X-ray six-beam pinhole topograph images were obtained for a silicon crystal with incident synchrotron X-rays. The polarization state of X-rays incident on the sample crystal was controlled by using a four-quadrant phase-retarder system [Okitsu et al. (2002). Acta Cryst. A58, 146-154] that can be rotated around the transmitted beam axis to generate arbitrarily polarized X-rays. Quantitative agreement was found between the experimental and computer-simulated topograph images based on the n-beam Takagi-Taupin dynamical theory under the assumption that the polarization state of the incident X-rays was identical with the experiment. This result confirmed the validity of the computer algorithm to solve the n-beam dynamical theory and the proper operation of the rotating four-quadrant phase-retarder system simultaneously.