Wavelength-modulated heterodyne grating shearing interferometry for precise displacement measurement

A wavelength-modulated heterodyne grating shearing interferometry using a birefringent crystal is proposed for two-dimensional displacement measurement. There is a difference in the optical path lengths of the p- and s- polarizations of the light beam in the birefringent crystal because of the double refraction caused by the birefringence. By passing through the unequal-path-length optical configuration, the wavelength-modulated light beam is converted into a heterodyne light beam having two frequencies. The modulated heterodyne light beam is further combined with grating-shearing interferometry based on the quasi-common-optical-path (QCOP) design concept. According to the working principle and the Jones calculation, the displacement information of a moving grating can be obtained by means of the optical phase variation resulting from the grating. Theoretical analysis shows that the measurement sensitivity of the proposed method is about 0.134°/nm. The experimental results indicate that the resolution is about 10 nm for the centimetric-level measurement range.