Apparent field of view calculation (1 Viewer)

[pompadour]

Could someone please explain - thanks. Sometimes the apparent field of view, AFOV is calculated as the real field of view, RFOV x magnification. For the actual ranges of RFOV and magnificn. found in bins, commonly 4° to 9°, and 6x and more, respectively, how would this give a relevant result?

From all I can find the stated x power in a bin is the linear magnificn. in the plane at right angles to the direction of view, i.e. it's the magnificn. of the real width (and of the real height) of the subject area in the image. It's not the magnificn. of its real angle. Is that correct?

The ISO formula goes by that. In final, directly usable form it's a = 2 x arctan (m x tan 1/2 r) where a and r are the apparent and real angles and m the magnificn.

The simpler a = r x m result is always, within the actual ranges mentioned above, significantly more.

At first glance using this seemd to me to be a mistake made by some possibly because it works for small angles such as those within the actual RFOV range in bins: i.e. the width of the field at 8° is 2x the width of the field at 4°, etc. (tan varying close enough to linearly with the angle).

But I find that is how Zeiss and apparently Swarovski calcualte the AFOVs stated in their websites (and elsewhere?) Seems the latter actually adjust this down to exclude distortion at the edge for each model separately! (I asked them about their figures through the query submit facilty in the website and they kindly explained.) Baffled.

 

[Chosun Juan]

..... But I find that is how Zeiss and apparently Swarovski calcualte the AFOVs stated in their websites (and elsewhere?) Seems the latter actually adjust this down to exclude distortion at the edge for each model separately! (I asked them about their figures through the query submit facilty in the website and they kindly explained.) Baffled.

Pomp, I have an inkling that the AFov = RFov x magnification, is a small angle approximation based on similar triangles, although I ain't wrinkly enough to know any more than nuffin' about the history of the derivation as applied to binoculars. I'll wait for some that were around when Moses was a boy to chime in! teehee

As for the last part ....... What The ?!! |8.|
First I've heard of this! Swaro SV's have minimal distortion at the edge, so somebody better start 'splanin how and why all that lot is about ...... :h?:


Chosun :gh:

 

[pompadour]

... What The ?!! |8.| ...

Exactly my words and my expression. Poetic affinity? Great minds...?

Attached table shows the differences. Added the last column now.

 

[Binastro]

. The differences may be because the magnification in the binocular often varies across the field.
Many binoculars have a sudden change of magnification at the edge of the field especially with distortion free eye pieces.

Then you have eyepieces such as those in the Nikon action VII and in the 15 x 70 revelation that have aspheric elements in the eyepieces.
As you pan across the field the magnification constantly changes in an undulating fashion.
I presume the aspheric element may be a plastic component fused or cemented to a glass component or possibly the glass can now be ground or possibly moulded into the complex shape.
So how you would actually calculate the fields is difficult to know.

In addition, magnifications are often not exactly as stated so again I'm not sure how accurate the calculations are.

For me when I look through one barrel of a binocular the apparent field of view is different with each eye. This may be because I have a difference of 1.5 dioptres between my two eyes.
So what I do is alternate between the two barrels and my two eyes. and then do the same for another binocular so I can directly compare the apparent field of view in the two or more binoculars that I'm testing.

Of course the easy way is just to multiply the supposed magnification by the real field of view which is easily found by reference to separations of reasonably bright stars.

The results are not perfect but they suit me and I do know that with strict calculations the apparent field of view will be smaller than with a simple calculation. A further complication is that I believe that the magnification of a binocular varies depending on whether you are shortsighted longsighted or neutral. And it may also vary depending how far your eyeball is from the eyepiece.

So I think the best method is a hands-on approach between two or more binoculars and just see which binoculars have the widest field of view if that is important to you.

It is to me as I value a wide or very wide field of view.

 

[henry link]

Rather than using the ISO standard or the simple real field x magnification calculation, Swarovski appears to me to actually measure the angle subtended by the apparent field, which would include the effects of distortion. Pincushion causes the apparent field to be larger than expected from the real field while barrel and angular magnification distortion cause it to be smaller.

The Swarovisions have a compound distortion pattern; pincushion in the center half of the field which then reverses to angular magnification distortion near the edge. I'm sure the "real" apparent field could be calculated for such a distortion scheme, but it's also easy to simply measure it. If you have a tripod head with a degree scale for panning motion you can sight the eyepiece field stop through the front of a binocular mounted on the head. Position a small object at one side of the field stop, then rotate the head until the object moves to the other side. Read the change in degrees on the panning scale. That's the true angle subtended by the apparent field.

 

[pompadour]

Binastro, Henry, thanks.

