Caustic coordinates in Platzeck-Gaviola test of conic mirrors.
The centers of curvature of all zones of a spherical mirror coincide at the center of that sphere. In the case of all other conies of revolution, however, the radii of curvature of dif­ ferent zones have different magnitudes; hence their centers of curvature do not coincide but lie along the caustic curve, as shown by Wadsworth. Based on this property Platzeck and Gaviola devised a test to measure the shape of a para­ boloid being figured. What they do is to measure the posi­ tions of the centers of curvature of different regions in the optical surface, then the results are compared with the theo­ retical values. The theoretical positions of these centers of curvature for a paraboloid are computed with two simple formulas given by Schroader, but to our knowledge the ex­ pressions for any conic of revolution have not been given. To derive the expressions for the caustic coordinates (η,ξ) of the centers of curvature of the conic surface (see Fig. 1), we
Profile measurement of a conic surface, using a He-Ne laser and a nodal bench.
A method of measuring the profile along one diameter of a conic surface is presented. Using some well-known formulas for the conic sections, useful mathematical relations are derived that, together with a simple experimental setup can be used for comparing theoretical and real values of the sagitta of the surface.
Resonant Auger decay study of C1s -> pi* core-excited OCS
The present work aims at characterizing short-lived C1s((-1)) pi*((1)) core-excited states of the OCS molecule based on the analysis of the vibrational fine structure and lineshape profiles of the high-resolution resonant Auger decay spectra recorded at the excitation energies along the C1s -> pi* resonance in the binding energy region 15-19eV. Very different behavior in terms of lineshape and resonant enhancement is observed for the (A) over tilde, (B) over tilde and (C) over tilde final states. This is explained by (1) the variation in the C-O bond lengths for the states involved in the electronic relaxation and (2) different contributions in terms of Mulliken population to the molecular orbitals determining the electronic character of the corresponding states. Since the final-state geometries are known from a number of previous experiments and ab initio calculations, the geometry of the C1s((-1)) pi*((1)) intermediate states can be predicted in analogy with e.g. the N-2, CO2 and N2O molecules. (C) 2009 Elsevier B.V. All rights reserved. (Less)