To be compared with the wavelength modulation technique for measuring two-dimensional (2D) cell parameters of a twisted nematic liquid crystal (TN-LC), we propose an amplitude-sensitive heterodyne ellipsometer (ASHE) of a single wavelength that is able to characterize TN-LC in 2D quantitatively. A quarter-wave plate (QWP) is rotated continuously in this setup to modulate the polarization state of the incident laser beam to obtain the amplitude ratio of the S and P waves versus the rotation angle of the QWP. Thus the cell parameters, including the twisted angle Phi, untwisted phase retardation Gamma, rubbing direction angle alpha, and cell gap d, of a TN-LC cell are obtained simultaneously by best fitting the detected amplitude ratio with a prediction based on the transfer matrix of TN-LC cell. 2D distributions of (Phi,Gamma,alpha,d) are then obtained either by scanning the TN-LC cell or by using a CCD camera for high-speed measurement. In this experiment, the stability of the amplitude-ratio measurement of the proposed ASHE was 0.5%. The goal is to integrate the rotating elliptical wave plate with the TN-LC cell in a heterodyne ellipsometer to obtain cell parameters at amplitude sensitivity. This increases not only the sensitivity of the measurement but also the possibility of extending the 2D distribution of cell parameters in real time.