Re: What Element of Optics Design Gives "Full-Screen"?
<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: toovira</div><div class="ubbcode-body">Which element?
Correct answer is the limiting element, which dictates "aperture stop" better know as f/# (f number or f stop).
In other words, whichever piece of optics limit your field of view dictates over all optical system aperture stop.
Kind of like you're asking what is the maximum of the plumbing system - it's the smallest pipe in the system - the limiting element. </div></div>
toovira,
there seems to be a mix-up happening here between aperture stop and field stop. Those are two distinctively different things and the one that limits the FOV of an optical system is the field stop.
An aperture stop limits the amount of light that passes the optical system and does not affect FOV at all.
I once made the sketches below to help explaining the connection between objective diameter, exit pupil and eye pubil when it comes to image brightness on a German forum. There's a little more information in the images than necessary for this case here, but it might be interesting to some anyway, so I’m going to try if I can manage a decent explanation in English this time.
This image is a <span style="font-weight: bold">heavily simplified</span> (seriously, keep that in mind) scetch of the optics in a riflescope.
[1] is the target. We're going to follow tho "rays" of light emerging from two points of the target through the scope, into the eye and right on the shooter's retina. The dashed blue ray emerges from the center of the target, the dashed yellow one from the edge (meaning the edge of the field of view of the scope).
The solid lines indicate those rays emerging from the two spots on our target but hitting the edge of the objective lens. Remember that any visible object reflects light in every direction (that's why you can move around and see stuff from different angles), and what the scope objective does is catch a "cone" of light emerging from every point of the target. Since this is a 2D sketch, the blue and yellow "cone of light" are represented by the dashed "center rays" and the solid "edge rays".
[2] The objective system, for the sake of simplicity represented here by a single lens focuses the light cones and creates
[3] an upside-dwon image of the target in the first focal plane. This is also where the reticle is placed in an FFP scope. There can also be a field stop placed in this focal plane, indicated by the black posts (of course this is a round hole in a real scope). In this example this field stop limits the FOV of the scope. You can see that the yellow bundle of rays just barely clears the edge of the field stop, a ray emerging from a point above the yellow dot would be focused on the black post and thus be blocked from the shooter’s view.
[4] is the erector system, again for the sake of simplicity this is just a single lens here, in a real scope it consists of several lenses that in part move back and forth in a variable scope and are housed in a complicated mechanical contraption. For now, it is enough to know that the erector system inverts (erects) the upside-down image from the first focal plane and creates another image in
[6] the second focal plane. This is where the reticle is placed in an SFP scope, an again a field stop can be placed here. In this sketch the field stop in the second focal plane is big enough to let all the rays pass, so the FOV is not restricted any further.
[7] is the ocular system (again shown as a single element) which allows the eye to look at the magnified image.
[8] The eye lens focuses the light on
[9] the retina. This image is upside-down again but our brains take care of that, kind of a mental erector system.
Now where’s that elusive aperture stop sitting? As with the focal planes, there’s two of them in the scope. The first one is simply
[2] the objective lens diameter. It limits the size of the cone of light that enters the objective (indicated by the two black arrows). The second one is positioned at
[5] in front of the second focal plane. Note that at the aperture stops the yellow (dashed) center ray crosses the optical axis, just as it does in the objective in position [2]. There isn’t necessarily an aperture in this position creating an aperture stop, but one could be placed there if desirable for some reason.
[8] is another aperture stop, this time not inside the scope but in the eye of the shooter. It is simply your eye pupil that is small in bright light and might be up to 8mm in diameter for younger people and with night adapted vision.
This gif animation shows what happens if you restrict the clear aperture (objective diameter) or decrease the eye pupil size.
Frame 1 is simply the optical system from the image above.
Frame 2 shows what happens when the eye pupil is smaller than the exit pupil of the scope. The iris acts as an aperture stop that limits the cone of light entering the eye. Note that this has nothing to do with the FOV, it just lowers the brightness of the image.
Frame 3 shows the bundles of light entering the scope (and the eye) when the objective diameter is limited (smaller aperture stop at position [2]). If you look closely, you will notice that the cone of light entering the eye is absolutely the same for frame 2 and frame 3, so both cases are optically equivalent for the shooter. The original point of the animation was to show that increasing the objective diameter is not going to increase image brightness indefinitely, but rather only as long as the eye pupil can keep up with the increasing exit pupil (remember exit pupil diameter equals objective diameter divided by magnification). Having a 12mm exit pupil is not going to yield a brighter image that a 7mm exit pupil if your eye pupil only opens to 7mm anyway.
For the case at hand it is also important to note that restricting the aperture stop [2] does nothing to the FOV at all. That is why the objective size of a scope has nothing to do with it’s FOV, which is a common misunderstanding.
An aperture stop determines the size of the “cone of light” that passes an optical system, a field stop determines the field of view, and those are basically independent of each other.
I hope some readers have made it to this point and not everyone has fallen asleep yet. Merry Christmas.
