## 4 Experimental Results and Discussion
According to the interferometer results in Figure 8b, the 10 Hz frequency point is selected as the experimental frequency point, which helps to avoid low-frequency noise and obtain an accurate relationship between the OPDs and voltages. The OPDs are shown in Figure 9. The OPD of each 10 Hz frequency point is fitted by second-order linear fitting based on the applied voltages, and the results are obtained as shown in Figure 10.  
As shown in Figure 10, it can be seen from the fitting curve equation that the coefficient of the second-order term is small, and the second-order term can be ignored. The relationship between OPDs and voltages is  
\[\Delta\approx 4.4869\times\mathrm{v}+3.02 \tag{17}\]  
In previous experiments, it was found that the voltage change in the steering mirror in the steady state is 0.15 mV. It is considered that the OPD obtained when the driving voltage amplitude is 180 mV is the actual result caused by the steering mirror. In accordance with the multiplier relationship between the steady-state voltage of 0.15 mV and the experimental voltage of 180 mV, the optical path difference by applying the steady-state voltage should correspondingly decrease throughout the entire frequency domain. Analogous to the OPD when the driving voltage amplitude is 180 mV, the OPD of the steering mirror in the steady state is obtained as shown in Figure 11. The OPD is less than 5 pm/\(\sqrt{\mathrm{Hz}}\) in the 1 mHz to 1 Hz frequency band when the voltage change applied to the steering mirror is 0.15 mV, so it meets the OPD requirement of 8 pm/\(\sqrt{\mathrm{Hz}}\) in the 1 mHz to 1 Hz frequency band. In previous work, the relationship between the rotary angles and driving voltages was calibrated, as shown in the following formula (Formula (18)):  
\[\varphi=1.069\times\
u+1.2182 \tag{18}\]  
Combining Equations (17) and (18), the obtained TTL noise is  
\[\Delta\approx 4.1973\times\varphi+1.88 \tag{19}\]  
From Equation (19), it can be inferred that there is a first-order proportional relationship between angle jitter and optical path difference. The constant bias in Equation (19) is caused by the interferometer noise floor. Figure 10: The fitting relationship between the driving voltage and the optical path difference. Figure 7:0 Frequency-domain results of different optical path differences. So far, we have achieved a measurement accuracy of 390 pm\(/\sqrt{\mathrm{Hz}}\) in the 1 mHz to 1 Hz frequency band. Through indirect analog experiments, we have not only verified that the optical path difference induced by the steering mirror reaches 8 pm\(/\sqrt{\mathrm{Hz}}\) but also identified the coupling relationship between angle jitter and optical path difference. The interferometer adopts the design concept of an equal arm, maximizing common-mode noise suppression and achieving measurement accuracy spanning four orders of magnitude. It also offers a robust experimental platform for pertinent studies on angle jitter noise suppression, laser Phase-Locked Loop control, laser frequency noise suppression, and related research. To directly achieve a measurement accuracy of 8 pm\(/\sqrt{\mathrm{Hz}}\) in subsequent research, we will implement a combination of active and passive temperature-control methods to suppress temperature fluctuation noise while also providing an improved vacuum environment.