Measuring the second order correlation function and the coherence time using random phase modulation

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.