Pfaffian systems and Radon transforms on affine Grassmann manifolds

Mathematische Annalen -     

Analytical Designing of Two-Aspherical-Mirror Anastigmats Permitting Practical Misalignments in a Soft-X-Ray Optics

A new analytical method of designing two-aspherical-mirror anastigmats was developed and applied to searching solution groups of soft X-ray microscopes of a large misalignment tolerance. The two-mirror anastigmat configurations were expressed by a practical variable related to pupil obstruction limiting the system throughput. Axial coma and other aberrations caused by a slight decenter of the system were then formulated to represent sensitivity to misalignment. These formulations enabled a global survey of solution groups as demonstrated by a designing example of soft X-ray microscopes with a magnification m = −1/50, which resulted in four solutions more insensitive to misalignment than a standard Schwarzschild optics in the soft X-ray region. Some solutions were also found to have much larger fields of view suitable for high resolution imaging as confirmed by computer ray tracing.     

Structure and molecular motion of poly(ethylene oxide) chains adsorbed on a silica-tethered poly(methyl methacrylate) by the spin label method

The spin-label method was used to study the structure and molecular motion of poly(ethylene oxide) (PEO) chains adsorbed on a silica-tethered poly(methyl methacrylate) (PMMA). Spin-labelled PEO with a narrow molecular weight distribution, having number averaged molecular weight (M _N)=6.0×10³, was adsorbed on the surface of the silica-tethered PMMA with various grafting ratios in carbon tetrachloride solution at 35?°C. ESR spectra were measured at various temperatures after the samples were completely dried. The ESR spectra are composed of two spectra arising from spin-labels attached to “train” and “tail” segments, which are strongly and weakly interacted with the silica surface, respectively. The fractional amount of the “tail” segments increases extremely with the grafting ratio of PMMA. Molecular mobility of the PEO chains estimated from the temperature dependence of the ESR spectra also decreases significantly with the grafting ratio of PMMA. Structure and molecular motion of the PMMA chains tethered on the silica were also studied using the spin-labelled PMMA. Consequently, parts of the PEO segments penetrate into the PMMA chains and is adsorbed on the silica surface (“train” segments), whereas parts of the PMMA segments protrude from the surface. The other PEO segments are entangled with the tethered PMMA chains (“tail” segments).