  We show that temporal two-photon interference effects involving the signal
and idler photons created by parametric down-conversion can be fully
characterized in terms of the variations of two length parameters--called the
biphoton path-length difference and the biphoton path-asymmetry- length
difference--which we construct using the six different length parameters that a
general two-photon interference experiment involves. We perform an experiment
in which the effects of the variations of these two parameters can be
independently controlled and studied. In our experimental setup, which does not
involve mixing of signal and idler photons at a beam splitter, we further
report observations of Hong-Ou-Mandel- (HOM-)like effects both in coincidence
and in one-photon count rates. As an important consequence, we argue that the
HOM and the HOM-like effects are best described as observations of how
two-photon coherence changes as a function of the biphoton path-
asymmetry-length difference.
