A general theory of the aberrations óf diffraction gratings and gratinglike optical instruments

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Abstract
We describe the aberrations of diffraction gratings without any restrictions on the symmetry of the substrate, the curvature of the grooves, or the position of the entrance slit. The theory can also be applied to holographic gratings, holographic lenses, synthetic holograms, zone plates, and other diffracting instruments. The description comprises second-order focusing conditions, including the generalization of the Rowland circle and the conditions for astigmatism, length, slope, and curvature of the focal lines, comatic and fourth-order aberrations. In particular we show the relations between the aberrations óf second and higher orders. The theory is applied in this paper to astigmatic mountings of the Rowland type, and to mountings of the Wadsworth and Eagle type that we call anastigmatic. We give special attention to the conditions for freedom of coma of anastigmatic mountings.

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