We propose theoretically an improved spectroscopic ellipsometer to study the optical properties of solids. In this system, the polarizer and the analyzer are rotating synchronously in the same direction at a speed ratio 1:3. The light intensity received by the detector contains six Fourier coefficients, one dc and five ac. One can independently extract the ellipsometric parameters as well as the optical constants of a sample using any of six different sets of the Fourier coefficients. A comparison among these sets is presented to find the optimal set corresponding to the minimum percent error in the calculation of the real and imaginary parts of the dielectric function. The results from the simulated spectra of the complex refractive index of c-Si, ZnSe, and GaP are presented.