Polarization dependence of the loss or gain of an optical device has been difficult to measure in a consistent and reproducible manner because it has been necessary to search for the extrema of transmission over a two-dimensional polarization space. It is shown for the first time that the global variation of the transmission through any linear, time-invariant optical device, over all states of polarization, can be found in a strictly deterministic, analytically complete manner by measuring the polarization responses to only three input polarizations. A series of fast, automated measurements of two test devices yielded standard deviations of 0.017 and 0.033 dB, and agreement with laborious manual measurements.