  A new approach to measure the second order correlation function $g^{(2)}$ and
the coherence time was investigated. The $g^{(2)}$ was calculated from the
photon pair time interval distribution by direct numerical self-convolution
with the high order correction. The accuracy of this method was examined using
an optical fiber based Hanbury-Brown-Twiss interferometer with a pseudo-thermal
light source. We found that the significance of the high order correction is
related to the factor $\bar{I}\tau_{c}$, which is the overlapping of the photon
wave packets. A novel technique was also demonstrated to measure the coherence
time $\tau_c$ of a light source using the random phase modulation. In
comparison with the conventional self-heterodyne detection, this method is more
suitable for a weak light source with a long coherence time.
