The relation between the phase shift and the mean optical power (MOP) output from a delay-line interferometer (DLI) port applied for phase-shift keying (PSK) signal demodulation is proven of a cosine law irrelevant to signal modulation condition. The variation amplitude of the MOP is proportional to the transition duration of the modulation pulses. This phenomenon is interpreted as the result of the statistical and waveform characteristics of the PSK. The conclusions verified by simulation and experiment are generalized to other modulation formats and then applied to phase detuning monitoring, delay time judgment of DLI, and independence of modulation data assessment.OCIS codes: 060.5060, 120.3180, 070.1170. doi: 10.3788/COL201210.070601. Delay-line interferometer (DLI) has been widely used in optical communication to demodulate phase-shift keying (PSK) signal for direct detection by converting the optical phase information to amplitude [1,2] . The phase shift of DLIs greatly affects the quality of the demodulated signal, that is, minor phase shift detuning results in an eye opening closing, lowered noise tolerance, and increased bit error ratio (BER) [3,4] . These deteriorations become more severe in the case of multi-level modulation formats. The tolerable phase shift detuning effects at a 1-dB optical signal-to-noise ratio (OSNR) penalty are about 16 • and 6 • for differential PSK (DPSK) and differential quadrature PSK (DQPSK) formats, respectively [4] . Such a stringent requirement puts a great challenge on the design, manufacturing, and packaging of the DLI-based demodulators. Precise temperature control combined with athermal package is required to stabilize the phase shift [5] ; however, long term stabilization cannot be guaranteed due to device aging and control circuit operation drifting. Consequently, an effective way for phase shift detuning monitoring is necessary. Some proposed approaches include the engineeringoriented BER monitoring [6] , optical frequency dithering [7,8] , phase dithering [9] , pilot insertion [10,11] , and two-dimensional waveform analysis [12] . However, they are more or less inefficient or unpractical. The BER approach needs a forward error correction module operating at the bit rate, which is difficult for high data rate. Moreover, this approach is unable to differentiate the mixed impairments induced by many factors, such as chromatic dispersion (CD), polarization mode mode dispersion (PMD), and noise. The frequency dithering cannot be applied to the modules manufactured by different vendors as they obey different private protocols. Pilot insertion demands a change of the current transponder structure. Meanwhile, the perturbation-free schemes are preferred for its simplicity and adaptability.In this letter, we treat the PSK signal itself as a probe signal, through which we study the influence on the output signal given by DLI phase shift detuning. The mean optical power (MOP) output from one DLI port varies with the phase shift in the form of a cosine, which is irrelevan...