Design of a Cell-Based Refractometer with Small End-Effects

In cell-based laser refractometers, interferometer pathlength uncertainty introduced by deformation and stress in the windows through which the beams pass can be the chief factor limiting measurement accuracy. The fractional contribution of pathlength uncertainty to our recent determination of the Boltzmann constant was ${9.8\times 10}^{-6}$ , and more than two times larger than the next largest uncertainty component. We briefly describe the error, and propose a design in which cell window effects contribute less than $3\times 10^{-6}$ fractional error to the measurement of helium refractivity; performance that would be competitive with state-of-the-art primary thermometry and barometry.