  We demonstrate lineshape measurement of an extreme-weak amplitude fluctuating
light source by using the photon-counting-based second-order correlation
spectroscopy combined with the heterodyne technique. The amplitude fluctuation
of a finite bandwidth introduces a low-lying spectral structure in the
lineshape and thus its effect can be isolated from that of the phase
fluctuation. Our technique provides extreme sensitivity suited for
single-atom-level applications.
