Absolute frequency measurements of the $D_1$ lines in $^{39}K, ^{85}Rb,$ and $^{87}Rb$ with $\sim$ 0.1 ppb uncertainty

We report values for the $D_1$-line frequencies with 0.13 ppb uncertainty in the alkali atoms $^{39}K, ^{85}Rb,$ and $^{87}Rb.$ The frequencies are measured using an evacuated ringcavity resonator whose length is calibrated against a reference laser locked to the $D_2$ line in $^{87}Rb.$ The measured frequencies, along with sub-ppb measurement of the atomic masses reported previously, form important links in a possible high-precision determination of the fine-structure constant using the photon-recoil shift measured in an atom interferometer. We also obtain, with improved precision, the hyperfine-coupling constants in the $P_{1/2}$ state of these atoms, and the fine-structure interval in the 5P state of Rb