AFOV again

[John Russell]

Last weekend I attended a meeting of a German optics forum in the old observatory in Bonn.
One of the attendees, Walter E. Schön, a regular contributor to the forum and a technical author gave a talk on the effects on perspective when using binoculars and also on the so-called rolling ball or globe effect.
He also demonstrated his method of measuring the apparent field of view, which was so interesting, I thought I would share it here.
The binoculars (or scope) are focussed to infinity and are set up with their optical axes perpendicular to a flat wall and with the eyepieces facing towards the wall. For the sake of accuracy, this distance should be maximized, ideally over 5m.
A laser pointer is then shone through the centre of the objective (Walter Schön uses a green laser to minimize any effects of lateral CA). The magnification causes the emerging angle from the eyepiece to be correspondingly higher than the angle of incidence.
The maximum horizontal divergence of the laser projection on the wall before it becomes obscured is marked left and right by an assistant. "Post-it" sheets would be ideal for this purpose.
The distance between the two "Post-its," d1 and the distance from the exit pupil to the wall, d2 are measured.
The AFOV is then: 2.tan^-1 (d1/2.d2).
Now why didn't someone at the ISO think of that? ;-)

[Kevin Purcell]

The AFOV is then: 2.tan^-1 (d1/2.d2).

The standard 2 * arctan( width / (2 * distance) )

Doesn't that give you the FOV not the AFOV?

You can get the AFOV if you know the magnification though that assumes no distortion e.g. the apparent field could be distorted giving a larger AFOV than you would expect.

I'm also curious about using the exit pupil position as the refereence for the distance. I would have picked the position of the objectives tough I'm not sure I can justify either.

Are there any requirements for getting the laser to fire parallel to the axis of the barrels?

It's a interesting technique for getting the FOV.

[Surveyor]

The standard 2 * arctan( width / (2 * distance) )

Doesn't that give you the FOV not the AFOV?


Kevin,

To get a better idea of what John is describing put a bino on a tripod and look through them backwards. Since the image will be the inverse of the power, i.e. 0.125x instead of 8x, you need to find a very high contrast target, such as a dark building edge against the sky, and align one edge of the field stop with that edge, then rotate the binocular, while paying attention to the amount of rotation, until the other edge of the field stop aligns with the high contrast edge. You should have rotated the bino about 50 or 60 degrees.

If you use a large protractor or have a tripod head marked in degrees you can get a pretty good idea of the AFOV. I use this method, but with the bino attached to a survey instrument, to get better readings at longer distances than John describes to minimize the distance errors, typically a kilometer or more. Hope this description is clear, if not I can attach pictures later.

Best.
Ron

[Kevin Purcell]

I now see I managed to miss the "with the eyepieces facing towards the wall" bit!

Yes, I have the bins around the wrong way in my mind.

[henry link]

Ron,

Thanks for posting this. I just tried your method using a flashlight beam at about 60' for the target and reading the rotating scale on a Gitzo 2380 head. It looks like a perfectly accurate method for the finding the true AFOV (including distortion) for any binocular or telescope eyepiece. BTW I think the aperture seen looking through the binocular backwards is the eyepiece fieldstop, not the exit pupil, that's why it works.

Henry

[Surveyor]

Yes, you are correct Henry, I just was not thinking. I think in terms of the acceptance angle, the field stop, as you point out. Sorry

Best
Ron

I have edited the first post for proper terminology. I think the best explanation would be that you are seeing the real image (focal plane) of the objective from the ocular end and seeing the real image (focal plane) of the eyepiece from the objective end.

[Howard220]

Ron,

BTW I think the aperture seen looking through the binocular backwards is the eyepiece fieldstop, not the exit pupil, that's why it works.

Henry

I made a small diameter hole (a little rough, though) in a piece of paper and centered it over the eye lens of my reverse porro Nikon 9x25 Travelite V's. The hole in the paper approximates the diameter of the exit pupil, which is allegedly 2.77mm. While looking through the objective end, the hole in the paper appears to match the aperture I see through the objective end. Therefore I'd conclude that the aperture we see is the exit pupil, not the field stop. ? (I hate being wrong in public!)

[Surveyor]

Hi Howard220.

The acceptance angle for the eyepiece is determined by the field stop diameter and focal length of the eyepiece and that is the angle we are trying to measure. The exit pupil is just an virtual aerial image of the real image of the objective. They are both the same image, but as Henry pointed out the AFOV is set by the eyepiece acceptance angle.

