Method for Calculation and Analysis of the Weights of Grating Mosaic Errors.

A method to calculate the weight of grating mosaic errors is proposed based on an analytical hierarchy process. An accurate mosaic error tolerance calculation formula is also presented that is useful for large-size grating fabrication by the mosaic method. The grating mosaic error weights and tolerances are analyzed for mosaic echelle gratings. The analytical error weight and tolerance results agree well with the experimental results. The mosaic grating's far-field intensity is 95.8%, which is higher than the 94% value from the simulation results.