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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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">P</mi><mi mathvariant="normal">a</mi></mrow></semantics></math></inline-formula>), 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>390</mn><mo> </mo><mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">m</mi></mrow><mo>/</mo><mrow><msqrt><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></msqrt></mrow></mrow></mrow></semantics></math></inline-formula> when the frequency is between 1 mHz and 1 HZ. By analogy, the optical path difference caused by the steering mirror reaches <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo> </mo><mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">m</mi></mrow><mo>/</mo><mrow><msqrt><mi mathvariant="normal">H</mi><mi mathvariant="normal">z</mi></msqrt></mrow></mrow></mrow></semantics></math></inline-formula> in the 1 mHz to 1 Hz frequency band. The proposed TTL noise model is subsequently verified.