【摘要】 基于传统外差探测相位敏感光时域反射计（Φ-OTDR）的解析模型，构建了包含光学预放大环节的外差探测Φ-OTDR系统的信噪比与解调相位精度的理论模型，并通过实验加以验证。结果表明：所提出的模型能够定量预测光学预放大增益对系统信噪比和解调相位精度的影响，为实现低功耗、高性能系统提供了增益优化的理论依据。该研究进一步表明，光学预放大方案对系统性能的提升效果取决于光电探测器的噪声特性。仅当系统加性噪声占主导地位，且热噪声与散粒噪声的方差比K大于特定阈值（典型值约为0.44）时，引入预放大掺铒光纤放大器（EDFA）才能提升系统性能，从而为工程实践提供了系统设计判据。更多还原

【Abstract】 Objective Phase-sensitive optical time-domain reflectometry（Φ-OTDR） is a distributed fiber sensing technology that exploits the phase information of Rayleigh backscattering（RBS） to detect longitudinal strain with high sensitivity. The signal-to-noise ratio（SNR） is a critical metric that governs the overall performance of a Φ-OTDR system. Optical pre-amplification using an erbium-doped fiber amplifier（EDFA） has been shown to enhance SNR by amplifying weak RBS signals; however, this process inevitably introduces amplified spontaneous emission（ASE） noise. Although prior studies have demonstrated SNR improvement with pre-amplification in chirped-pulse Φ-OTDR systems employing both direct and heterodyne detection, these investigations considered only additive noise sources—such as thermal and shot noise—without adequately accounting for phase noise. To date, a comprehensive and universal model capable of predicting whether pre-amplification consistently enhances phase precision based solely on device parameters remains lacking. This study aims to develop a theoretical framework for heterodyne-detection Φ-OTDR systems incorporating optical preamplification, validate this framework experimentally, and provide theoretical guidance for optimizing amplifier gain to achieve highperformance sensing with low power consumption.Methods In this paper, a heterodyne detection Φ-OTDR system is employed with two schemes: scheme A（conventional）, in which RBS light directly enters the photodetector, and scheme B（pre-amplified）, in which RBS light is pre-amplified by an EDFA before detection. Theoretical analysis establishes SNR models for both systems. For the conventional system, the SNR is expressed as a function of RBS power and the ratio K between thermal and shot noise variances. For the pre-amplified system, the model incorporates additional ASE-related noise components, including local-ASE noise, signal-ASE noise, and ASE-ASE noise. The optimal EDFA gain（GM） that maximizes SNR is analytically derived, and the optimal gain range is extended using a 1 dB SNR tolerance. Subsequently, the demodulated phase precision is modeled by combining contributions from additive noise(σ_φ-a) and phase noise(σ_φ-p) dependent on laser linewidth. A discriminant criterion comparing K with ηF-1（where η is the quantum efficiency and F is the EDFA noise figure） is derived to determine whether pre-amplification enhances system performance. Finally, using a single-pulse heterodyne-detection Φ-OTDR system as an example, experiments are performed to validate the aforementioned analyses. Experimental validation employs two lasers with linewidths of approximately 80 Hz and 1.5 kHz, three OLO power levels（11 dBm, 7 dBm, and -1 dBm） corresponding to K values of 0.19, 0.48, and 3.05, and various pre-amplification gains.Results and Discussions The theoretical SNR model was comprehensively validated through experiments. At three distinct OLO power levels, experimental SNR agreed well with theoretical predictions（Fig. 5）. Comparison between conventional and preamplified schemes revealed three scenarios. 1) When K = 0.19（P_L= 11 dBm）, pre-amplification degraded SNR. 2) When K = 0.48（P_L= 7 dBm）, SNR remained nearly unchanged. 3) When K = 3.05（P_L=-1 dBm）, pre-amplification significantly improved SNR. These results confirm that comparing K with ηF-1（typically ～0.44） determines whether pre-amplification is beneficial: it is effective only when K > ηF-1. For phase precision analysis in low phase noise scenarios（80 Hz linewidth）, experimental results matched theoretical predictions incorporating both additive and phase noise. The theoretical phase precision ■ ratios were 1.10, 0.99, and 0.60 for K = 0.19, 0.48, and 3.05, respectively, quantitatively confirming the discriminant’s accuracy. Furthermore, when the gain was reduced from the optimal 24.8 dB to 10 dB at K = 3.05, phase precision remained nearly unchanged, demonstrating the model’s ability to reduce power consumption without compromising performance. In high phase noise scenarios（1.5 kHz linewidth） at K = 3.05, phase precision with and without pre-amplification nearly overlapped at the fiber near-end due to dominant laser phase noise. In contrast, at the fiber far-end, pre-amplification improved phase precision. The experimental phase precision ratios matched theoretical predictions at both near-end（approaching 1） and far-end（0.6）, confirming that the model accurately predicts phase precision variations across different scenarios.Conclusions In conclusion, this paper establishes a comprehensive theoretical framework for SNR and demodulated phase precision in heterodyne-detection Φ-OTDR systems with optical pre-amplification. The study derives optimal EDFA gain and a practical gain range to minimize power consumption while maintaining acceptable performance. The research demonstrates that pre-amplification does not universally improve system performance; its effectiveness depends critically on photodetector noise characteristics. Specifically, pre-amplification enhances phase precision only when additive noise dominates and the thermal-to-shot noise variance ratio（K） exceeds（ηF-1）（typically ～0.44）, a criterion directly evaluable from device parameters without time-consuming experiments. By integrating both additive and phase noise effects, this work provides practical design criteria for engineering applications, enabling informed decisions regarding pre-amplification implementation and gain optimization for balanced performance and efficiency.更多还原