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We show theoretically how a sequence of spatial light modulators (SLMs) can be used to compensate polarisation and phase errors introduced by a spatially variant homogeneous waveplate with any polarisation eigenmode and arbitrary retardance distribution. The resultant compensation is applicable to all pure input polarisation states. The properties of such a system are easily described using Jones calculus in terms of the retardance distribution on each SLM. However, it is not straightforward to determine from the Jones matrices the arrangements nor the settings of each SLM required to implement an arbitrary spatially variant retarder. In order to address this problem, analytic solutions for the required SLM settings are obtained through the construction of a geometrical model on the Poincaré sphere. These solutions are validated against numerical models. These models can be used, for example, to control a multi-pass SLM system acting as the correction device in an efficient vectorial adaptive optics system.

Arbitrary complex retarders using a sequence of spatial light modulators as the basis for adaptive polarisation compensation