Both temporal and/or spatial modulation are mandatory in current solar polarimetry [Appl. Opt. 24, 3893 (1985); 26, 3838 (1987)]. The modulating and demodulating processes are mathematically described by matrices O and D, respectively, on whose structure the accuracy of Stokes parameter measurements depend. We demonstrate, based on the definition of polarimetric efficiency [Instituto de Astrofísica de Canarias Internal Report (1994); ASP Conf. Ser. 184, 3 (1999)], that the maximum efficiencies of an ideal polarimeter are unity for Stokes I and for (Q 2 + U 2 + V 2)1/2 and that this occurs if and only if O T O is diagonal; given a general (possibly nonideal) modulation matrix O, the optimum demodulation matrix turns out to be D = (O T O)-1 O T; and the maximum efficiencies in the nonideal case are given by the rms value of the column elements of matrix O and are reached by modulation matrices such that O T O is diagonal. From these analytical results we distill two recipes useful in the practical design of polarimeters. Their usefulness is illustrated by discussing cases of currently available solar polarimeters. Although specifically devoted to solar polarimetry, the results here may be applied in practically all other branches of science for which polarimetric measurements are needed.
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