Chris and Joe nailed it. The basic idea is simply to shoot at a POA...

...that's so near the muzzle that neither gravity nor scope turret adjustments can (significantly) change the relationship between boreline and Line-of-Sight at the target.

This is potentially a more accurate measurement of ballistic scope height than could ever be made with a mechanical estimate (no matter how careful) of the geometric distance between scope and barrel centerlines, because true scope height is defined as the distance between line of departure and LOS, not at the scope bell, but at the muzzle.

The fly in the ointment (as Steve points out) is that not even the most accommodating scope AO could possibly be adjusted for such a ridiculously short range - e.g., one foot or less.

Which is the reason for the pinhole. It reduces parallax and out-of-focus-fuzz enough to make an adequately accurate shot possible.

The procedure is.

1. Cut a square of Al foil and by my method or another, make a circle on it the same size as the scope objective bell.

2. Poke a ~1/16" pinhole in the center.

3. Place the foil circle over the scope bell, aligning it as accurately as possible. Adjust the scope to its shortest parallax range and lowest magnification settings.

4. Make a suitable target, mount it on a guaranteed-zero-bounceback backstop (!), and illuminate the target with a very (very) bright light. A lot of light is needed, because the tiny aperture will greatly attenuate the brightness of the target. I try to use direct sunlight, but a high wattage halogen might suffice.

5. While wearing good eye protection take the shot with the muzzle as close to the target as the quality of the backstop makes prudent. Be aware that it make take some patience to position your eye properly to find and see the tiny image of the pinhole.

6. Measure the distance between POA and POI as the true scope height.

I've tested the method with several different scopes, and find that it seems to work with any normal eye-relief (e.g., ~3") riflescope, but not long eye-relief pistol scopes. There's something about the optics of pistol scopes that prevents the pinhole from being expanded to fill the field of view sufficiently to make it possible to aim the shot.

Steve