Best
Ron

[Surveyor]

For any who may be interested. I made up a paper protractor this morning. Just cut it out and tape or glue to a paper plate, or just use by itself. Use a cardboard box and two push pins, one for the pivot point and one for the index.

[Howard220]

Hi Howard220.

The acceptance angle for the eyepiece is determined by the field stop diameter and focal length of the eyepiece and that is the angle we are trying to measure. The exit pupil is just an virtual aerial image of the real image of the objective. They are both the same image, but as Henry pointed out the AFOV is set by the eyepiece acceptance angle.

Best
Ron

Hi Ron,

I've never been able to understand aerial image, virtual image, real image... so I'm afraid I'm lost. What I *do* understand is what you say above in your last sentence. Along that line, I once removed a threaded brass ring from inside the barrel of an old Edmund orthoscopic telescope eyepiece and thereby increased the AFOV. I then understood why the ring was there... there were optically "bad edges" under it.

[Kevin Purcell]

For any who may be interested. I made up a paper protractor this morning. Just cut it out and tape or glue to a paper plate, or just use by itself. Use a cardboard box and two push pins, one for the pivot point and one for the index.

Thanks, Ron. That will come in handy.

And one can make it as big as ones printer!

[ronh]

Thanks John, that is an interesting method and must have been a fun get together.

Lacking a laser beam, you could just look through the objective and sight the extremes of visibility on the wall, and apply the same formula.
Ron

[Steve C]

For any who may be interested. I made up a paper protractor this morning.

Ron,

You post a lot of really useful stuff like this. So, for this and several other things you have posted, thank you.

Now I gotta go get a laser pointer after work today. ;)

[John Russell]

Lacking a laser beam, you could just look through the objective and sight the extremes of visibility on the wall, and apply the same formula. Ron

Yes Ron, that's quite possible. Walter Schön has since pointed out that a distance of 2m from the wall is sufficient to give plus or minus 0,3° accuracy for AFOV.
The reason for focussing to infinity is merely to get a sharp image of the laser on the wall. The AFOV is determined by the field stop.
However, if one were measuring true FOV of a binocular with external focussing, even distances of 10m or 15m would require mathematical correction because the extension of the eyepieces (or objectives) results in an increase of magnification and a reduction of FOV.

John

[Kevin Purcell]

Thanks John, that is an interesting method and must have been a fun get together.

Lacking a laser beam, you could just look through the objective and sight the extremes of visibility on the wall, and apply the same formula.
Ron

You might find a cheap laser point at your local CheapMart store. Even built into a pen. Should be good enough for this application even if it is red.

[spyglass2]

I've always wondered....is the FOV stated by the mfr measured or calculated? Now this may be "proprietary" info, but the reason I asked was due to a comparo I once did (and didn't really intend to do so, just happened) of my friend's Celestron Ultima 10x42 with a stated fov of 6.6* (a clone of the Swift Ultralite) and my 10x42SE. Looking into the woods from his 2nd floor balcony at some deer at a salt lick he put about 40m from the house, all three of them were visible thru the SE with just a slight amount of light on either side of the two tails of the two facing each other at the lick. Just out of curiousity, I picked up the Ultima for a peek, expecting a little wider scene (6.6* vs 6.0*). To my surprise, the Nikon appeared ever so slightly wider....this with the eyecups on each glass down and able to see the edges (so I was seeing all there was).

So, if field stops are used in the optical train, would the advertised fov be given before or after the stops were inserted. Any ideas?

[Howard220]

I'm going to guess "calculated," as I suspect there are variations in magnification (at least) not only among brands, but among individual samples.

[edz]

the true Afov of eyepieces as stated by the manufacturer can be measured. It always includes the distortion in the eyepiece, generally pincushion, which makes the stated Afov somewhat wider than the (calculated backwards) Afov that we see by the extent of our image field. The effective Afov, the Afov that we see (Tfov = effective Afov/power) is always based on the field stop diameter. Although usually not easily available for binocular eyepieces, most simple telescope eyepieces can be easily measured and the Afov based on field stop can be calulated. FS dia / EP focal length x 57.3° (1 radian) = effective visual Afov. This will always give you the effective Afov and hance you can then calculate the real Tfov, to within a fraction of 1%. It is often 4° to 8° less then the manufacturers stated Afov with distortion, generally greater for wider angle eyepieces.

I believe ISO is concerned with the real Afov of an eyepiece, since that is the angle that the eye subtends when looking into the eyepiece. It includes the distortion.

edz

[Surveyor]

....is the FOV stated by the mfr measured or calculated?


