AFOV's, FOV's & barlows thrown in.....

[Kokatha man]

I'm startin' this thread fer a mate o' mine that, although he's learnin' fast; seems to (have enough common sense to) doubt some of my maxims re this topic!

I dunno what happenned to the thread on barlows where some of us stated that eye relief was extended to varying degrees by the use of a barlow. (I'll do a check in a mo and see if anyone's added more to that thread since I last viewed it)

But what this young fella wants are 2nd, 3rd and 4th opinions on what happens to the field of view when barlows are employed; particularly as opposed to using an ep that would give the same magnification as the barlow/longer focal length ep combo's magnification.

I understand that the "true field of view" which my mate (I think) calls "the size of the peep-hole" is a product of field stop diameter x 57.3 divided by the scopes focal length and that the maximum FSD of inch & a quarter ep's = 27mm and 46mm for 2" ep's. I am also aware of the "maxim" about factoring down FSD by a magnitude of 2in your choice of ep's for different "views."

He wants to maintain the largest TFOV he can as he bumps up the magnifications on his scope when he changes to a shorter FL ep. He has told me he presumes that using his wide angle 32mm 2" ep with a 2" barlow (2x) would give him the same magnification as just using a 16mm ep but with a wider FOV than the 16mm by itself.

Not having used a 2" (2x) barlow I am technically (and literally) in the dark on that one but intuitively "feel" there is still going to be losses - from an inch & a quarter perspective, and without bringing barlows into the equation, I believe that (imho) you can't raise the magnification and retain the same TFOV - it just can't be done; although if the ep with the shorter FL is of a different type (ie types with a wider FOV) and the increase in magnification isn't a large jump; then it is possible to maintain the FOV and have (somewhat) greater magnification.

So, what I'm asking is for people to comment on the preceding 2 paragraphs, and also to specifically provide information on the influence of barlows (both 2" and 1&1/4") on FOV with ep's.

I hope to be enlightened further myself with accurate responses: and even (shudder!) should my young mate have more than a modicum of truth on his side - and destroy any standing I have with him on these matters - I can at least continue to criticize his absolutely ghastly alcoholic accompaniment to one of Australia's most iconic gourmet meals! ps, not the brand bro, but the specific brew itself!

Cheers, Darryl.





Naturally, the FOV's of the shorter and longer FL eps is one factor, so let's hear people's opinions for:

(a) Comparing a shorter FL ep to a longer FL ep, both of whom (theoretically at least)

[syzygy]

For any given eyepiece design, where the apparent field is not being vignetted by the field stop (or anything else), then it's fairly simple I think.

Magnification = Telescope Aperture / Diameter of Exit Pupil

True Field = Apparent Field / Magnification *

So inserting a 2x barlow, at the appropriate spacing before the eyepiece, is going to halve the exit pupil diameter and therefore the true field.

All that using a barlow lens does is preserve the eye relief, which may make the full field easier to see than with a short FL eyepiece of the same design. The cost is adding more lenses in the light path.

* Wide field eyepiece designs generally cannot maintain a constant magnification across the entire apparent field. This distortion produces a variance to the simple formula for true field size. It is small though, and constant for a given eyepiece design.

[Kokatha man]

Hi syzygy

Don't have any probs "grasping" the mechanics syzygy: I think any number of simple analogies confirms the concept. (and as you point out as I did, presuming identical ep types)

Just that I've never used your formula for calculating magnification by dividing the scope aperture by the exit pupil but of course it does equate and probably provides one of the best mathematical as well as analogous explanations.

Using one of my ep's, an 11mm T6 nagler in an f5 newt with aperture of 250mm (10") I calculate the Exit Pupil as 2.2mm using the formula for exit pupil calculations:

Exit Pupil = ep F length/ F ratio

If I was to apply your formula: Magnification = Telescope Aperture / Diameter of Exit Pupil I would arrive at 114x (approx) - the same as dividing the ep's focal length into the scope's focal length and arriving at 114x.

Synchronously, calculating the True FOV by the method (AFOV/magnification) gives approx 43 arc minutes - the same as with the calculations from TFOV = ep field stop diam/ep focal length.

Nothing dramatic about any of that, naturally the equations are all inter-connected, just that I'd never thought about calculating magnification by dividing scope aperture by exit pupil diameter: though in many ways it's the most graphic analogy as to why we get the images we do via telescopes: the "pupils as big as saucers" analogy.

Regards, Darryl.

[Kokatha man]

Meant to say in my para 6:

TFOV = ep Field Stop diam x 57.3/focal length of scope

Regards, Darryl.

[ngcles]

Hi Darryl, (his mate) and all,

First principles.

