# Research on Phase Stabilization Algorithm of Femtosecond Timing System
## 2 System Introduction  
To achieve phase-stable transmission of high-frequency reference signals over long distances and extended periods, it is essential to precisely control two key technical parameters of the signal distribution system: short-term additional timing jitter and long-term phase drift. Moreover, factors such as temperature fluctuations and mechanical vibrations require careful attention due to their substantial impact on phase stability. In our experimental setup, we implement significant measures to stabilize the environmental temperature, thereby mitigating its influence on phase stability. To counteract the challenges posed by mechanical vibrations, we enclosed the optical fibers in foam boxes, effectively minimizing external disturbances. Furthermore, the power of the laser plays a crucial role in phase stability. In our experiments, we meticulously adjusted the received laser signal power to align precisely within the photodiode's monotonic linear response region. This adjustment enhances the accuracy of photoelectric conversion, thereby contributing to improved phase stability of the system.  
To effectively reduce short-term timing jitter to the desired target, a laser module with a linewidth on the order of kilohertz is selected. This module can generate continuous-wave laser signals at 1560.48 nm, and its wavelength stability can reach an accuracy of \(10^{-10}\). By modulating the high-frequency reference signal onto this laser carrier, the system's short-term additional timing jitter can be maintained at the femtosecond level.  
To suppress the long-term phase drift of the high-frequency reference signal, it is first necessary to construct an optical fiber network that modulates the high-frequency reference signal onto the laser signal and collects its phase information using the independently developed radio-frequency electronic equipment. This equipment is capable of detecting delay variations at the femtosecond level or even smaller. After collecting the phase information, it is transmitted to a computer for feedback control.  
The system design introduces a feedback loop based on a PID (Proportional-Integral-Derivative) control algorithm to calculate the phase compensation feedback value [15]. This feedback value is then converted into control commands for the fiber stretcher and optical delay line, which are transmitted to the corresponding devices. This design ensures that the system's long-term phase drift is controlled at the femtosecond level, achieving high-precision phase-stable transmission. The system architecture based on the above design is shown in Figure 1. In this figure, AM refers to the Analog Modulator, where the high-frequency reference signal is modulated onto the laser carrier. The ODL, or Optical Delay Line, serves as a device for coarse phase adjustment of the signal.  
Phase measurement accuracy is the core foundation of femtosecond timing systems, directly affecting the overall performance and precision of the system. High-precision phase measurement ensures accurate time synchronization, thereby enhancing the reliability and effectiveness of experiments and applications.  
The design of the phase detection system down-converts the high-frequency RF signal to an intermediate frequency using non-I/Q sampling and undersampling techniques and removes higher-order harmonic interference in the spectrum through multi-stage CIC filters [16]. To further improve the accuracy of amplitude and phase measurements, the system employs a reference tracking algorithm to compensate for various errors in the sampling clock [17]. This design can achieve high-precision signal processing with lower hardware complexity, reaching femtosecond-level phase measurement.  
Figure 1: System topology diagram.