  Building on the recent experimental achievements obtained with scanning
electron microscopy on ultracold atoms, we study one-dimensional Bose gases in
the crossover between the weakly (quasi-condensate) and the strongly
interacting (Tonks-Girardeau) regime. We measure the temporal two-particle
correlation function and compare it with calculations performed using the Time
Evolving Block Decimation algorithm. More pronounced antibunching is observed
when entering the more strongly interacting regime. Even though this mimics the
onset of a fermionic behavior, we highlight that the exact and simple duality
between 1D bosons and fermions does not hold when such dynamical response is
probed. The onset of fermionization is also reflected in the density
distribution, which we measure \emph{in situ} to extract the relevant
parameters and to identify the different regimes. Our results show agreement
between experiment and theory and give new insight into the dynamics of
strongly correlated many-body systems.
