  Multiphoton interference is an important phenomenon in modern quantum
mechanics and experimental quantum optics, and it is fundamental for the
development of quantum information science and technologies. Over the last
three decades, several theoretical and experimental studies have been performed
to understand the essential principles underlying such interference and to
explore potential applications. Recently, the two-photon interference (TPI) of
phase-randomized weak coherent states has played a key role in the realization
of long-distance quantum communication based on the use of classical light
sources. In this context, we investigated TPI experiments with weak coherent
pulses at the single-photon level and quantitatively analyzed the results in
terms of the single- and coincidence-counting rates and one- and two-photon
interference-fringe shapes. We experimentally examined the Hong-Ou-Mandel-type
TPI of phase-randomized weak coherent pulses to compare the TPI effect with
that of correlated photons. Further experiments were also performed with two
temporally- and spatially separated weak coherent pulses. Although the observed
interference results, including the results of visibility and fringe shape, can
be suitably explained by classical intensity correlation, the physics
underlying the TPI effect needs to be interpreted as the interference between
the two-photon states at the single-photon level within the utilized
interferometer. The results of this study can provide a more comprehensive
understanding of the TPI of coherent light at the single-photon level.
