In space gravitational wave detection, the inter-satellite link-building process requires a type of steering mirror to achieve point-ahead angle pointing. To verify that the background noise does not drown out the gravitational wave signal, this paper designed a laser heterodyne interferometer specifically designed to measure the optical path difference of the steering mirror. Theoretically, the impact of angle and position jitter is analyzed, which is called tilt-to-length (TTL) coupling. This interferometer is based on the design concept of equal-arm length. In a vacuum (${10}^{-3} \mathrm{P}\mathrm{a}$), vibration isolation (up to 1 Hz), and temperature-controlled (approximately 10 mK) experimental environment, the accuracy is increased by about four orders of magnitude through a common-mode suppression approach and can reach $390 \mathrm{p}\mathrm{m}/\sqrt{\mathrm{H}\mathrm{z}}$ when the frequency is between 1 mHz and 1 HZ. By analogy, the optical path difference caused by the steering mirror reaches $5 \mathrm{p}\mathrm{m}/\sqrt{\mathrm{H}\mathrm{z}}$ in the 1 mHz to 1 Hz frequency band. The proposed TTL noise model is subsequently verified.

In the detection of gravitational waves in space, during the science phase of the mission, the point-ahead angle mechanism (PAAM) serves to steer a laser beam to compensate for the angle generated by the relative motion of the two spacecrafts (SCs) during the approximately 10 s of flight time a laser beam will take from one SC to reach a distant SC of three million kilometers away. The Tilt-to-length (TTL) noise budget for the PAAM is constrained to less than $8 \mathrm{pm}/\sqrt{\mathrm{Hz}}$ within the frequency range of 1 mHz to 1 Hz. This constraint requires that the measurement noise of the interferometer remains below this threshold to guarantee the precision needed for gravitational wave detection in space. In the present work, an equal-arm heterodyne interferometer, which is fixed in a vacuum system with multilayer thermal shields, is proposed for the OPD (Optical Path Difference) measurement. The background measurement noise of the system is smaller than $60 \mathrm{pm}/\sqrt{\mathrm{Hz}}$ within the frequency range of 1 mHz to 1 Hz. This corresponds to an 84.6% noise reduction at 1 mHz compared to similar unshielded interferometers utilizing conventional bonding methods, demonstrating that the proposed system effectively suppresses measurement noises, particularly thermal noise, in the low-frequency range.