Form Measurement of a 300 mm Ellipsoidal Binary Grating Using a Spatio-Temporal Fourier Method

Abstract For conventional laser Fizeau phase-shifting interferometry, form measurement of ellipsoidal binary gratings remains challenging because of the discontinuous grating structure with groove depths exceeding half the illumination wavelength. In this study, we propose a spatio-temporal Fourier analysis method that extends conventional laser Fizeau interferometry for full-field form measurement of ellipsoidal binary gratings. By applying a three-dimensional Fourier transform to phase-shifted interferograms, combined with spatial low-pass filtering, the low-spatial-frequency phase is extracted. Moreover, the background intensity is utilized for segmentation masks, enabling independent segmentation and reconstruction of the upper and lower grating surfaces. Simulations show that the residual reconstruction errors remain below 6.5 nm root-mean-square for a groove depth of 2.65 μm. Experimental validation using a 30 mm flat grating agrees well with state-of-the-art point-scanning optical profilometric measurements, where a 300 mm ellipsoidal grating was successfully characterized. The proposed method extends conventional Fizeau interferometry to enable accurate full-field surface form metrology of ellipsoidal binary gratings.