Hello Spyglass2,

In my opinion, the rated FOV is a calculated, nominal value. All binoculars have a tolerance limit. ISO 14133-1:2006 for general purpose optics:

Magnification a, Γ ± 5 %
Field of view in object space a, b ± 5 %
Entrance pupil diameter c ± 5 %
Exit pupil diameter ± 10 %
Eye relief (mm) 5 +− 0,5
Zero-setting error of dioptre scale (m–1) ± 1
Image rotation (degrees) ± 1,5
Disparity of image rotations d (minutes of arc) 40
Relative difference in magnification d 2 %
Focusing difference of telescopes of binoculars when focused by means of
the centre focusing mechanism within the focusing range (m–1) 1

As can be seen, since the TFOV is acceptance angle (AFOV) of the eyepiece divided by the power, and power can be off 5%, the exit pupil 10% etc. As Henry Link often points out, even unknown and unspecified aberrations alter both the object space and image space angular values.

But the ISO limits the deviation of the TFOV to a 5% measured value.

The only way to know your TFOV for sure is to measure it. For my Promaster, the stated nominal is 7.5* TFOV, so any value from 7.125 to 7.875* is acceptable. The actual measured values are 7.43* left and 7.6* right side and an average measured AFOV of 59*. The specified 60* AFOV is probably more correct, the tolerance of my AFOV measurements are unknown at this point.

There is a further restriction on the relative power difference between tubes of 2 % and I am not sure if ISO intends for this to be a limit for only that one specification or extend to the determining factors. The differences imply a power difference of 2.3%. This is an academic question since I cannot measure any parameters to any better than a percent or two.

Hope this helps. Best.
Ron

[henry link]

I spent some time today measuring the AFOV of a group of Nikon binoculars using Ron's (Surveyor) tripod scale method. It couldn't be easier; no formulas, no distance measurements, just read the numbers on the scale as you swing a small target from one side of the fieldstop to the other. The same method could be used to measure the real field by looking through the binoculars in the normal way, but that would require a more finely graduated scale than the one on my Gitzo head.

Ron can correct me if I'm wrong, but the measurement using this technique appears to give an accurate indication of the true AFOV, the angle subtended by a combination of the ISO formula + distortion. If the true field specs are accurate (not guaranteed) then the measured departure from the IOS formula would indicate the percentage of the AFOV that is added by distortion. Below is a list of the Nikon binoculars I measured. The first number is Nikon's AFOV spec (based on the ISO standard) and the second number is my measurement of the true AFOV (to the closest 0.5 degrees).

Prostar 7x50 - 48.1/49.5
EII 8x30 - 63.2/67.5
SE 8x32 - 55.3/57.5
EII 10x35 - 62.9/67.5
Astoluxe 18x70 - 64.3/65

Looking through these binoculars I can't detect any pincushion in the Astroluxe and can see that the EII's have the most pincushion, which is in good agreement with the measurements.

[Surveyor]

Henry,

I have been meaning to do further experimenting with this, but since AFOV is not high on my list of priorities, I keep putting it off. I also do not have any published specs on these values.

I suspect that the method described actually measures the true acceptance angle, but I suspect that it is being modified by magnification differences. I think I may have found a way of correcting that but have not got around to trying it yet. The last time I mentioned the method no one showed any interest, so I have just been doing as a curiosity instead of a routine parameter.

Refer to a simple test at http://www.birdforum.net/showpost.php?p=1337144&postcount=7 (http://www.birdforum.net/showpost.php?p=1337144&postcount=7) At the time of this post I did not know the specification of the Zeiss. This little Zeiss, I found out later, has a spec of 351’ @ 1000 yds. which would give the results of acceptance angle=53.6 degrees and ISO angle of 50.2 degrees. Using the protractor posted, I measured the right barrel just now at 52.5* but without the benefit of a good target.

When time permits, probably next weekend, I will bring my 1 arc second “protractor” home and set up several binos. I think by measuring both the acceptance angle and then swapping ends and measuring the true field of view that I can get a better definition.

Note that above I say I have measured the Promaster at 59* and I think it has a spec of 60*. The ISO prediction for that bino is 55.34*.

I also measured an 8x36 Monarch. I only measured the TFOV on the right side at 6.97 degrees and the eyepiece acceptance angles as 54.35 left and 54.33 on the right side (probably should be 56 degrees). These angles should be considered very approximate. The prediction of my AFOV program says 56* acceptance angle and ISO 52.2*. The above figures suggest a magnification of 7.8x for the right tube and I may have measured the power of these before. I will hunt for that.

