X-ray four-quadrant diamond phase-retarder system to compensate for off-axis and chromatic aberrations

An X-ray transmission-type double phase-retarder system that can compensate for off-axis aberration (phase-shift inhomogeneity due to angular divergence of incident X-rays) has been developed and its advantage over a conventional single transmission-type X-ray phase retarder was demonstrated. However, it was noticed that the transmission-type X-ray phase retarder suffers from not only off-axis aberration but also chromatic aberration (phase-shift inhomogeneity due to energy spread of incident X-rays). In this paper, a transmission-type X-ray four-quadrant phase-retarder system is proposed that can compensate for both off-axis and chromatic aberrations. The X-ray four-quadrant phase-retarder system is composed of four transmission-type X-ray phase retarders. The scattering planes of four phase-retarder diamond crystals are set to be inclined by 45 degree, 135 degree (= 45 degree + 90 degree), 225 degree (= 45 degree + 180 degree) and 315 degree (= 45 degree + 270 degree), respectively, with respect to the plane of incident polarization. Under the conditions of 7709 eV photon energy, 1.5 eV energy spread and 45" angular divergence (FWHM) of incident X-rays, the X-ray four-quadrant phase-retarder system created 0.98 degree of vertical-linear polarization from horizontal-linear polarization. This value was favorably compared to 0.89 and 0.96, which were obtained by the single and double phase-retarder systems, respectively. The principle of the X-ray four-quadrant phase-retarder system will be described together with its advantage over the single and double phase-retarder systems.