Precision spectroscopy of the A²Π←X²Σ⁺ transition in BaF

High-resolution spectroscopy on the (Formula presented.) electronic system of (Formula presented.) is performed using a cold molecular beam produced by a buffer gas source. The hyperfine structure in both (Formula presented.)  ground and (Formula presented.)  excited states is fully resolved and absolute transition frequencies of individual components are measured at the sub-MHz level making use of frequency-comb laser calibration. Sets of molecular constants for the (Formula presented.) and (Formula presented.) levels are determined, with improved accuracy for the (Formula presented.) band origins and spin-orbit interaction constants for the (Formula presented.)  excited states, that represent the presently measured highly accurate transitions for low-J states as well as previously determined transition frequencies in Fourier-transform emission studies for rotational levels as high as (Formula presented.). The extracted molecular constants reproduce the measured transition frequencies at the experimental absolute accuracy of 1 MHz. The work is of relevance for future laser cooling schemes, and is performed in the context of a measurement of the electron dipole moment for which BaF is a target system.