  Fluorescence-detected Fourier transform (FT) spectroscopy is a technique in
which the relative paths of an optical interferometer are controlled to excite
a material sample, and the ensuing fluorescence is detected as a function of
the interferometer path delay and relative phase. A common approach to enhance
the signal-to-noise ratio in these experiments is to apply a continuous phase
sweep to the relative optical path, and to detect the resulting modulated
fluorescence using a phase-sensitive lock-in amplifier. In many important
situations, the fluorescence signal is too weak to be measured using a lock-in
amplifier, so that photon counting techniques are preferred. Here we introduce
an approach to low-signal fluorescence-detected FT spectroscopy, in which
individual photon counts are assigned to a modulated interferometer phase
('phase-tagged photon counting,' or PTPC), and the resulting data are processed
to construct optical spectra. We studied the fluorescence signals of a
molecular sample excited resonantly by a pulsed coherent laser over a range of
photon flux and visibility levels. We compare the performance of PTPC to
standard lock-in detection methods and establish the range of signal parameters
over which meaningful measurements can be carried out. We find that PTPC
generally outperforms the lock-in detection method, with the dominant source of
measurement uncertainty being associated with the statistics of the finite
number of samples of the photon detection rate.
