  Vectorial polarized fields of light has been applied to detect the rotational
velocity by the rotational Doppler effect, but the measurement was made for the
rotation of a single-particle system. When the rotational surface is rough, the
scattered vectorial Doppler signal spectrum is complex. In this paper, we make
the complex spectrum analyses using orbital angular momentum modal expansion
method. It is found that the highest peak in the Fourier form of the complex
spectrum is obtained at the frequency shift 2l{\Omega} related to the
topological charge (l) of the incident vortex light and the rotational velocity
({\Omega}) of the rough surface. Based on the complex spectrum analysis, we
construct a method to measure the magnitude and direction of the rotational
velocity simultaneously for a general object, which has the practical
application in remote sensing and astronomy.
