Abstract We demonstrate a method to determine the longitudinal phase-space distribution of a cryogenic buffer gas cooled beam of barium-fluoride molecules based on a two-step laser excitation scheme. Temporal resolution is achieved by a transversely aligned laser beam that drives molecules from the ground state $X^2\Sigma^+$ to the $A^2\Pi_{1/2}$ state around 860\;nm, while the velocity resolution is obtained by a laser beam that is aligned counter-propagating with respect to the molecular beam and that drives the Doppler shifted $A^2\Pi_{1/2}$ to $D^2\Sigma^+$ transition around 797\;nm. Molecules in the $D$-state are detected background-free by recording the fluorescence from the $D-X$ transition at 413 nm. A temporal resolution of 11\;$\upmu$s and a velocity resolution of 6\;m/s is obtained. In order to calibrate the absolute velocity, we have determined the Doppler free transition frequencies for the $X-A$ and $X-D$ transitions with an absolute accuracy below 0.3\;MHz. The high resolution of the phase-space distributions allows us to observe a variation of the average velocity and velocity spread over the duration of the molecular beam pulse. Our method hence gives valuable insight into the dynamics in the source.
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