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In previous studies addressing polarization evolution in optical fibers, the frame of reference in which polarization rotation in twisted optical fibers is described lacks the compatibility with the modeling of some fiber sensor applications. We therefore introduce a formulation of the polarization evolution in a twisted optical and birefringent fiber, which is based on a laboratory coordinate system. We employ coupled mode theory using the fundamental modes of a single mode fiber as a basis. We treat the birefringence of the polarization maintaining fiber and the twist induced birefringence as perturbations introduced into this mode system. We demonstrate the derivation of the coupling coefficients and solve the coupled mode equations for different sets of problems. We compare our results to existing formulations and find an excellent agreement between the theories for highly birefringent fibers.