Programmable linear retarder using liquid crystal variable retarders with calibration for non-ideal beam splitter properties

This study introduces an optically equivalent system for a programmable linear retarder, capable of arbitrarily changing the fast axis and phase retardation without any mechanical rotation apparatus. The programmable linear retarder comprises a quarter-wave plate and a pair of liquid crystal variable retarders, paired with a retroreflection scheme for implementation. The non-ideal characteristics of the non-polarizing beamsplitter in the optical system were recognized and corrected to ensure that the linear phase retardation and fast axis orientation of the programmable linear retarder closely match the design values. Additionally, the programmable linear retarder was employed for incident light's polarization conversion. Experimental results illustrate that the actual measured linear phase retardation, fast axis orientation, and the emergent light's polarization state after polarization conversion closely align with the design and theoretical values, confirming the proposed method's validity.