Swaro website. I think well of them for providing such a parameter. Felt actual measurement was best, but that this is not how they arrived at their figure, for two reasons. In the reply by Customer Service there's no explicit mention of that but of "complex ... calculation". Second, till H.'s explanation just couldn't figure out how to do that, thinking, further, that it's for this reason AllBinos measure the real field but not the apparent.

Arek, that too will be really useful! Much appreciate, of course, what the site provides already.

Also, Swaro.'s figure for some models is quite a bit higher than ISO. Wonder if this could be more than acc. to B.'s explanation.

Zeiss website. Every figure is r x m! To what does this correspond in reality? The table above shows the considerable differences. See at 8° for example. I now realise, from B.'s reply, its rough utility, but seems odd for a co. of this repute to overstate performance just in this manner.

Still baffled, by that!

 

[ronh]

I don't think Zeiss overstates its apparent fields. The FLs at least have considerable pincushion distortion, which makes the apparent field bigger than the ISO prediction, which is correct only in the absence of distortion. I believe I recall reading here that r x m is exactly right for for the amount of pincushion that exactly cures shape distortion, and in my experience (8x42 and 10x56), and also according to some of Henry's photographic tests of distortion, that is just how the FL's are corrected (ie, a small circle viewed at the edge looks like a circle, rather than squashed). FWIW Henry found Leica to have a bit more distortion, but personally I can't tell the difference. I think you will find that Leica uses r x m too.

Thanks for your chart comparing ISO to r x m.
Ron

 

[pompadour]

Ron, thanks. Such a close coincidence - takes me back to What the! mode. Considering how many bird watchers (?and astronomers) value a large FOV, including many in BF, surprising that this effective apparent FOV larger than (I'd think) generally assumed is not mentioned much here or, even more, announced by the makers. In the websites Nikon uses ISO, Leica maintains their usual discreet silence.

 

[dalat]

Considering how many bird watchers (?and astronomers) value a large FOV

Isn't it anyway the real FOV that matters? Distorion on the edge may give the impression of a larger field of view, but it doesn't show more birds.

To me, the calculation of apparent FOV is something of rather academic interest, but not of practical importance.

Of course I also appreciate the impression a large apparent FOV gives (for example my Zeiss 10x32 is nice for this). But when comparing binos, I never look at figures of apparent FOV, I compare real FOV of the binos with the same magnification.

 

[Holger Merlitz]

Ron, thanks. Such a close coincidence - takes me back to What the! mode. Considering how many bird watchers (?and astronomers) value a large FOV, including many in BF, surprising that this effective apparent FOV larger than (I'd think) generally assumed is not mentioned much here or, even more, announced by the makers. In the websites Nikon uses ISO, Leica maintains their usual discreet silence.

It has been mentioned above: The ISO standard is valid for binoculars which are free of rectilinear distortion, while the angle condition (a = m*A, a = apparent angle, A = true angle, m = paraxial magnification) considers the presence of a significant amount of pincushion distortion (in fact, it is correct for binoculars with zero angular distortion).

Now, in real life no binocular is perfectly free of distortion. The (relative) distortion is defined as

Vr = [tan(a/2)/tan(A/2) - m] / m

and it amounts to zero in case of the tangent condition tan(a/2) = m tan(A/2). Including this relative distortion, the apparent angle of view is calculated via

a = 2*atan[m*(Vr+1) * tan(A/2)],

and, as to be expected, this turns into the ISO formula in the case Vr = 0.

Unfortunately, hardly any manufacturer specifies the amount Vr of relative distortion, and therefore it is impossible to calculate the apparent angle of view for a binocular of given true angle of view and magnification. Most of the manufacturers are simply using the angle condition when specifying their apparent angle of view, which is not far from reality when considering their pincushion distortion. Since Nikon is implementing rather less distortion, they decided to use the ISO formula instead, which in turn is rather inaccurate in case of the Nikon EII.

Cheers,
Holger

 

[typo]

Damn! Just when you think you've got a grasp of one technicality you find out you haven't. :-C

Thanks Holger! :t:

David

 

[pompadour]

Dalat, I did think the same way - you don't see more birds (or stars). Maybe I've been a bit carried away by praise in BF and elsewhere for a large apparent field of view, relevant ~ 60° for terrestrial use: the "walk-in" effect, and more relaxed viewing, which would matter to most people. (Haven't myself been able to see such a field of view yet since I learnt this.) In another BF thread/s these days they say for astronomy the FOV in a bin can also be too much and disturbing - I guess "space-walk in" is not so natural.

Holger, thanks. I now see the relevance of directly multiplying the angle - took a bit of time! By "here" in "not mentioned much here" I meant not this thread but BF, and brought up less than I would expect, as the paragraph above might explain. I'd guess - excuse my ignorance - that Vr is pretty difficult to calculate effectively for the optical system of a bin. If that is correct it may be simpler to measure a. Then if Vr is necessray the formula gives it. This assumes A is relatively easy to obtain (by measuring if not calculating).

