  I present several classes of analytical and semi-analytical solutions for the
design of high-speed rotary optical delay lines that use a combination of
stationary and rotating curvilinear reflectors. Detailed analysis of four
distinct classes of optical delay lines is presented. Particularly, I consider
delay lines based on a single rotating reflector, a single rotating reflector
and a single stationary reflector, two rotating reflectors, and two rotating
reflectors and a single stationary reflector. I demonstrate that in each of
these cases it is possible to design an infinite variety of the optical delay
lines featuring linear dependence of the optical delay on the rotation angle.
This is achieved via optimization of the shapes of rotating and stationary
reflector surfaces. Moreover, in the case of two rotating reflectors a
convenient spatial separation of the incoming and outgoing beams is possible.
For the sake of example, all the blades presented in this paper are chosen to
fit into a circle of 10cm diameter and these delay lines feature in excess of
600ps of optical delay.
