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Phase corrections in the optical interferometer for Si sphere volume measurements at NMIJ

To determine the volume of solid density standards, manufactured as Si-crystal spheres, an optical interferometer is used to measure their diameter at the NMIJ. To support and complement these measurements, the effect of the Gouy phase has been studied analytically and numerically. In measurement, the sphere is placed between the end-mirrors of a Fizeau cavity and the distances between the cavity mirrors and the sphere are measured, as well as the cavity length. The present analysis outlines a model of the interferometer operation and quantifies the Gouy-phase correction in the diameter measurement.