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Future energy scaling of high-energy chirped-pulse amplification systems will benefit from the capability to coherently tile diffraction gratings into larger apertures. Design and operation of a novel, accurate alignment diagnostic for coherently tiled diffraction gratings is required for successful implementation of this technique. An invariant diffraction direction and phase for special moves of a diffraction grating is discussed, allowing simplification in the design of the coherently tiled grating diagnostic. An analytical proof of the existence of a unique diffraction grating eigenvector for translational and rotational motion that conserves the diffraction direction and diffracted wave phase is presented.

Diffraction grating eigenvector for translational and rotational motion