Telescope Reviews: How to measure apparent field of view

I posted this in the obvious forum, Eyepieces, but as it's of great interest to bino users I offer it here, as well...
NOTE: I repeat it verbatim, rather than re-work it so as to be directly applicable to a binocular as such. But the interested reader will easily adapt the methodology, I'm sure.

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I'm inspired to throw this out there after seeing so many questions and comments regarding the determination of AFoV. In the following, such considerations as scale distortion and estimating/calculating inaccessible field stop diameters are obviated. There are two methods one could use:

1) Project the fully illuminated field stop.
2) Measure the angle between sight lines to opposite sides of the visible field stop.

The first method is a little more complicated, in that it requires fairly accurate measurements of both the projected diameter (two measurements) and the change in projection distance. I'll outline the method, as it's instructive in understanding the overall concept of determining AFoV.

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AFoV From Projection of the Fully Illuminated Field Stop

If you've ever employed eyepiece projection for Solar observation, you'll recall that at sufficiently high power (or when using an eyepiece which has a small AFoV) the Sun's image will completely fill the field of view. If the Sun is then centered, the projected circle's edge is the image of the field stop itself, which nominally is in focus with the image.

If you were to measure the diameter (D1) of the projected circle, re-position the screen farther back by some measured distance (S) relative to the first position and then re-measure the now-larger circle diameter (D2), you would find AFoV from:

AFoV = ATN[(D2/2) / {(D2/2} /(D1/2) * S}]

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AFoV Using Sight Lines to Opposite Sides of the Visible Field Stop

This is the easier method, and hence the recommended one. To understand its workings, recall that when looking into an eyepiece, the field stop is seen as a black circle "framing" the view. What you must do is measure the angle subtended by this circle's diameter.

It's difficult to do when your eye is at the eye point, so how to get around this? Simply move your eye well back--a foot or more is good--and orient the sight line so that first one "side" of the field stop is seen in the now apparently small eye lens, and then the opposite "side."

Here's how to do this easily:

1) On an 8.5"x11" sheet of paper, make a straight line along one of the 11-inch sides, roughly 1/4-1/2 inch from the edge.

2) Lay the sheet on a table, near one corner for ease of working, and orient the sheet so that the line points away from you. Lay the eyepiece on its side, and on the far end of the line.

3) Rotate *and* position the eyepiece so that, while you're sighting along the line, either the left or right edge of the field stop bisects the eye lens *and* is aligned with the line on paper. (You can see that this becomes more accurate the farther away from the eyepiece you are.)

4) Without moving the eyepiece whatsoever, swing your sight line so that the opposite edge of the field stop bisects the eye lens.

5) Carefully make two marks along the line of sight, one near your eye and the other close to the eye lens. Or you could lay down a ruler to act as a second sight line, then draw a line along it. Remove the eyepiece, extend the second line so as to intersect the original line and measure the angle with a protractor. Voila!

With care, you can determine AFoV's to within 1 degree or better.

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Home-made 11X50 right angle bino, 8.1 deg. FOV
Modified 26X100 bino, 3.5 deg. FOV

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