An X-ray double phase retarder system composed of two transmission-type phase retarders is proposed and developed in order to compensate for off-axis aberration (phase-shift inhomogeneity due to angular divergence of incident X-rays). The scattering planes of the two phase retarders are set to be inclined by 45 degrees with respect to the plane of incident polarization, but the two phase retarders give Bragg reflections in opposite directions. By using this X-ray optical system, vertically polarized X-rays with a 0.99 degree of linear polarization were obtained from horizontally polarized synchrotron radiation with a horizontal beam divergence of 20 arcsec (0.1 mrad). This value is favorably compared with the value of 0.87 which was obtained using a conventional single phase retarder of identical total thickness, 627 microns. The comparison was made at the nickel K-absorption edge (8333 eV) with the condition that 47% of incident X-rays were transmitted through the two phase retarder crystals. The crystals were (100)-oriented diamond plates giving asymmetric 111 Laue reflections.

X-ray polarization-contrast images resulting from X-ray linear dichroism (XLD) in the hard X-ray region have been successfully recorded for the first time. The apparatus used consisted of an X-ray polarizer, double X-ray phase retarders and a high-spatial-resolution X-ray charge-coupled device (CCD) detector. The sample used was a hexagonal close packed (h.c.p.) cobalt single-crystal foil of thickness about 12 microm. The experiment was performed at X-ray energies of 23 and 29 eV above the cobalt K edge (7709 eV), at which the maximum linear dichroisms (approximately 3%) were observed, with their signs reversed, in the XLD spectrum measured with quadruple X-ray phase retarders. The contrasts in the images at the two X-ray energies were reversed as a result of the XLD in the sample. Furthermore, the values of the contrast in the images arising from the linear dichroism (approximately 3%) were in good agreement with those yielded by the XLD spectrum.

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 transmissiontype X-ray four-quadrant phase-retarder system is proposed that can compensate for both off-axis and chromatic aberrations. The X-ray fourquadrant 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 HH angular divergence (FWHM) of incident X-rays, the X-ray fourquadrant 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.

X-ray polarization-contrast images resulting from X-ray magnetic circular dichroism (XMCD) in the hard X-ray region have been successfully recorded for the first time. The apparatus used consisted of an X-ray polarizer, double X-ray phase retarders, and a high-spatial-resolution X-ray charge-coupled-device detector. The sample used was a hexagonal-close-packed cobalt polycrystal foil having a thickness of about 4 microns. The X-ray polarization-contrast image resulting from XMCD was observed at a photon energy of 10 eV above the cobalt K-absorption edge (7709 eV). The observed contrast in the image was reversed by inversion of the magnetic field. Furthermore, the contrast was reversed again at a photon energy of 32 eV above the cobalt K-absorption edge.

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