In many laboratories of universities and industrial organizations, commercial polariscopes have the feature that the relative position of the two quarter-wave plates is fixed. This is due to the requirement of transforming a plane polariscope to a circular polariscope with greater precision and ease. Unfortunately, these polariscopes cannot implement Patterson and Wang's [Strain 27, 49-56 (1991)] phase-shifting algorithm because this algorithm requires that the second quarter-wave plate and the analyzer of the circular polariscope be capable of independent rotation. A new phase-shifting method that can be applied under these constraints is proposed. A comparative study with Patterson and Wang's [Strain 27, 49-56 (1991)] algorithm shows very good agreement. Furthermore, it is shown that four phase steps are sufficient to determine both the isoclinic and the isochromatic parameters.
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