The magnification an eyepiece provides is a function of the focal length of the telescope divided by the focal length of the eyepiece. Eg 200mm aperture 'scope with 1000mm fl and 10mm fl eyepiece gives x100 magnification.

The exit pupil is a function of the aperture in mm, divided by the magnification in use. Eg 200mm aperture / x100 = 2mm exit pupil. Alternately, it is also approximated by diviiding the fl of the eyepiece by the f/ ratio of the telescope

The Apparent Field Of View (AFOV) is the angle (expressed in degrees) your eye must turn through to shift your gaze from one side of the field stop to the other. By and large, it will be determined by the diameter of the field stop inside the barrel of the eyepiece. Lets assume for the sake of the exercise it is a 50 deg AFOV eyepiece like many popular Plossl eyepieces are.

The True Field Of View (TFOV) is the angular diameter of the actual field (slice of sky) visible within the eyepiece when used in the telescope. It is approximated (in degrees) by dividing the AFOV by the magnification the eyepiece provides with a telescope. For eg with the above 'scope/eyepiece 50 deg AFOV / x100 = 0.5 degrees diameter true field.

Eye relief is the maximum distance the cornea of the eye can be from the top glass element of the eyepiece (the eye-lens) while you can still see the whole of the field-stop within the eyepiece.

You asked for specific comment on these two paragraphs:

"He wants to maintain the largest TFOV he can as he bumps up the magnifications on his scope when he changes to a shorter FL ep. He has told me he presumes that using his wide angle 32mm 2" ep with a 2" barlow (2x) would give him the same magnification as just using a 16mm ep but with a wider FOV than the 16mm by itself.

Not having used a 2" (2x) barlow I am technically (and literally) in the dark on that one but intuitively "feel" there is still going to be losses - from an inch & a quarter perspective, and without bringing barlows into the equation, I believe that (imho) you can't raise the magnification and retain the same TFOV - it just can't be done; although if the ep with the shorter FL is of a different type (ie types with a wider FOV) and the increase in magnification isn't a large jump; then it is possible to maintain the FOV and have (somewhat) greater magnification."

Re the first paragraph:

In the other thread I think you referred to, Dennis wrote (partial extract):


16mm 82 degrees.
FOV 31.5 min
Magnification 156.2
Dawes limit 0.5”
Magnitude 15.6

30mm 43 degrees.
FOV 31 min
Magnification 83.3
Dawes limit 0.5”
Magnitude 15.3

And I added immediately below (partial extract):

"The view through the 43 deg AFOV eyepiece while about the same size will be much less aesthetically pleasing, will have a slightly brighter background sky, the view will seem much more "compressed" and because of the narrowness of the AFOV, will seem a bit like looking down a sewer pipe. (Emphasis added)

The 82 deg AFOV ep while showing essentially the same slice of sky will be much more like looking out of a porthole, show a more contrasty view and more detail will be more easily discerned due to the higher magnification -- assuming it is a high quality occular -- which an 82 deg AFOV usually implies! All round much nicer!" (Emphasis added)

And I add specifically now, No, the TFOV will be almost exactly the same as I said (see figures by Dennis above). He (your mate) wants to maintain the highest TFOV while bumping up the magnification -- well the only answer is to get a shorter focal-length but wide-field design eyepiece of some sort with a larger AFOV. The TFOV is determined by the AFOV/magnification. To maximise TFOV, get a bigger AFOV -- there is no free lunch! Your comment in the second par: "I believe that (imho) you can't raise the magnification and retain the same TFOV - it just can't be done" is succinct and correct. You cannot "buy" TFOV while also raising magnification unless you use a different eyepiece with a larger AFOV

Re the Barlow. If it is a 2x Barlow for example, in effect it doubles the magnification the eyepiece produces with the 'scope. As the TFOV is a function of AFOV/magnification, if you double the magnification, you halve the TFOV.

As the exit pupil is aperture/magnification, if you double the magnification by adding a 2x barlow, then you must also, axiomatically, halve the exit pupil.

The eye relief is a different matter. The eye relief is an in-built characteristic of the eyepiece itself and is not affected by the design, aperture or focal length of the 'scope. If say a 30mm ep has an eye-relief of 20mm and is then used in a 2x barlow (and in effect acts like a 15mm ep which would normally have less eye-relief), the eye relief of the eyepiece remains at 20mm because that is built into the eyepiece. In the same way, an eyepiece with a 20mm eye-relief will have exactly the same eye-relief characteristic in a 200mm f/5 Newtonian as it will in a 400mm f/10 Schmidt/Cassegrainian, though the magnification and accordingly TFOV will be dramatically different.

Hope this is of some help.


Best,

Les D
Contributing Ediitor
AS&T