  We explore the absorption and scattering properties of one dimensional
parity-time ($\mathcal{PT}$)-symmetric photonic crystal. In addition to the
familiar transmittance and reflectance, we give the definition of the
generalized absorptance to include the amplifying effect of the dielectric with
negative imaginary part of the permittivity, moreover, we present the
mathematical expressions of the transmittance, reflectances and absorptances
from both sides of this photonic crystal with N periods in terms of the
elements of the transfer matrix of the primitive cell. The complex band
structure of this photonic crystal is studied and the corresponding evolutions
of the exceptional points, $\mathcal{PT}$-exact phase and $\mathcal{PT}$-broken
phase are disclosed. Near the exceptional points, we find some singular
behaviors, the transmittance and reflectances from both sides are all greater
than one and even all reach large values at the same time, then the
corresponding absorptances from both sides are negative. In the band gap, the
transmittance is zero, the reflectance form one side can be very large, while
the reflectance from the other side is very small, we call this phenomenon
unidirectional weak visibility. We believe that these phenomena are very
beneficial for the design of the optical devices.
