Eyepiece AFOV calculation...Luminos

[jetstream]

For a while now I have been pondering the Celestron Luminos specs and decided to try to prove mathematically something I've noticed.That is the AFOV listed may be a bit misleading,but maybe in a good way.....Last night I measured my field stop(10mm) with accurate dial calipers and it came out to .67"(17.01mm)-very close to the listed spec...so....How can an apparent field of view of 82' support this?Well maybe it can't.Too use a formula that APM telescope people use-I'm not quoting them here- eTFOV=FS/FL * 180/Pi.So lets use the Luminos as an example:

eTFOV=17/10 *180/3.1416

=1.7 x 57.2956 =97.4' 97' not 82'

I noticed a discrepancy when calculating the TFOV,as there are 2 common formulas:AFOV/Mag & FS/telescope focal length * 57.3-they should coincide,but here they are off.10mm Luminos,82'/63(my scope)= 1.3', or 17/630 * 57.3=1.546 too far off.But using the 97.4'/63=1.546' the same,but this indicates a 97' APPARENT FIELD OF VIEW and for a price of $120.00.

My 10mm is a very good eyepiece(at f7) and we will see how the 7mm fares.Anyway, for the money getting an almost 100' eyepiece is great for me at least.When I get the Dob,I'll see if I'm looking at a flock of Seagulls!!

PS-feel free to correct any math here,I am interested in opinions

[John]

Is the field stop of the Luminos accessible then ?. I thought it was buried inside the eyepiece somewhere. Did you need to take the eyepiece apart to get to it ?.

The Ethos 10mm has a 17.7mm field stop so if the Luminos is 17mm then it would be closer to 100 degrees than 82. A timed drift test would determine the true field of view which would help double check your findings.

[jetstream]

John,I hope I measured the right thing,I'll try to attach picture.No I didn't take the eyepiece apart,but there is bottom ring that I believe is the field stop and looking thru eyepiece there is no smaller ring,I just see the baffles.I first noticed a bigger TFOV when I started comparing eyepieces and this started me on this path(to discovery).I will also include a picture of my 16mm Nagler T5 as a comparison,and on this one the field stop looks "buried" inside.

I don't see how to put the pictures on here...any ideas...?I'm no good on computer

[cs1cjc]

If the field stop is internal, then its effect will be scaled by the field lens.

The view through a eyepiece is distorted, though this may not be significant for eyepiece with a field of view of less than about 60 degrees. The angular magnification can be constant (as in Ethos eyepieces, for example), or the rectilinear view can be correct (as for many eyepieces designed for terrestrial use), but not both. These are Theta and tan(Theta) mappings respectively, where Theta is the angle from the principle axis. For eyepieces with an apparent field of view to about one radian (nearly 60 degrees) so going to up to 0.5 radian off axis, the difference between these two is less than 10% and would be hard to notice. However the two diverge increasingly quickly and at 40 degrees off axis, tan(Theta) is 20% bigger than Theta, while at 50 degrees it is 37% bigger. Quite commonly the eyepiece view is a compromise somewhere between large angular magnification distortion (AMD) and rectilinear distortion. However it does mean that the apparent field of view and the true field of view are not tightly linked for wide angle eyepieces. There is a very extensive literature about this distortion and human perception of it. Links for further reading below:

http://www.televue.com/engine/TV3b_page.asp?return=Advice&id=113

http://www.telescope-optics.net/distortion.htm

http://www.holgermerlitz.de/globe/distortion.html

[jetstream]

If the field stop is internal, then its effect will be scaled by the field lens.

