  We report on a novel bichromatic fluorescent imaging scheme for
background-free detection of single CaF molecules trapped in an optical tweezer
array. By collecting fluorescence on one optical transition while using another
for laser-cooling, we achieve an imaging fidelity of 97.7(2)% and a
non-destructive detection fidelity of 95.5(6)%. We characterize loss mechanisms
of our scheme, many of which are generically relevant to the fluorescent
detection of trapped molecules, including two-photon decay and admixtures of
higher excited states that are induced by the trapping light.
