Compact grating displacement measurement system with a 3?×?3 coupler

We present a compact displacement measurement system possessing the capability of nanometer-scale precision. On basis of integrating single grating with 3×3 coupler for phase shift in interference signal, the present scheme features advantages of simple structure, convenient alignment, and insensitivity to air turbulence. Linear comparisons between our system and HP5530 show a residual error less than 81 nm during step motions along a 10 mm round-trip, and a discrepancy less than 15 nm in the case of 200 ?m movement. We also demonstrate a measurement stability test in a duration of 300 s, which shows the proposed scheme potentially performs better than HP5530 in terms of long-term stability.