  We theoretically and experimentally investigate the optimal conditions for
the Bell experiment using spontaneous parametric down conversion (SPDC)
sources. In theory, we show that relatively large average photon number
(typically $\sim$0.5) is desirable to observe the maximum violation of the
Clauser-Horne-Shimony-Holt (CHSH) inequality. In experiment, we perform the
Bell experiment without postselection using polarization entangled photon pairs
at 1550 nm telecommunication wavelength generated from SPDC sources. While the
violation of the CHSH inequality is not directly observed due to the overall
detection efficiencies of our system, the experimental values agree well with
those obtained by the theory with experimental imperfections. Furthermore, in
the range of the small average photon numbers ($\leq0.1$), we propose and
demonstrate a method to estimate the ideal CHSH value intrinsically contained
in the tested state from the lossy experimental data without assuming the input
quantum state.
