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Optical Deformations in Solar Glass Filters for High Precision Astrometry

Measuring the solar diameter at all position angles gives the complete figure of the Sun. Their asphericities have implications in classical physics and general relativity, and the behavior of the optical systems used in the direct measurements is to be known accurately. A solar filter is a plane-parallel glass with given absorption, and here we study the departures from the parallelism of the faces of a crystal slab 5 mm thick, because of static deformations. These deformations are rescaled to the filter's dimensions. Related to the Solar Disk Sextant experiment and to the Reflecting Heliometer of Rio de Janeiro a simplified model of the influences of the inclination between the external and the internal surfaces of a glass solar filter, is discussed.