Measurements at multiple distinct polarization measurement states are taken to define the polarization state of an input, for example to calculate a Stokes vector. High accuracy and/or capability of frequent recalibration are needed, due to the sensitivity of measurement to retardation of the input signal. A multiple measurement technique takes a set of spatially and/or temporally distinct intensity measurements through distinct waveplates and polarizers. These can be optimized as to orientation and retardation using initial choices and also using tunable elements, especially controllable birefringence elements. A device matrix defines the response of the device at each of the measurement states. The matrix can be corrected using an iterative technique to revise the device matrix, potentially by automated recalibration. Two input signals (or preferably the same signal before and after a polarization transform) that are known to have a common polarization attribute or other attribute relationship are measured and the common attribute and/or attribute relationship is derived for each and compared. The device matrix is revised, for example by iterative correction or by random search of candidates to improve the accuracy of the device matrix. Optional tunable spectral and temporal discrimination provide additional functions.