Imaging with a rectangular phase grating applied to displacement metrology

We achieved displacement metrology with a high-amplitude signal by using a rectangular phase grating as the pupil in a grating imaging system. The imaging phenomenon with a pupil transmission grating that has a bilevel profile with a 50% duty ratio is discussed on the basis of the optical transfer function. By optimizing the imaging condition, we obtained high-contrast images with high light power under a magnified or demagnified imaging system. The amplitude of the signal in the displacement measurement was four times higher than that of the conventional grating imaging system with amplitude gratings.