In the current paper, distortions in digital demodulation schemes with harmonic phase modulation for interferometric optical sensors are considered. In particular, the influence of target signal variations on phase demodulation errors is theoretically evaluated. An analytical expression describing the phase error magnitude dependence on the first derivative and mean value of the measured signal and amplitude of the phase modulation in the case of a simple 4-point demodulation algorithm is derived. After that, an approach for synthesizing algorithms with suppressed sensitivity to target signal variations is developed. Based on this approach, a novel 4+1 demodulation algorithm is proposed. It is shown analytically that the demodulation error of the new 4+1 algorithm is proportional to the second derivative of the target signal, and therefore, is typically several orders of magnitude smaller than in the case of the 4-point algorithm. The correspondence between analytical expressions and real phase errors induced by target signal variations is verified by means of numeric simulation.

In the current paper, we have developed an analytical apparatus that allows us to calculate the phase error produced by miscalibration of modulation parameters. The case of harmonic modulation is considered, and the analysis is performed for cases of miscalibration for two parameters: amplitude and start phase. Two demodulation algorithms are considered: a conventional 4-point algorithm, based on an ordinary least-squares approach, and a previously developed 4+1 algorithm with high immunity to phase error, induced by change of target phase on the demodulation interval. Predictions, given by developed analytical equations, are verified by means of numeric modeling.

No abstract

No abstract

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.