Volume Determination of Fused Quartz Spheres

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Abstract
The volume determination of fused quartz spheres used for the absolute measurement of the density of water is described. The diameters of the spheres are measured with an optical interferometer, in which the sphere is placed between two parallel étalon plates of accurately known separation, and the diameters are obtained by measuring the gaps between each étalon surface and the sphere. Two wavelengths, 633 nm of a frequency stabilized He-Ne laser and 441 nm of a He-Cd laser, are employed in order to use the method of exact fractions. Details are given of a special arrangement for the interferometer which overcomes the low reflectivity of the surface of the fused quartz. A method to eliminate the spurious effect due to the transparency of the quartz sphere is also described. The diameters (about 85 mm) have been measured with standard deviations of 5 to 12 nm, which correspond to 0.16 to 0.43 ppm in terms of the volume. The total uncertainties of the volume are estimated to be 0.26 to 0.48 ppm.

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