An analytical method based on the moment generating function (MGF) is proposed for assessing the performance of direct-detection (DD) orthogonal frequency division multiplexing (OFDM) optical receivers with radio-frequency (RF) demodulation. The MGF-based method is a generalization of the method previously reported in the literature for DD baseband OFDM optical receivers. The proposed method relies on the analytical derivation of equivalent filters that describe the combined effect of electrical filtering + RF demodulation + FFT operation + equalizer of the OFDM receiver for the real and imaginary parts of the signal at the equalizer output. The method takes into account imperfections of the RF demodulator, namely power and phase imbalance between the RF demodulator arms and different electrical filtering on its arms. Numerical results show excellent agreement between the bit error probability estimates provided by the proposed method and estimates obtained from Monte Carlo simulation, in the absence and presence of receiver imperfections.