It was very hard to get good measurements because the apparent magnification is about 0.125 and 60 degrees wide and when viewing, a shadow or dark transparent band several degrees wide would manifest itself along the edge making the edge hard to determine and appearing to shift a little with the shadows appearance.


On another note I have found that measuring the field stops in the exit pupil with a good optical sighting magnetic compass, Suunto KB 14 in this case, that I get very close to the ISO value.

I will get back after some more testing.

Best
Ron

[Surveyor]

Henry

I did find a review card for my Monarch were I had measured the power at infinity of the right tube dated 5/08. I had measured the power at 7.91x. Hmmm, I had actually posted the information here on BF 01/08, http://www.birdforum.net/showpost.php?p=1115520&postcount=1

Ron

[henry link]

Ron,

I'm assuming that the AFOV measurement using the tripod scale method includes distortion because I can see the distortion as I swivel the binocular. I'd never realized before trying this method that the distortion visible when looking through a binocular backwards is the exact reverse of the distortion seen in normal use, so a binocular with pincushion in normal use will show exactly the same amount of barrel distortion when looked through backwards. Of course this makes perfect sense because the distortion is caused by changes in magnification toward the edge of the field so, looking backward, you see the same change in minus magnification reversed. In the group of Nikon binoculars I tested the EII's showed obvious barrel distortion when looked through backwards while the Astroluxe looked just as free of rectilinear distortion from either direction.

Henry

[Surveyor]

Henry, yes I agree about the distortion. You are seeing all in the field of view. I had not paid any attention to the direction of the bow before, I will check that out.

[henry link]

Ron,

I just photographed a piece of graph paper through the objective end of two binoculars with different distortion characteristics. Both are 8x with nearly identical AFOV. On the left is a Fujinon 8x30 FMT-SX which has almost no rectilinear distortion (very slight pincushion) and on the right a Zeiss 8x56 FL which has obvious pincushion. Looking backwards through the binoculars in the photos, the Fujinon still looks almost distortion free (very slight barrel) and the Zeiss shows obvious barrel distortion. I think this method could be very useful for identifying the type and measuring comparative amounts of distortion in different binoculars.

Henry

Edit: Maybe I should mention that the Fujinon is not "better" because it has less rectilinear distortion. The pincushion was intentionally added to the Zeiss to reduce the "rolling globe" effect when panning. Some people will find panning with the Fujinon unpleasant.

[Surveyor]

Henry,

This is a very good idea, Henry. This prompted me to photo a Leupold 7x20 IF (labeled Leica Red Dot) that is the only binocular I have that will make me queasy when I am using them in a plane or helicopter.

Instead of the usual rolling ball this binocular appears more like pulling a tablecloth with a landscape scene on it across a round table, with maybe a very slight dome to it. The last 10% from the center looks like the table cloth is going straight down, the view expands very quickly from the trailing edge and compresses very quickly on the leading edge while getting less severe as the view travels around the outside of the view to the top and bottom and then increasing compression as it approaches the trailing edge. Looking at edge’s, in a normal still view, you see a little pincushion, then in the last 15 to 20%, the pincushion changes to barrel distortion, very weird.

I have over 10,000 hours in aircraft and these things darn near make me airsick. They are very sharp in the center and I like them, I just have to avoid panning or movement with them.

Look at the very ends of the grid lines. Looks to me like the field stop encases the lens so that the edge distortion is prevalent.

I have attached the measured angles, though these are quick and rough, limited distance of about 200’. Also pictured, my "protractor".

Best
Ron

[mooreorless]

Hi Ron, I like your protractor, kind of expensive though.;) The picture of the grid lines gives me a headache just looking at them.
Regards,Steve

[henry link]

Ron,

I've seen exactly that same wavy pattern of pincushion distortion changing to barrel at the field edge in at least one other binocular and several telescope eyepieces. It looks like the barrel distortion is supposed to correct or at least control the amount of pincushion, but it doesn't quite work out because the distortion curves are not exactly complementary.

Nice "protractor". I don't think anyone else will be measuring field widths to the arc second.

Henry

[Surveyor]

For those interested, I have added a 1/10-degree and a 1-minute vernier to the paper Protractor.

[Kevin Purcell]

Thanks, Ron. I was going to suggest a vernier. I guess telepathy works! ;)

Hey, two verniers one for 0.1 degree and the other for 1 minute. Excellent.

