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Abstract In this paper, we provide a fairly standard derivation of the power spectrum of photocurrent and limited displacement resolution of laser heterodyne detection system. And the phase noise with different oscillation lineshapes of the heterodyne detection system is discussed. Based on the one-dimensional probability distribution model of phase noise, the minimum resolvable displacement and noise-equivalent mean square displacement are established, which represent the minimum detectable amplitude and noise limited resolution respectively. According to the numerical results, we obtain the variation of displacement resolution against the key parameters including the laser wavelength, the detection distance, the laser linewidth and the signal power. It reveals that the phase fluctuation has a significant effect on the power spectrum of photocurrent. Besides, both the probability density distribution of phase noise and displacement resolution have heavy dependence on laser oscillation lineshapes. And the noise-equivalent mean square displacement is inversely proportional to the root-mean-square of a measurable light power. The noise-equivalent mean square displacement can reach 3. 5 × 1 0 − 15 m ∕ Hz under the given parameters. Our findings provide a quantitative reference for the displacement resolution and engineering application of the heterodyne detection. [ABSTRACT FROM AUTHOR]

We present an ameliorated arctangent algorithm based on phase-locked loop for digital Doppler signal processing, utilized within the heterodyne detection system. We define the error gain factor given by the approximation of Taylor expansion by means of a comparison of the measured values and true values. Exact expressions are derived for the amplitude error of two in-phase & quadrature signals and the frequency error of the acousto-optic modulator. Numerical simulation results and experimental results make it clear that the dynamic instability of the intermediate frequency signals leads to cumulative errors, which will spiral upward. An improved arctangent algorithm for the heterodyne detection is proposed to eliminate the cumulative errors and harmonic components. Depending on the narrow-band filter, our experiments were performed to realize the detectable displacement of 20 nm at a detection distance of 20 m. The aim of this paper is the demonstration of the optimized arctangent algorithm as a powerful approach to the demodulation algorithm, which will advance the signal-to-noise ratio and measurement accuracy of the heterodyne detection system. [ABSTRACT FROM AUTHOR]