The view through a eyepiece is distorted, though this may not be significant for eyepiece with a field of view of less than about 60 degrees. The angular magnification can be constant (as in Ethos eyepieces, for example), or the rectilinear view can be correct (as for many eyepieces designed for terrestrial use), but not both. These are Theta and tan(Theta) mappings respectively, where Theta is the angle from the principle axis. For eyepieces with an apparent field of view to about one radian (nearly 60 degrees) so going to up to 0.5 radian off axis, the difference between these two is less than 10% and would be hard to notice. However the two diverge increasingly quickly and at 40 degrees off axis, tan(Theta) is 20% bigger than Theta, while at 50 degrees it is 37% bigger. Quite commonly the eyepiece view is a compromise somewhere between large angular magnification distortion (AMD) and rectilinear distortion. However it does mean that the apparent field of view and the true field of view are not tightly linked for wide angle eyepieces. There is a very extensive literature about this distortion and human perception of it. Links for further reading below:

http://www.televue.c...n=Advice&id=113

http://www.telescope.../distortion.htm

http://www.holgermer...distortion.html

Thanks for the links & info,I'll read them in a bit.Is it possible to have 82' AFOV with a 17mm field stop?These eyepieces work,but they are described by Celestron as for use in flat field scopes-like their Edge SCT-but honestly in my small refractor they work really well.

[AlexB67]

For a while now I have been pondering the Celestron Luminos specs and decided to try to prove mathematically something I've noticed.That is the AFOV listed may be a bit misleading,but maybe in a good way.....Last night I measured my field stop(10mm) with accurate dial calipers and it came out to .67"(17.01mm)-very close to the listed spec...so....How can an apparent field of view of 82' support this?Well maybe it can't.Too use a formula that APM telescope people use-I'm not quoting them here- eTFOV=FS/FL * 180/Pi.So lets use the Luminos as an example:

eTFOV=17/10 *180/3.1416

=1.7 x 57.2956 =97.4' 97' not 82'

I noticed a discrepancy when calculating the TFOV,as there are 2 common formulas:AFOV/Mag & FS/telescope focal length * 57.3-they should coincide,but here they are off.10mm Luminos,82'/63(my scope)= 1.3', or 17/630 * 57.3=1.546 too far off.But using the 97.4'/63=1.546' the same,but this indicates a 97' APPARENT FIELD OF VIEW and for a price of $120.00.

My 10mm is a very good eyepiece(at f7) and we will see how the 7mm fares.Anyway, for the money getting an almost 100' eyepiece is great for me at least.When I get the Dob,I'll see if I'm looking at a flock of Seagulls!!

PS-feel free to correct any math here,I am interested in opinions

There seem to be some varied opinions on this and from what I can see confusion also. The field stop formula as you quote is not accurate even though mostly used, I believe it should be

FOV = 2 * arctan (fstop/ (focal length * 2)) (of top of my head, not 100% sure )

Also the definition AFOV = Mag * TFOV only work in the small angle linear approximation. Have a look at this paper first of all,

http://adsabs.harvard.edu/abs/1995JBAA..105..242G

it is very informative. I had to go through a lot of this stuff writing my calculator and researched it quite a bit. If you punch FOV calculation in google you will find some hot debates on that topic at cloudy nights too

[John]

I still think a timed star drift is the ultimate test of what the true field of view being delivered actually is.

[jetstream]

Going to go get the calculator...! I kind of heard there was a debate on this issue.For me I like the views of the Luminos and the wde FOV it provides.So I have a question....regardless of the AFOV calculation am I right to assume that the TFOV = FS/Focal length telescope * 57.3?I think I got this off Televues website.

[John]

John,I hope I measured the right thing,I'll try to attach picture.No I didn't take the eyepiece apart,but there is bottom ring that I believe is the field stop and looking thru eyepiece there is no smaller ring,I just see the baffles.I first noticed a bigger TFOV when I started comparing eyepieces and this started me on this path(to discovery).I will also include a picture of my 16mm Nagler T5 as a comparison,and on this one the field stop looks "buried" inside.

I don't see how to put the pictures on here...any ideas...?I'm no good on computer

I think thats just the lower lens set retaining ring / baffle Gerry. The actually field stop will be in between the optical elements inside the barrel somewhere as it is with the Nagler. These 82 degree eyepieces share quite a similar optical design I reckon.

[John]

Going to go get the calculator...! I kind of heard there was a debate on this issue.For me I like the views of the Luminos and the wde FOV it provides.So I have a question....regardless of the AFOV calculation am I right to assume that the TFOV = FS/Focal length telescope * 57.3?I think I got this off Televues website.

