We investigate the effects of link parameters and the channel correlation coefficient on the detection threshold, Q-factor, and bit-error-rate (BER) of a free-space optical system employing a differential signaling scheme. In systems employing differential signaling schemes, the mean value of the signal is used as the detection threshold level, provided that differential links are identical or highly correlated. However, in reality, the underlying links are not essentially identical and have a low level of correlation. To show the significance of the link parameters as well as the correlation coefficient, we derive analytical relations describing the effect of weak turbulence and we determine the improvement of Q-factor with the channel correlation. Further, for the same signal-to-noise ratio, we demonstrate that a link with a higher extinction ratio offers improved performance. We also propose a closed-form expression of the system BER. We present experimental results showing improved Q-factor for the correlated channel case compared to the uncorrelated channel.