Nano-displacement measurement using a Littman-configured interferometer based on orbital angular momentum beams

In this work, we present a Littman-configured interferometer based on orbital angular momentum (OAM) beams for nano-displacement measurement. The petal-like interferogram is generated by the interference of two conjugate OAM beams: a reference beam and a measured beam, which is diffracted from a scale grating. The one-dimensional displacement of the grating, whether in-plane or out-of-plane, can be precisely determined by demodulating the rotation angle of the interferogram using a circular cross-correlation algorithm. Theoretically, a 1^o rotation of the interferogram corresponds to an in-plane displacement of 2.313 nm or an out-of-plane displacement of 1.067 nm. Experimental results indicate that in-plane displacement measurements exhibit a maximum error of 1.299 nm for a step displacement of 300 nm, whereas out-of-plane displacement measurements demonstrate a maximum error of 1.898 nm for a step displacement of 200 nm. The displacement resolutions are both better than 2 nm. In the in-plane X-direction, integrating a scale grating with the OAM interferometer within a Littman-configured structure effectively transfers the measurement standard from the laser wavelength to the grating pitch. In contrast, the out-of-plane displacement is influenced by both the grating pitch and the wavelength. This approach enhances environmental robustness while maintaining high displacement resolution.