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.