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A sensitive method for measuring the magnitude and angle of the fast axis of low level linear birefringence in optical materials has been developed over past 20 years. However, different optical alignments have been determined using the same data processing method. All possible optical alignments and their corresponding data processing are investigated in this paper to explore the mechanism of data processing. Proper applications of the system with different optical alignments are then suggested according to the investigation results. Furthermore, based on a specific optical alignment for low level birefringence measurement, quantitative error due to angle misalignment of optical components is evaluated, providing a guide to improve measurement accuracy.