X-ray transmission phase palates are described based on the dynamical theory of X-ray diffraction. Polarization-tunable X-ray optics using transmission phase plates for synchrotron radiation (SR) were proposed and were used to transform horizontal polarization of SR to circular or vertical polarization at a bending-magnet beamline, BL-15C at the Photon Factory (PF) . Combination of x-ray transmission phase plates and X-ray polarization analyzer enabled us to determine full state of polarization in the X-ray spectral region. With this polarization analysis method, polarizations of X-rays from an elliptical multipole wiggler installed on BL-28 at the PF were successfully estimated.