  Exact measurement of the second-order correlation function $g^{(2)}(t)$ of a
light source is essential when investigating the photon statistics and the
light generation process of the source. For a stationary single-mode light
source, Mandel Q factor is directly related to $g^{(2)}(t)$. For a large mean
photon number in the mode, the deviation of $g^{(2)}(t)$ from unity is so small
that even a tiny error in measuring $g^{(2)}(t)$ would result in an inaccurate
Mandel Q. In this work, we have found that detector dead time can induce a
serious error in $g^{(2)}(t)$ and thus in Mandel Q in those cases even in a
two-detector configuration. Our finding contradicts the conventional
understanding that detector dead time would not affect $g^{(2)}(t)$ in
two-detector configurations. Utilizing the cavity-QED microlaser, a
well-established sub-Poissonian light source, we measured $g^{(2)}(t)$ with two
different types of photodetectors with different dead time. We also introduced
prolonged dead time by intentionally deleting the photodetection events
following a preceding one within a specified time interval. We found that the
observed Q of the cavity-QED microlaser was underestimated by 19% with respect
to the dead-time-free Q when its mean photon number was about 600. We derived
an analytic formula which well explains the behavior of the $g^{(2)}(t)$ as a
function of the dead time.
