We have measured spectra from ∼2 to 5 eV in all 15 elements of the normalized Mueller matrix for (110) Si at an angle of incidence of θ a∼70°, as an initial demanding performance test of a novel dual rotating-compensator multichannel ellipsometer. The Mueller matrix spectra, deduced from 36 waveform integrals collected over a single optical cycle of 0.25 s, can be analyzed to extract the bulk isotropic dielectric function ε b= ε 1b− iε 2b and the surface-induced dielectric function anisotropy Δ ε s=Δ ε 1s− iΔ ε 2s. Starting from the 15 Mueller matrix elements, six sample parameters are determined, namely the real and imaginary parts of the complex amplitude reflection ratios ρ pp, ρ ps, and ρ sp. The surface-induced anisotropic response (Δ ε s) d=[ ε s(11̄0)− ε s(001)] d is deduced from an average of four independent spectra, two in ρ sp and two in ρ ps=− ρ sp using the first order term in d/ λ from an expansion of the partial transfer matrix. Here d is the surface anisotropic layer thickness and λ is the vacuum wavelength. Because both the real and imaginary parts of (Δ ε s) d are now accessible, the results can be fit using a Kramers–Kronig (K–K) consistent oscillator model. The key advantage of the newly-developed instrument is the ability to perform spectroscopic measurements in real time that simultaneously provide bulk isotropic and surface- or interface-induced anisotropic optical responses.