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.