後續透過降低誤差訊號的零交越頻率對拍頻功率的靈敏度，並導入雙頻寬數位帶通濾波器(Dual Bandwidth Digital Bandpass Filter， DBW-DBPF)[2]的鎖頻方法，進一步改善了拍頻鎖定的短期與長期穩定度，讓鎖定後的拍頻在平均時間 205 s時，達到 10.5 Hz 的頻率不穩定度。;This study demonstrates the transfer of optical frequency stability from a home-built 885 nm optical clock to a standard 10 MHz instrumental timebase， utilizing an optical frequency comb (OFC) to bridge the optical and radio frequency domains. By implementing a digital band-pass filter (DBPF)-based frequency offset locking system on a Red Pitaya FPGA board， the beat note ($f_{beat}$) was successfully locked to the center frequency of the DBPF， achieving phase-locking of the carrier-envelope offset frequency ($f_{ceo}$).
In terms of system optimization， the locking performance of the beat note was enhanced by adjusting the DBPF bandwidth. Furthermore， an IIR notch filter was employed to suppress a 1.6 kHz PZT resonance peak， enabling a higher loop gain and thereby strengthening low-frequency noise suppression. Stability analysis reveals that the frequency stability gap between $f_{rep}$ and the 885 nm optical clock in the short term (0.1–1 s) is primarily limited by the instability of the frequency counter itself， whereas the long-term stability (beyond 100 s) is bounded by the 885 nm optical clock. This demonstrates that the proposed DBPF locking method possesses sufficient performance to transfer the optical frequency stability to $f_{rep}$. Ultimately， the Allan deviation of the output 10 MHz signal reaches $6.04 \times 10^{-13}$ at an averaging time of 2048 s.
In addition， by reducing the sensitivity of the error signal′s zero-crossing frequency to beat note power and introducing a Dual-Bandwidth DBPF (DBW-DBPF) locking scheme， both the short-term and long-term locking stabilities of the beat note were further improved， reaching a frequency instability of 10.5 Hz at an averaging time of 205 s.
