Measurement of a high-density grating period based on a prism-grating interferometer

To achieve accurate and efficient measurement of large-scale, high-density grating periods, this study presents a prism-grating interferometer and an improved measurement algorithm. The high-density grating was fixed on a translation stage; a laser interferometer collected the stage's real-time displacement data, which were jointly processed with interference signals from the prism-grating interferometer to solve the grating period accurately. Based on a first-order Taylor expansion least-squares iterative mechanism, the improved algorithm optimizes nonlinear models via linearization, ensuring measurement accuracy while reducing single-iteration time to 62.9% of the traditional least-squares method and significantly cutting iteration counts. Experimental verification conducted on a reflective grating with a period of 833 nm and a clear aperture of 360×20<i>m</i><i>m</i> shows that within the 360 mm measurement range (covering 360 groups of 1 mm intervals), the average grating period is 833.3367±15.7<i>p</i><i>m</i>, and the average relative repeatability reaches 4.2 ppm. This combined scheme offers high precision and efficiency, providing a reliable technical solution for large-scale, high-density grating period measurement and adapting to diverse precision scenarios in semiconductor manufacturing and ultra-precision machining.