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We show that there are a number of ways to transform an arbitrary polarization state into another with just two quarter wave plates (QWPs). We have verified this geometrically using the trajectories of the initial and final polarization states corresponding to all the fast axis orientations of a QWP on the Poincare sphere. The exact analytical expression for the locus of polarization states has also been given, and describes the trajectory. An analytical treatment of the equations obtained through matrix operations corresponding to the transformation supports the geometrical representation. This knowledge can be used to obtain the Mueller matrix by just using QWPs, which has been shown experimentally by exploiting projections of the output states on the input states.

We present a method for calibration and data extraction for a nonoptimized Mueller matrix polarimeter. The advantage of this type of method is a reduction in measurement time for multiwavelength systems or in systems with slow response times. The calibration process requires the measurement of four known polarization devices. Here we use free-space transmission, a horizontal and a vertical linear polarizer, and a quarter-wave retarder with its fast axis at 30° to the horizontal. Experimental measurements of rotating quarter-wave and half-wave retarders show that accurate results can be obtained with the proposed method.

A method for simultaneous measurement of the retardance and the fast axis angle of quarter-wave plate using one photoelastic modulator is presented. A laser beam passes through a polarizer, a photoelastic modulator, the quarter-wave plate to be measured, and an analyzer to be detected. Before and after the quarter-wave plate is rotated 45° at any initial fast axis direction, two detection signals are obtained to resolve simultaneously the retardance and the fast axis angle. In experiments, a quarter-wave plate was measured with fast axis angles from −89° to 90°. The average and the standard deviation of the retardances at different fast axis directions are respectively 89.50° and 0.17°. The maximum measurement deviation of the fast axis angle is 0.5°. The usefulness of the method is verified.

In a recent study we reported on the gradient index (GRIN) lens Stokes polarimeter (GLP) [Opt. Lett.39, 2656 (2014)10.1364/OL.39.002656OPLEDP0146-9592]. With a simple architecture, this polarimeter can measure the state of polarization in a single shot. In this article, we present further studies for improving the performance of the GLP. Detailed discussions are presented on the optimization process of the GLP based on different choices of data from the CCD images. It is pointed out that many optimization techniques, although developed for other types of Stokes polarimeters, can also be applied to the GLP because the GRIN lens can traverse all possible retardance and fast axis modulations.