Analysis and removal of five-dimensional mosaicking errors in mosaic grating.

Combining the mathematical relationships between the grating wavefront and surfaces with the spatial relationships between the two grating wavefront, a mathematical model of the mosaicking errors is established to mosaic gratings. The five-dimensional mosaicking errors will respectively be calculated and then removed by the adjustment mechanisms. Mosaicking experiments are performed by using two gratings. First, by using zeroth order, the longitudinal offset is calculated and removed. Second, by using the diffraction order, the in-plane angle and grating spacing are calculated and removed, while the tip and tilt angles are calculated and removed. And then a mosaic grating is obtained.