Numerical calculation of the mosaic error betweenmosaic gratings

The theoretical calculation model for a mosaic error was established based on the plane equation for a grating surface and the relationship equation for a mosaic grating surface. A mosaic grating was obtained based on this model. In the experiment, the mosaic error was calculated based on the diffraction wavefronts of two groups of mosaic gratings that were obtained simultaneously with a Zygo interferometer. The difference between the wavefront of the mosaic grating and the average wavefront of the mosaic grating element was 0.031λ. The maximum far-field intensity of the mosaic grating was 90% of that without an error. This model provides a theoretical basis for the numerical mosaic between gratings. In addition, the mosaic error can be calculated with this model, and the quality of the mosaic grating can be evaluated.