How to optically rotate images in small increments (for eyeglasses)? 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.

 A: 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:

And here is the result from a ray-tracer:

A: 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.
A: 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:


*

*Ray-optical negative refraction and pseudoscopic imaging with Dove-prism arrays

*METATOY

*Image rotation devices - a comparative survey 
A: 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. 
