Two-dimensional grating interferometer with nanometer accuracy

A two-dimensional grating interferometer with the nanometer accuracy is proposed, which employs a transmissive two-dimensional diffraction grating and a corner cube prism in its optical configuration. The distinctive features of this optical path configuration are as follows: (i) Fourfold optical subdivision is achieved based on the principle of secondary diffraction, enhancing optical subdivision capability. (ii) The utilization of a corner cube prism configuration enables parallel retroreflection of diffracted light, facilitating ease of optical alignment. Utilizing a two-dimensional transmissive grating with a period of 4 µm (resulting in an optical signal period of 1 µm after fourfold optical subdivision), the two-dimensional grating interferometer achieves measurement resolutions better than 8 nm along the x and y directions. Within a 100 µm range, the grating displacement errors are superior to ±38 and ±36 nm. The repeatability (standard deviation of error) during a reciprocating motion with a 4 µm stroke is superior to 14 nm. The proposed two-dimensional grating interferometer enables nanoscale resolution measurements, showcasing notable linear measurement capabilities and repeatability. It finds potential applications in ultra-accuracy positioning and machining equipment. The utilization of gratings with smaller periods holds the promise of realizing picometer-level measurement potential.