That formula seems correct to me.

As long as you like the eyepiece, thats all that matters

[jetstream]

I still think a timed star drift is the ultimate test of what the true field of view being delivered actually is.

John,what is a drift test?And how do you do it?And how does it indicate the AFOV? This sounds like an affirmative approach to this question of AFOV....calculation from testing,sounds like the best to me.

[John]

You time how long it take a star to drift across the field of view at the widest point. This article explains it:

http://www.astromart.com/articles/article.asp?article_id=188

[AlexB67]

That formula seems correct to me.

As long as you like the eyepiece, thats all that matters

Not that it worries me in practice. I just look at the stars , but that "correctness" is a debatable topic, it seems to be the one used and mostly accepted, but it does assume that tan(x) ~ x. Try the arctan version and the standard one, they will give slightly different answers and the bigger the angles the more it differs. Certainly for the non-field stop formula this matters, and differs lot where I tested out these calculations for wide angle eyepieces what method you use and the answers you get, as shown in that paper I quoted earlier.

[AlexB67]

To illustrate my point how different answers can be obtained, and work backwards to what the apparent view should be that is quoted by different eyepiece manufacturers is a little tricky business. On my dev build of my own calculator see the two screens attached what happens with two types of calculations, one were the linear approximation is assumed, the other one not. An appreciable difference is observed. IMO these calculators should give people the options to pick what is appropriate, as it will also depend how the measurements are done and turned into figures, if that sort of makes sense.

I hope to release this tool in the near future for everyone to use. but I keep adding more stuff and working on it, it is because of that I had to think about a lot of this stuff

[jetstream]

I just have to say that when I notice things that are a little different or have an unusual spec it piques my curiousity-especially when it is raining out for days! Alex that calculator will be great,I can't wait to try one!I just talked to Celestron about the Luminos-the 10mm has a field stop of 17mm & they said the actual stop is the smallest diameter of the barrel....& also said that on most eyepieces the retaining ring is the same diameter....I'm not so sure about that,but in this case it does match their specs.Their engineers said it is an 82' AFOV.The rep said he never heard of the AFOV calculation I used.But anyway the eyepiece will be here tomorrow & I'll giver a try soon.The rep also said the drift test is the real way too see for ourselves,thanks John.

[AlexB67]

The rep also said the drift test is the real way too see for ourselves,thanks John.

Yes it is in terms of finding the true FOV or perhaps better called effective FOV in my view, but working backwards and relating it to the apparent FOV of the eyepiece is often where the disagreements come when I see these topics discussed. Even the measurements have some issues to content with, like distortions, particularly near the edges, and then on top of that it also depends what formulae you use working backwards.

[cs1cjc]

For the angles involved in telescopes (typically less than 3 degrees so semi-angle less than 1.5 degrees), the angle (in radians), the sin of it and the tan of it are effectively the same so double the angle and you also double the sin and tan. In this case, 0.026179939, 0.026176948, 026185922, respectively according to the calculator on my computer for 1.5 degrees and 0.052359878, 0.052335956, 0.052407779 for 3 degrees. Once the angles become greater then this (close) identity breaks.

The formula of field stop/focal length for true field of view is thus accurate. While star drifting is one way of measuring the true field of view, the simpler way (for telescopes whose focal length remains fixed as you focus it) is simply to set up a ruler and view it. You need at least one eyepiece with a known field stop either measured directly (best) or from manufacturer's data (use with caution).

[John]

If the optics in the eyepiece have been optimised over an 82 degree apparent field of view, having an additional 10 or so degrees might not be a great benefit anyway - the results might not be that pretty if your scope is fastish !

I like Al Naglers aim for Tele Vue "show no field unless it's sharp"

[AlexB67]

For the angles involved in telescopes (typically less than 3 degrees so semi-angle less than 1.5 degrees), the angle (in radians), the sin of it and the tan of it are effectively the same so double the angle and you also double the sin and tan. In this case, 0.026179939, 0.026176948, 026185922, respectively according to the calculator on my computer for 1.5 degrees and 0.052359878, 0.052335956, 0.052407779 for 3 degrees. Once the angles become greater then this (close) identity breaks.

