Object-image-grating self-tiling to achieve and maintain stable, near-ideal tiled grating conditions

We propose and demonstrate an object-image-grating self-tiling method for doubling the effective aperture of a grating by tiling it with its image to form an object-image-grating pair. With the aid of the object-image relation, the line-density variation, angular tip, and longitudinal piston errors within a tiled grating no longer exist. The method helps achieve and maintain a near-ideal tiled grating by using a simple far-field method. Because one tiled grating requires only one beam line, a single probe laser can be used for first-installation adjustments and long-term maintenance monitoring, with no wavelength or incident angle limitations.