  We derive theoretically an exact relation between Tan's universal contact and
the photo-excitation rate of a strongly interacting Fermi gas, in the case of
optically transferring fermionic pairs to a more tightly bound molecular state.
Our deviation generalizes the relation between Tan's contact and the
closed-channel molecular fraction found earlier by Werner, Tarruell and Castin
in Eur. Phys. J. B \textbf{68}, 401 (2009). We use the relation to understand
the recent low-temperature photo-excitation measurement in a strongly
interacting $^{6}$Li Fermi gas {[}Liu \textit{et al.}, arXiv:1903.12321{]} and
show that there is a reasonable agreement between theory and experiment close
to the unitary limit. We propose that our relation can be applied to accurately
measure Tan's contact coefficient at finite temperature in future experiments.
