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In order to develop lightweight and high angular resolution x-ray mirrors, we have investigated hot plastic deformation of 4 in. silicon (111) wafers. A sample wafer was deformed using hemispherical dies with a curvature radius of 1000 mm. The measured radius of the deformed wafer was 1030 mm, suggesting that further conditioning is indispensable for better shaping. For the first time to our knowledge, x-ray reflection on a deformed wafer was detected at A1 [K.sub.a] 1.49keV. An estimated surface roughness of OCIS codes: 340.7470, 350.1260, 170.3890.

We present a detailed study of the performance of the Astro-E x-ray telescope (XRT) onboard the Astro-E satellite. As described in preceding papers the ground-based calibrations of the Astro-E XRT revealed that its image quality and effective area are somewhat worse than that expected from the original design. Conceivable causes for such performance degradation are examined by x-ray and optical microscopic measurements at various levels, such as individual reflectors, sectors, and quadrants of the XRT and their alignments. We can attribute, based on detailed measurements, the degradation of the image quality to a slope error in the individual reflectors and the positioning error of reflectors. As for the deficit of the effective area, the shadowing of x rays within the XRT body is the dominant factor. Error budgets for the performance degradation of the Astro-E XRT are summarized. The ray-tracing simulator, which is needed to construct the response function for arbitrary off-axis angles and spatial distributions of any celestial x-ray sources, has been developed and tuned based on the results of detailed measurements. The ray-tracing simulation provides results that are consistent within 3% with the real measurement except for large off-axis angles and higher energies. We propose, based on knowledge obtained from all the measurements and simulations, several plans for future developments to improve the performance of the nested thin-foil mirrors. OCIS codes: 340.0340, 340.7440, 340.7470, 340.7480.

X-ray characterization measurements of the x-ray telescope (XRT) onboard the Astro-E satellite were carried out at the Institute of Space and Astronautical Science (Japan) x-ray beam facility by means of a raster scan with a narrow x-ray pencil beam. The on-axis half-power diameter (HPD) was evaluated to be 1.8'-2.2', irrespective of the x-ray energy. The on-axis effective areas of the XRTs for x-ray imaging spectrometers (XISs) were approximately 440, 320, 240, and 170 [cm.sup.2] at energies of 1.49, 4.51, 8.04, and 9.44 keV, respectively. Those of the x-ray spectrometer (XRS) were larger by 5-10%. The replication method introduced for reflector production significantly improved the imaging capability of the Advanced Satellite for Cosmology and Astrophyics (ASCA) XRT, whose HPD is ~3.6'. The increase in the effective area by a factor of 1.5-2.5, depending upon the x-ray energy, compared with that of the ASCA, was brought about by mechanical scale up and longer focal lengths. The off-axis HPDs were almost the same as those obtained on the optical axis. The field of view is defined as the off-axis angle at which the effective area becomes half of the on-axis value. The diameter of the field of view was ~19' at 1.49 keV, decreasing with increasing x-ray energy, and became ~13' at 9.44 keV. The intensity of stray light and the distribution of this kind of light on the focal plane were measured at the large off-axis angles 30' and 60'. In the entire XIS field of view (25.4 mm x 25.4 mm), the intensity of the stray light caused by a pointlike x-ray source became at most 1% of the same pointlike source that was on the optical axis. OCIS codes: 340.0340, 340.7440, 340.7470, 340.7480.

X-ray telescopes (XRT's) of nested thin foil mirrors are developed for Astro-E, the fifth Japanese x-ray astronomy satellite. Although the launch was not successful, the design concept, fabrication, and alignment procedure are summarized. The main purpose of the Astro-E XRT is to collect hard x rays up to 10 keV with high efficiency and to provide medium spatial resolution in limited weight and volume. Compared with the previous mission, Advanced Satellite for Cosmology and Astrophysics (ASCA), a slightly longer focal length of 4.5-4.75 m and a larger diameter of 40 cm yields an effective area of 1750 [cm.sup.2] at 8 keV with five telescopes. The image quality is also improved to 2-arc min half-power diameter by introduction of a replication process. Platinum is used instead of gold for the reflectors of one of the five telescopes to enhance the high-energy response. The fabrication and alignment procedure is also summarized. Several methods for improvement are suggested for the reflight Astro-E II mission and for other future missions. Preflight calibration results will be described in a forthcoming second paper, and a detailed study of images will be presented in a third paper. [C] 2001 Optical Society of America OCIS codes: 340.7440, 340.7470, 340.7480.