Comment by nine_k

I once saw a servo with two smooth optical encoders. A disc, each side is white with a black off-center ellipse on it. Each side lit with a LED through a narrow slit, with a photo diode measuring the reflected brightness.

Each angle has its value of the optical signal, down to the ellipse's symmetry. Two ellipses, painted at an angle between their axes, give a unique pair for each angle, even amenable to interpolation.

This must be quite resistant to both electromagnetic interference and to fast / jiggy rotation. It's more bulky though, and likely requires calibration.