Patent ID: 6947618

Claim:
A polarization controlling system for controlling the state of polarization of a light beam comprising: a) a waveplate having: a substantially constant retardance 2λ; a variable rotation axis ŵ={circumflex over (x)} Cos(θ)Cos(φ)+ ŷ Sin(θ)Cos(φ)+ {circumflex over (z)} Sin(φ); and N variable retarders, N≧2, the retarders for being disposed sequentially along a propagation direction to receive the light beam, each variable retarder having a fast axis disposed at substantially 45° from the fast axis of each nearest variable retarder, each variable retarder having a variable retardance r x , x having an odd or even value between 1 and N, each retarder having an odd value x having a rotation quaternion X(r x )={Cos(r x /2), Sin(r x /2){circumflex over (x)}}, each retarder having an even value x having a component rotation quaternion Y(r x )={Cos(r x /2), Sin(r x /2)ŷ}; wherein a total rotation quaternion Q ( X ( r 1 ) Y ( r 2 ) X ( r 3 ) . . . )= . . . X ( r 3 )* Y ( r 2 )* X ( r 1 ); and b) controlling means for controlling the retardances r x in dependence upon at least one solution to Q(X(r 1 )Y(r 2 )X(r 3 ) . . .)∞ . . . X(r 3 )*Y(r 2 )*X(r 1 ) ={Cos(λ), Sin(λ)ŵ}.