Interferometric techniques are widely used for interrogation of various optical sensors. Techniques utilizing harmonic auxiliary phase modulation are of special interest from a practical point of view, as they do not require a large bandwidth and dynamic range of a phase modulator, yet are capable of accurately demodulating target phase signals when jointed with proper demodulation algorithms. The current paper presents a universal theoretical apparatus aimed at estimating the influence of the noise of an interference signal on noise of the demodulated phase. Two demodulation algorithms developed in our previously published paper [Appl. Opt. 56, 7960 (2017)APOPAI0003-693510.1364/AO.56.007960] are analyzed in terms of their susceptibility to additive noise. By comparing the obtained results with the Cramer–Rao bound, optimal conditions for these algorithms are found.