The formula of field stop/focal length for true field of view is thus accurate. While star drifting is one way of measuring the true field of view, the simpler way (for telescopes whose focal length remains fixed as you focus it) is simply to set up a ruler and view it. You need at least one eyepiece with a known field stop either measured directly (best) or from manufacturer's data (use with caution).

yeah I should have clarified better, if you calculate the aFOV (see this page http://www.astro-okulare.de/English/kennzahle.htm) and the argument for arctan is large the you need to use that form, ignoring arctan is not a good way to go in that case. In the small angle case for the field stop formula and calculating tFOV it is fine AFAIK. I would still like to derive them for my own edification to see it to through as I did for the nonfield stop case to be at complete peace where I understand it clearly. Anyone can point me to a paper or book covering the field stop cases with derivations would be handy

I would like to add in this day and age with computers why bother approximating atan or tan when it is button press anyway, even if negligible, I often see people use the approximate formulae trying to derive apparent FOV from true FOV when the small angle case is not appropriate, but if they are printed everywhere and they are accepted as general formulae then confusion arises. For edification it is better IMHO to know the exact formula, and know and appreciate when the approximations of rounding up are valid, not the other way round.

One of the reasons I added the options in my calculator so people can see the differences, or when comparing with other tabulated data and calculators and wonder why the answers are different ( where I believe them to be wrong in some cases at least). In such cases they can work backwards from that data and work out what I think they should have calculated using the more accurate expressions using my calculator.

[AlexB67]

If the optics in the eyepiece have been optimised over an 82 degree apparent field of view, having an additional 10 or so degrees might not be a great benefit anyway - the results might not be that pretty if your scope is fastish !

I like Al Naglers aim for Tele Vue "show no field unless it's sharp"

Better to have a nice 50 useful degrees instead of paying for 60 and have 10 of it not so useful

[John]

Better to have a nice 50 useful degrees instead of paying for 60 and have 10 of it not so useful

Exactly

[Stargazer_00]

I quite liked the views of the Luminos I just absolutely hated the ridiculous caps on the tops of them. So much so I actually returned my 10mm and 15mm to FLO because I didn't want to live with them.

[AlexB67]

On that topic I said earlier, I had a bit of time to spare so went through the derivation starting with the definition for magnitude by myself ( as defined by the ISO ) and in that paper I linked, and had a look at the field stop cases. I also had a small bug in my code for the field stop formula that threw me off a bit, so sorry if I caused any confusion, but I had slightly the wrong idea about one aspect of it.

To sum up, the way I see it, the stuff I said for the non field stop formula is valid as per that paper, but I muddled myself with the field stop formula a little in that I had a small conversion error of 60 ( the conversion from degrees to arc minutes instead of 180/pi on one line of code. Without thinking about it too hard at the time, I attributed that to approximation in the formula, Wrong AlexB, so I duly slapped myself

Anyway it is true the formula for the field stop case when relating afov to tfov is indeed

tfov = 2 * arctan ( field stop / ( 2 * focal length scope )

that is, by my pen and paper derivation, but the difference in that case is negligible, and one can comfortably use the standard form that is mostly quoted. Of course there are still other approximations in there ( another debate ). In any case, for edification it does no harm to appreciate where this comes from. I guess I am not the readily accept a formula at face value until I understand the origins a bit more and feel satisfied

[John]

I hate maths

I love looking through ultra wide eyepieces though

[AlexB67]

I wouldn't know what wide angle is, never owned one I am happy with 50 - 60 though. Only when I get a bigger scope like a 10 inch bucket would I want at least one good wide angle 2 inch eyepiece I guess. The beauty of my small scope and short focal length is I can be a cheapskate and still get nice enough wide views ... when I do get that 30mm Vixen NPL eventually, but the stock 25mm is not horrible by any means I find

Anyway this thread was useful discussion for me, because it made me think about this stuff a bit more, and test things out. I sorted out a few things having had the whole afternoon to work on my calculator, making some changes and sorting out some other bugs, the mistakes can be spotted in those screenshots