There's one more aspect of combos and apertures that I want to cover before we close out this topic.
Consider the following setup:
This is the same setup I've been using up above to illustrate effects on CA and resolution.
But now I want to talk about geometry.
Here are two pictures that may make your head hurt. They're straight out of the camera except for being resized. There's no change to any of the optics except which lens was stopped down. And no, that right-hand image is not flipped.
That's correct -- stopping down the rear lens causes inverted perspective, so that things closer to the lens look smaller
What's going on is that moving the position of the limiting aperture changes the position of the entrance pupil.
In the first case, stopping down the front lens puts the entrance pupil in the middle of that lens, resulting in a normal perspective where things that are closer to the lens look bigger.
In the second case, stopping down the rear lens essentially puts the entrance pupil way in front of the front lens, actually on the back
side of the focus plane. Things that are closer to the entrance pupil still look bigger, as you might expect when I say it that way. But because the entrance pupil is on the back side of the focus plane, this means that things look bigger when they are farther away from the lens. Magnification increases with distance from the lens!
This probably all seems like something from Alice in Wonderland. But perhaps a few ray diagrams will clear things up.
Here are the overview pictures.
Zooming in on the object and the lens makes it easier to see.
If this still seems a bit like Alice in Wonderland, be assured that it's really all very simple. Any aperture just selects a subset of all rays that would otherwise pass through the lenses. Those rays form the image, so the image has whatever geometry corresponds to the rays that got selected. In the absence of the aperture, rays are collected corresponding to many different perspectives -- a whole spectrum of them ranging from normal to orthographic to inverted. Moving the aperture back beyond the telecentric position simply selects rays that correspond to a geometry of inverted perspective. See this article
for more discussion and illustrations of that concept.
Again, not all combos will act this same way. It depends on details of the lenses. But most of them will, to some extent. What's required is only that the aperture of the rear lens appears
to be located farther back than one focal length of the front lens. For the case shown here, the zoom that I'm using as rear lens has an aperture that appears
to be very far back, actually behind the lens mount. Of course that's not where it is physically located, but what counts is where it appears
to be, looking through the glass in front of it.
Terminology: in the technical literature, an optical system that has normal perspective is called entocentric
(often misspelled endocentric
), and one that has inverted perspective is hypercentric
. So, starting with a normal lens and moving the limiting aperture farther back, the sequence is entocentric, then telecentric, then hypercentric. The transitions between these regimes is gradual, so more accurately the sequence is strongly entocentric, then progressively weaker entocentric, then telecentric at one specific placement of the aperture, then weakly hypercentric, then progressively stronger hypercentric.
Edited to add: These ray diagrams came from LINOS Photonics WinLens 4.4. That's a free download available from http://www.winlens.de/
. I see it's also obsolete, apparently having been replaced by WinLens 3D. Progress never stops... The triplet in this model combo is WLTR001 from their standard library.
Edited to add: terminology.