AFOV again (1 Viewer)

John Russell · Jul 16, 2009

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 · Jul 16, 2009

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 · Jul 17, 2009

Kevin Purcell said:
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 · Jul 17, 2009

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 · Jul 17, 2009

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 · Jul 17, 2009

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 · Jul 17, 2009

henry link said:
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 · Jul 17, 2009

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 · Jul 17, 2009

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 · Jul 17, 2009

Surveyor said:
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 · Jul 17, 2009

Surveyor said:
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 · Jul 17, 2009

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 · Jul 17, 2009

Surveyor said:
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 · Jul 17, 2009

ronh said:
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 · Jul 17, 2009

ronh said:
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 · Jul 18, 2009

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 · Jul 18, 2009

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 · Jul 18, 2009

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 · Jul 18, 2009

spyglass2 said:
....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 · Jul 18, 2009

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.

AFOV again (1 Viewer)

Well-known member

Well-known member

The more I understand, the more I understand why I

Well-known member

Well-known member

The more I understand, the more I understand why I

Well-known member

The more I understand, the more I understand why I

The more I understand, the more I understand why I

Attachments

Well-known member

Well-known member

Well-known member

Well-known member

Well-known member

Well-known member

Well-known member

Well-known member

Well-known member

The more I understand, the more I understand why I

Well-known member

Similar threads

Users who are viewing this thread