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

Abstract

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.

Wavefront spacing and Gouy phase in presence of primary spherical aberration

“…A precise knowledge of the Gouy phase is crucial in a wide variety of metrological techniques. Examples are measurements of acceleration [22], distance [23], refractive indices [24], and volumes [25].…”

Accurate measurements of the Avogadro and Planck constants by counting silicon atoms

“…In this case, the wavefront evolution with beam propagation makes the locally detected phases different from those that would be expected from a geometrical wavefront translation [36]. This phenomenon plays a particular role in the reconstruction of the sphere topography.…”

Realization of the kilogram by the XRCD method

“…Although the sphere should be rotated by a mechanism installed underneath it, this configuration has a strong advantage of being able to optimize the visibility of interference fringes [75]. The fractional fringe order of interference for the gaps between the sphere and the etalon, d 1 and d 2 , is measured by phase-shifting interferometry using optical frequency tuning [14,76], with an optical frequency comb used as the optical frequency standard [57]. This comb is used as the primary length standard of NMIJ.…”