[jcbouget]

The two methods described here are interesting.

In the first method ( described by John Russell), I don’t see why the laser beam must be pointed at the center of the objective : if there is severe off-axis vignetting, the rays passing through the center of the objective don’t pass through the eyepiece. I have two binoculars like that : the Zeiss 10x40 BGAT and the Meade 10x50. The problem in the Meade is eyepiece vignetting. In such binoculars, the laser beam should be decentered to give valid results.

Until now, I used a procedure similar to this one :
http://www.cloudynights.com/ubbthreads/showthreaded.php/Cat/0/Number/720055/page/0/view/collapsed/sb/5/o/all/vc/1
My estimation of the accuracy is about 0.2°.

I have tried the method described by Surveyor with several binoculars. I have a geared mount to do the test. I can measure the rotation angle of the knob in order to have an accurate evaluation of the rotation of the mount. I have found that to increase greatly the precision, it is possible to use a second binocular, which widens the small image seen through the objective of the tested binocular.
With all these precautions, the accuracy is again about 0.2°

Here are the results for 9 binoculars, first with the method described in the link above, then with Surveyor’s method :
Meade 10x50 : 66.02° - 66.04°
Zeiss 10x40 BGAT : 61.38° - 61.20°
Zeiss 10x42 FL : 61.22° - 61.07°
Canon 10x42 IS : 63.22° - 62.93°
Canon 12x36 IS II : 58.78° - 58.49°
Nikon 12x50 SE : 58.47° - 58.58°
Zeiss 15x60 BGAT : 64.01° - 64.09°
Fujinon 16x70 FMT SX2 : 63.01° - 63.07°
Takahashi 22x60 : 48.11° - 48.18°
The difference between the two methods never exceeds 0.3°.


On 3 binoculars, I have also measured precisely the real field of view, and the magnification at the center of the image at infinity :
Nikon 12x50 SE : 5.02° - 12x
Zeiss 15x60 BGAT : 4.33° - 14.8x
Fujinon 16x70 FMT SX2 : 4.11° - 16.05x

With these results, one can calculate a theoretical AFOV according two formulae :
The first one is the classic approximation : AFOV = M x FOV
The second one is the ISO method : AFOV = 2 x arctan( M x tan( FOV/2 )) in which M and FOV are measured.
It is interesting to compare the two calculated AFOV with the measured AFOV :
Nikon 12x50 SE : approx : 60.2° - ISO formula : 55.5° - measured : 58.6°
Zeiss 15x60 BGAT : approx : 64.1° - ISO formula : 58.5° - measured : 64.1°
Fujinon 16x70 FMT SX2 : approx : 66° - ISO formula : 59.9° - measured : 63.1°


My results and those obtained by Henry Link show that AFOV must be measured. I remember someone who claimed that the Nikon Astroluxe 18x70 was much more impressive than the Zeiss 15x60 because the AFOV was supposed to be 72°, instead of 65° for the Zeiss. He had owned both binoculars. Obviously he was more impressed by the official specs than by his own observations. But I have learned the hard way how reviews on the web could be totally misleading.

My second conclusion is that the method described by Surveyor is excellent. Just think to examine the image with another binocular to get accurate results.

Jean-Charles

[henry link]

Good work, both here and on the focal length thread, Jean-Charles!

Using a second binocular certainly improves the potential accuracy. My remaining problem is a rather coarse scale on the Gitzo head I'm using. I remeasured a few binoculars using a second binocular. I was curious about the difference in our measurements of the same eyepiece used in the Nikon 8x32 SE and 12x50 SE. My result this time was about 58 degrees, closer to your measurement, but still not quite there.

I'm also surprised by the very short focal length of the Zeiss 15x60. Does it use an air spaced doublet tele-objective, like the older Oberkochen Porros?

Henry

[jcbouget]

Henry, I have tried the variant suggested by Ron :

Lacking a laser beam, you could just look through the objective and sight the extremes of visibility on the wall, and apply the same formula.

The binocular must be focused approximately at infinity, and the image examined with another binocular. It works very well also !
The distance one must take into account is the distance between the eyepiece and the wall minus the eye-relief, because the marginal rays considered here cross in front of the eyepiece.
I have tested three binoculars with this method :

Meade 10x50 : 66.14°
Zeiss 10x40 BGAT : 60.95°
Nikon 12x50 SE : 58.31°

I think the accuracy is about 0.3°. Maybe you can try this method.


You can read my answer about the Zeiss 15x60 in the focal length thread.

Jean-Charles