Ray equation for a spatially variable uniaxial crystal and its use in the optical design of liquid-crystal lenses

To be able to design optical systems (e.g., variable focus or zoom lenses) made from liquid-crystal devices, it is necessary to be able to ray trace in a birefringent medium where the angle of the optical axis is a function of position in the device. To our knowledge, the theory required to achieve this has not previously been published, and we derive a suitable algorithm and give some examples of its use.