David, I've been wondering how Holger feels when he sees queries in BF he has answered in his book just published. Does one say, "Actually, I've written a book, where I attempt to address such things. If you do read my humble work, this is mentioned on page abc-def" or "This is dealt with in my book. Please see page ghi" or "Read my * book!" But gracefully he again addresses the issue.

 

[Binastro]

.the apparent field of view is most important for astronomy whereas it seems that for birdwatching the real field of view is what counts.

When I got my first Nagler eyepiece I think 7 mm I was blown away.
Jupiter and its moons looked exactly the same at the edge of the field and the centre.
The apparent field was described as 82° and sometimes from memory 84°.
I think 82° is mentioned nowadays.

Because my telescope had a fixed mount rather than a driven mount the apparent field of view is critically important because it doubles the time you can observe compared with say an orthocopic eyepiece.
In addition you see very many more stars at the same magnification.
And you're more likely to pick up a telescopic meteor or artificial satellite.

However, personally I do not like the hundred degree eyepieces as you have to move your eye around to see the full field and I find it very disturbing to use.
But many people love these 100° eyepieces and also the new 110° versions.
There is also a 120° eyepiece and there was a similar 120° version I think in the 1950s for submarine periscope's.

However, when it comes to finding the faintest star or getting the best resolution or planetary detail my three element 8mm RKE eyepiece soundly beats these very wide field multielement eyepieces.
And maybe the Zeiss four element eyepieces may be better although they are very expensive.

Similarly, I much prefer the 10 x 50 Minolta standard with a usable 7.65 or 7.8° field even though the coatings are not as good as with the modern 10 x 50.
The gains from the large field out weigh the slightly fainter stars seen with modern coatings.
I really wish that someone made a 10 x 50 or 12 x 50 similar binocular with modern coatings and an extra wide-angle field.
I don't think this will happen as manufacturers don't want to make porroprism binoculars any more and they certainly don't want to make extra wide-angle.

However, 69° fields old measure are available from Leica and Canon. Even though the Canon state that they are 67° but they measure wider.

 

[Holger Merlitz]

Dalat, I did think the same way - you don't see more birds (or stars). Maybe I've been a bit carried away by praise in BF and elsewhere for a large apparent field of view, relevant ~ 60° for terrestrial use: the "walk-in" effect, and more relaxed viewing, which would matter to most people. (Haven't myself been able to see such a field of view yet since I learnt this.) In another BF thread/s these days they say for astronomy the FOV in a bin can also be too much and disturbing - I guess "space-walk in" is not so natural.

Holger, thanks. I now see the relevance of directly multiplying the angle - took a bit of time! By "here" in "not mentioned much here" I meant not this thread but BF, and brought up less than I would expect, as the paragraph above might explain. I'd guess - excuse my ignorance - that Vr is pretty difficult to calculate effectively for the optical system of a bin. If that is correct it may be simpler to measure a. Then if Vr is necessray the formula gives it. This assumes A is relatively easy to obtain (by measuring if not calculating).

David, I've been wondering how Holger feels when he sees queries in BF he has answered in his book just published. Does one say, "Actually, I've written a book, where I attempt to address such things. If you do read my humble work, this is mentioned on page abc-def" or "This is dealt with in my book. Please see page ghi" or "Read my * book!" But gracefully he again addresses the issue.

The optical designer knows the amount of distortion precisely, of course, and it would be helpful if the makers would just specify that number. But I guess, "distortion" sounds odd when printed on a glossy brochure, and the marketing guys would not like to see these technical issues addressed. AFOV can be measured but it is a bit more tricky than measuring TFOV (in fact, I have never tried myself, but I have read instructions of those who have).

Just wait - my book is not out yet! Once done, I will simply cite page number and a link to amazon where you can buy it ;-)

Cheers,
Holger

 

[John Russell]

AFOV can be measured but it is a bit more tricky than measuring TFOV (in fact, I have never tried myself, but I have read instructions of those who have).

As Henry mentioned above, it's really quite simple. One only has to mount the bin on a tripod with a calibrated panorama head and view a vertical line through the objective at the left and right edges of the field stop.

However, I should point out that as it will be difficult to align the exit pupil with the axis of rotation, it is preferable to choose a distant object like the edge of a building to reduce parallax errors. Nevertheless, one should be able to attain an accuracy of +/-1°.

An alternative method is to mount the bin perpendicular to a wall with its eyepieces facing the wall. A laser (ideally green) is then shone through an objective and the extremities of its reach, left and right, are marked on the wall.

The AFOV is then 2.arctan D/2d, where D is the measured distance on the wall and d is the distance from the exit pupil to the wall.

John