# Signal detection algorithms for interferometric sensors with harmonic phase modulation: distortion analysis and suppression

## TL;DR

This paper analyzes distortions in digital demodulation for interferometric sensors with harmonic phase modulation, deriving expressions for phase errors and proposing a new algorithm that significantly reduces sensitivity to target signal variations.

## Contribution

It introduces a novel 4+1 demodulation algorithm that minimizes phase errors caused by target signal variations, improving accuracy over traditional methods.

## Key findings

- Analytical expression for phase error dependence on signal derivatives.
- The 4+1 algorithm's error is proportional to the second derivative of the target signal.
- Numerical simulations confirm reduced phase errors with the new algorithm.

## Abstract

In 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 first derivative and mean value of measured signal and amplitude of the phase modulation in case of 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 new 4+1 algorithm is proportional to the second derivative of target signal, and therefore, is typically several orders of magnitude smaller than in case of 4-point algorithm. The correspondence between analytical expressions and real phase errors, induced by target signal variations is verified by means of numeric simulation.

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Source: https://tomesphere.com/paper/1904.13139