Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal

All 16 elements of the Mueller matrix of an optical system (sample) can be encoded onto, hence can be retrieved from, a single detected signal using a class of photopolarimeters with modulated polarizing and analyzing optics. The general theory of operation of such polarimeters is presented. We also propose a specific new photopolarimeter whose polarizing and analyzing optics are modulated by synchronously rotating two quarter-wave retarders at angular speeds ω and 5ω. When the light flux leaving such polarimeter is linearly detected, a periodic signal $\mathcal{J}=a_0+{\sum }_{n=1}^{12}(a_n\hspace{0.17em}\text{cos}\hspace{0.17em}n{\omega }_{f}t+b_n\hspace{0.17em}\text{sin}\hspace{0.17em}n{\omega }_{f}t)$ is generated, with fundamental frequency ω_f = 2ω. From the Fourier amplitudes a₀, a_n, b_n, to be measured by performing a discrete Fourier transform (DFT) of the signal ℐ, the 16 elements of the Mueller matrix are simply determined.