Using reciprocal models can lead to confusion...sorry.
Curvature is based on....the radius of...the light cone you mention. That's all.
Divergence of convergence is the measure of the rays passing apart or together.
One should not measure with outside rays that are spreading apart.
To relate it to your method:
You mentioned moving the pin-hole off-axis. When you do that, it sees a different ray passing through from a different place
in the lens, and next lens, etc. As the volume the different pinhole-positions increses, it subtends a conical area, or actually
cones passing through the instrument. you are sampling bits of the light cone, and when you see black it was blocked..
I agree the question is straightforward, or at least that the test methind should make it straightforward.
When you talk about the light-cone in straightforward use, aren't you talking about a solid flat beam
coming from a star in parallel, which is then formed into a light cone that might be blocked somewhere along the line?
I'm just saying......for the answer to be straighforward, you really need parallel light passing into the objective
or the eyepiece. If a laser is moved to spot A and the beam is still parallel to the beam form spot B, this is good.
Having flashlight shining from a foot away (assuming a point source) is equivalent to pivoting a laser to make non-parallel rays...
...there is a 'curvature'. The small focal length of the eyepiece does make it less sensitive, but the deviation of these
rays from parallel is problematic. It violates your wish for something 'straighforward' (literally). It gets more
confused with a large reflector on the flashlight, of uneven finish...just shine it at the wall and it's obvious.
If you move a laser and keep it parallel .... perfect.
If you have a distant source and move a pinhole....perfect (if it's focused for infinity).
If you shine a flash in either end from a foot away, it's not like either of those....it's a set of dispersing beams a foot away.
Unless....you just use a collimating (distance-beam-focus) flashlight.
Simply pivoting a laser pointer a foot away without shifting it to make a parallel beam would be the equivalent problem.
My 'observation cone' looking into an objective from one foot away has me looking into the lens at an angle,
and that makes the iris appear to be blocking the objective. That is just an illusion. From 20 feet away, the iris would not
be in the way at all (in binoculars I have looked at). I am looking at the objective at an angle close-up, and that
distorts my view of what's behind it. Another term for this is: a magnifying glass.
Is the difference insignificant at 1 foot? Then magnifiers would not exists.
encourage you to take a look...it's right there. The baffle tunnel also usually appears to be straight
when it's actually conical. Another magnification illusion, and a nifty one, because the magnification
increases as you go down the tunnel. But.....from 20 ft away, you don't see it at all.
Edited by MartinPond, 14 October 2014 - 10:05 AM.