Grating mosaic based on image processing of far-field diffraction intensity patterns in two wavelengths

A practical grating mosaic method is proposed based on quantitative image processing of three far-field diffraction intensity patterns in two wavelengths. This method aims at making a perfect mosaic of two planar gratings that can substitute for a single and larger grating without introducing wavefront aberration at any wavelength. The zeroth-order and first-order far-field patterns of one wavelength are analyzed for separating and eliminating the angular mosaic errors. The first-order far-field patterns of two wavelengths are applied for separation of the lateral and longitudinal phase errors. Then the three patterns are considered together to enlarge the target range of coarse adjustment required for further fine adjustment in longitudinal position. Experimentally, angular and positional detection sensitivities of less than 6 microrad and 14 nm were achieved, respectively, and the periodicity in positional adjustment was checked, which departed less than 1.8% from the theoretical period. The performance of the perfect mosaic grating was diagnosed with the far-field diffraction intensity pattern in a third wavelength, and the necessity for a perfect mosaic was verified.