  Time-resolved photon-counting plays an indispensable role in precision
metrology in both classical and quantum regimes. In particular, time-correlated
single-photon counting (TCSPC) has been the key enabling technology for
applications such as low-light fluorescence lifetime spectroscopy and photon
counting time-of-flight (ToF) 3D imaging. However, state-of-the-art TCSPC
single-photon timing resolution (SPTR) is limited in the range of 10-100 ps by
the available single-photon detector technology. In this paper, we
experimentally demonstrate a time-magnified TCSPC (TM-TCSPC) that achieves an
unprecedentedly short SPTR of 550 fs for the first time with an off-the-shelf
single-photon detector. The TM-TCSPC can resolve ultrashort pulses with a
130-fs pulsewidth difference at a 22-fs accuracy. When applied to photon
counting ToF 3D imaging, the TM-TCSPC greatly suppresses the range walk error
that limits all photon counting ToF 3D imaging systems by 99.2 % (130 times)
and thus provides unprecedentedly high depth measurement accuracy and precision
of 26 {\mu}m and 3 {\mu}m, respectively.
