A multichannel ellipsometer in the dual rotating-compensator configuration has been designed and constructed for applications in real time Mueller matrix ellipsometry (approx. 2-5 eV) of anisotropic surfaces and films. The sequence of optical elements for this instrument is denoted PC1r(omega(1))SC2r(omega(2))A, where P, S, and A represent the polarizer, sample, and analyzer. C-1r(omega(1)) and C-2r(omega(2)) represent two MgF2 biplate compensators that rotate at frequencies of omega(1)/2pi = 10 Hz and omega(2)/2pi = 6 Hz, synchronized for a ratio omega(1):omega(2) of 5:3. Spectra in the 16 Mueller matrix elements of a transmitting or reflecting sample can be established from the 25 non-zero Fourier coefficients of the irradiance waveform acquired in a single 0.25 s optical cycle. Initial high speed Mueller matrix measurements have been performed on weakly anisotropic samples that push the instrument to its precision/ accuracy limits. These include the (110) Si surface with maximum cross-polarization ellipsometric angles of psi(ps) similar to 0.1degrees and nanostructured thin films with maximum psi(ps) similar to 1degrees. (C) 2003 Elsevier B.V. All rights reserved.