  In a recent article, we have shown how quantum fluctuations of the background
geometry modify Hawking's density matrix for black hole (BH) radiation.
Hawking's diagonal matrix picks up small off-diagonal elements whose influence
becomes larger with the number of emitted particles. We have calculated the
"time-of-first-bit", when the first bit of information comes out of the BH, and
the "transparency time", when the rate of information release becomes order
unity. We have found that the transparency time is equal to the "Page time",
when the BH has lost half of its initial entropy to the radiation, in agreement
with Page's results. Here, we improve our previous calculation by keeping track
of the time of emission of the Hawking particles and their back-reaction on the
BH. Our analysis reveals a new time scale, the radiation "coherence time",
which is equal to the geometric mean of the evaporation time and the light
crossing time. We find, as for our previous treatment, that the
time-of-first-bit is equal to the coherence time, which is much shorter than
the Page time. But the transparency time is now much later than the Page time,
just one coherence time before the end of evaporation. Close to the end, when
the BH is parametrically of Planckian dimensions but still large, the coherence
time becomes parametrically equal to the evaporation time, thus allowing the
radiation to purify. We also determine the time dependence of the entanglement
entropy of the early and late-emitted radiation. This entropy is small during
most of the lifetime of the BH, but our qualitative analysis suggests that it
becomes parametrically maximal near the end of evaporation.
