Effect of the changes in refractive index of air on grating diffraction wavefront

Reduction of groove errors on the grating wavefront caused by the refractive index of air is a critical issue in ruling grating fabrication when using an interferometer to provide position feedback. We establish a mathematical model of the relationship between the grating wavefront and the refractive index of air. We then introduce two methods to measure the air's refractive index, analyze the effects of temperature, pressure and humidity on the grating wavefront, and use the advantages of the two methods to obtain the groove error compensation value. Comparative ruling experiments prove that grating wavefront quality is significantly improved after compensation of the groove errors caused by the refractive index of air.