In this paper, the performance of multiple-bit delay detection (MBDD) systems in optical differential phase shift keying (DPSK) is investigated. Assuming that the dominant noise in the system is originated by the optical amplifier and using Gaussian approximation, we present a closed form equation which predicts the overall bit-error-rate (BER) performance of the system as a function of the number of delay segments, optical signal-to-noise ratio (OSNR) at the receiver, and bandwidth of the optical bandpass filter. It is shown that with a large number of delay segments, the performance of MBDD system approaches to the performance of homodyne coherent detection.