  We observed the Crab pulsar in October 2008 at the Copernico Telescope in
Asiago - Cima Ekar with the optical photon counter Aqueye (the Asiago Quantum
Eye) which has the best temporal resolution and accuracy ever achieved in the
optical domain (hundreds of picoseconds). Our goal was to perform a detailed
analysis of the optical period and phase drift of the main peak of the Crab
pulsar and compare it with the Jodrell Bank ephemerides. We determined the
position of the main peak using the steepest zero of the cross-correlation
function between the pulsar signal and an accurate optical template. The pulsar
rotational period and period derivative have been measured with great accuracy
using observations covering only a 2 day time interval. The error on the period
is 1.7 ps, limited only by the statistical uncertainty. Both the rotational
frequency and its first derivative are in agreement with those from the Jodrell
Bank radio ephemerides archive. We also found evidence of the optical peak
leading the radio one by ~230 microseconds. The distribution of phase-residuals
of the whole dataset is slightly wider than that of a synthetic signal
generated as a sequence of pulses distributed in time with the probability
proportional to the pulse shape, such as the average count rate and background
level are those of the Crab pulsar observed with Aqueye. The counting
statistics and quality of the data allowed us to determine the pulsar period
and period derivative with great accuracy in 2 days only. The time of arrival
of the optical peak of the Crab pulsar leads the radio one in agreement with
what recently reported in the literature. The distribution of the phase
residuals can be approximated with a Gaussian and is consistent with being
completely caused by photon noise (for the best data sets).
