope has a dawes limit of 0.45" arc seconds. The dawes limit is really of little use the Planetary observer, as it applies to stellar images. Planetary detail behaves quite differently, and the resolution that can be achieved is directly related to the contrast of the objects we are looking at. A great example that can be used from modern images is Saturn's very fine Encke division in ring A. The narrow gap has an actual width of just 325km - which converts to an apparent angular width at the ring ansae of just 0.05" arc seconds - well below the Dawes criterion of even at 50cm telescope. In `fact, the division can be recorded in a 20cm telescope under excellent seeing, exceeding the Dawes limit by a factor of 11 times!. How is this possible?.

As mentioned above, contrast of the features we are looking at is critical to how fine the detail is that we can record. The Planets are extended objects, and the Dawes or Rayleigh criterion does not apply here as these limits refers to point sources of equal brightness on a black background. In fact it is possible for the limit to be exceeded anywhere up to around ten times on the Moon and Planets depending on the contrast of the detail being observed/imaged."

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

I think we are talking about different things here - resolving and detecting.

Here is counter argument to what is written above that might explain what I mean by that - what is angular diameter of a star? Much less than 50mas angular width of Encke division. Looking at the list of resolved stars - about 1mas. But there is much more unresolved stars that have smaller angular diameters still - and we see them all.

In that same sense we see Encke division.

That is detecting a feature and yes it does depend on contrast of the feature (as does resolving).

Now let's discuss resolving a feature - imagine Encke division is not a single clean gap, but something more like this:

(actual image of Encke gap)

How separated two gaps need to be before we can detect that they are separate features? What is their distance at which we can resolve them and say - look it's not single gap, there are two gaps with ridge between them (or there are two stars rather than one in that binary system).

That is the meaning of resolve vs detect.

[John]

I think often we see the Encke Minima rather than the Encke Division.