The four sets of two optimum rotation angles for a polarimeter consisting of a quarter-wave plate in conjunction with a linear polarizer, both of which are free to rotate, are determined. These angles are obtained by maximizing the determinant of the system measurement matrix. The determinant for this system is approximately twice the value of the determinant when only the quarter-wave plate is free to rotate. In addition, the condition numbers of the measurement matrix decrease with the additional consideration of a rotatable linear polarizer.
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Amrit Ambirajan (1995) studied this question.