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In this paper, we characterize the impact of laser phase noise (PN) in direct-detection optical OFDM (DDO-OFDM) and identify its many differences from those in coherent optical OFDM (CO-OFDM). The analytical models for the diverse PN effects, including power degradation, phase rotation term (PRT), and inter-carrier interference (ICI), are given in terms of critical system parameters with or without the small PN assumption. In particular, the analytical upper-bound of the ICI power with a simple form is also provided. We also present a bit error rate (BER) estimation approach which is proven to be reliable for an optical signal-to-noise-ratio (OSNR) penalty lower than ~ 2 dB. In addition, the PN tolerances, in terms of OSNR penalty, are also numerically analyzed and discussed with different QAM formats, data rates, laser linewdiths, and subcarrier numbers.