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As the result of an accident, one or more nerves that control the rotation of my left eye were damaged. The result is that my left eye views the world rotated clockwise several degrees, compared to my normal (and dominant) right eye. I'm told that it is not possible to construct a lens that rotates images, other than a camera lens that inverts an image a fixed 180 degrees. Has anyone created a portable optical system that rotates images in small adjustable increments?

As shown in the attached image, the yellow line represents the plane of vision in my normal right eye, and the red line represents the rotated, or tilted, vision in my left eye.

As shown in the attached image, the yellow line represents the plane of vision in my normal right eye, and the red line represents the rotated, or tilted, vision in my left eye.

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    $\begingroup$ When the optometrist is measuring the astigmatism in my vision he tries various different angles of cylindrical components and some of them cause the letters to skew. I presume this is due the the mismatch between the cylindrical components of my eye and the lens. This suggests that a lens ground with differing cylindrical components on each face might manage small adjustments. I presume this is non-linear and trades focus for rotation, however. $\endgroup$ – dmckee Jan 5 '14 at 21:13
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    $\begingroup$ Out of interest: what is your experience of sight when you're not at the optometrist? Do you "see" a defect: for example you do see two images of letters when you look at signs? I'm intrigued to know whether or not your mind compensates for the "instrument data" in the same way that people who wear upside-down glasses (rotation of 180 degrees) stop seeing everything upside down after a while and instead their mind corrects the data so that they see everything right way up through their glasss. Unlike astigmatism or other "aberration" the transformation wrought by the "defect" is invertible. $\endgroup$ – WetSavannaAnimal Jan 5 '14 at 23:51
  • $\begingroup$ Why necessarily optically? With technology these days you can have a pretty good camera which is small enough to fit in glasses with integrated displays and rotate the images on-the-fly via a miniaturised computer like a raspberry pi on your belt (alongside a decent battery). This would probably be a lot cheaper and quicker than any optical technique, and not as bulky as it sounds when the system is finalised, and it can be a great temporary solution. $\endgroup$ – Mister Mystère Mar 5 '14 at 23:18
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Great question! I suspect it's a research problem.

My brother-in-law, Chris Croke, and R. A. Hicks, Designing coupled free-form surfaces have shown how to do particular image transformations with mirrors, and the paper says it is also possible with lenses.

Quoting from the abstract:

Here we present a method for the coupled design of two free-form reflective surfaces which will have a prescribed distortion. ... it is motivated by viewing the problem in the language of distributions from differential geometry

Here is a pair of mirrors that rotates an image by 45 degrees:

enter image description here

And here is the result from a ray-tracer:

enter image description here

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    $\begingroup$ Could you edit in the main conclusions, just to future-proof the answer and make it more googleable? $\endgroup$ – Rody Oldenhuis Jan 6 '14 at 10:44
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I don't know how small these can be made, but a Dove prism is able to rotate images at arbitrary angles

Additionally, if you don't want to use a prism, a K mirror will do the trick. See this link on pages 13-14. The one they show has three bounces, but you can make it have four as well.

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I want to elaborate on the answer about Dove prisms above. It looks as though, in principle, arrays of prisms can be used to achieve some pretty remarkable optical transformations without sacrificing thinness. These devices are like meta-materials that work on the ray optical level, and are a bit like Fresnel lenses. Some links:

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The conditions called cyclotropia usually treated with surgery, experiments with double dove prisms are going well but slow and nothing on market. Most like when it does first come to the optical market it will be as a type of mounted monocular or some combination of the double dove prism model but similar too the stick on Fresnel prism commonly found today.

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