Weird optics

Weird optics
Image by P^2 – Paul
If you push a macro too far past telecentric, you get a pericentric lens, where the perspective is inverted: farther objects appear larger than closer objects.

It leads to weird optical effects, like being able to see five sides of a die at once.

No photoshop magic here. This is essentially straight from the camera: just a resize to something small enough to upload in tolerable time.

7 thoughts on “Weird optics

  1. prompted by this discussion in the Light Science & Magic group.

    This is two lenses taped together (with hockey tape, from Canada, eh!): A Pentax DA*50-135 on the camera, operating at 50mm, and an unknown brand 75-mm focal length magnifier taped on the front.

    It works as well, but with a smaller field of view, with a cheap FAJ75-300 (at 75mm) and an even cheaper Pentax SMC A 50/2.0 coupled by a reversing ring.

  2. Paul,

    Contact DARPA and show them this.

    You can get a great g’vment contract to build a rifle scope that sees around corners 🙂


  3. DARPA grant sounds like a great plan. It will probably take years before they realize you need to be less than 20mm from the target to see it 🙂 The "6" (top) of that die is just 3 mm from the lens surface here: hard to get light onto it.

    There is more subtlety to this than at first glance. Just mashing a couple of lenses together may or may not work. The secret is all in where the entrance pupil of the imaging (camera) lens is. In the case of a telecentric lens (where perspective is zero), the objective lens is placed exactly one (of its) focal length away from the imaging lens’ entrance pupil. A typical case would have a normal lens on the camera, with its entrance pupil somewhere around where the mounting flange is. The objective lens of, say, 135 mm focal length, would be placed 135mm away from that location. This would yield zero perspective in the resulting image: things would appear to remain constant size independent of distance from the lens.

    In order for this inverse perspective case to be true, the objective lens must be at a distance greater than its focal length from the imaging lens’ entrance aperture. In the case above, the 75 mm objective lens is (very roughly) 180 mm from the camera lens’ entrance aperture.

    This is really easy to demonstrate if you have two ordinary 50-mm lenses: With one on your camera place them front-to-front (freehand), and look at a glancing angle (through the viewfinder) to a sheet of graph or lined paper — anything with parallel lines going off to "infinity." Vary the distance between the lenses. You’ll see that with the lenses close together, the lines appear normal (converging to a vanishing point). As you increase the distance between the lenses the lines will become parallel even though some parts of the scene are far and some are near. Increase the distance between the lenses still further and the perspective will invert: parts of the paper farther from the camera will appear to have lines closer together farther apart! than paper closer to the camera.

    Hurts the head.

  4. The lens has to be wider than the object in order to collect light from multiple sides at once. This works with the macro on my big SLR Nikon but not with the lens on my tiny Sony Cybershot.

  5. works with the macro on my big SLR — if by this you mean you see this inverted-perspective effect with the macro lens alone, then I’m surprised. Shocked, even. Doubly shocked, if it’s from Nikon.

    But with an external lens, it’s easy to do even with a point&shoot. On my Panasonic TZ2, a 28mm external lens won’t work, but 50mm and 250mm do. Since there’s no manual focus on this camera though, it’s miserable to use like this.

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