Interferometric Measurement of Wave-Front Aberrations in Gratings and Echelles*

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Abstract
Modern production of diffraction gratings requires rapid and reliable methods of evaluating quantitatively the wave fronts produced, to determine errors in blank figure and groove positioning. Comparison of methods, including cross ruling, moiré patterns with replicas, Foucault knife-edge tests, phase contrast determinations, and various types of interferometry, supplemented by determinations of ghost intensities, indicates that for errors greater than about λ/40, comparison of the wave front with that from a reference mirror in a Michelson interferometer used in the Twyman-Green manner gives the most nearly adequate conditions for good visibility and sensitivity. Tests at great diffraction angles, necessary for high sensitivity, give patterns of higher contrast and greater intensity than those obtained with the Fizeau plano-interferometer. Exposure times of 10 sec give all needed information about errors.Analysis of the straight-line fringe system obtained shows that in a given order m, a spacing error expressed in fringes is given by Δa=a/m per fringe deviation in the interference pattern, if the spacing constant a is also expressed in fringes. The spacing error per fringe aberration in the interferometer has the same absolute value for all gratings and echelles, irrespective of their spacing constant, provided that the interferograms are taken at the same angle of incidence, and in light of the same wavelength. This provides an important way of directly comparing the quality of various diffraction instruments, and of estimating their intrinsic resolving powers separate from the aberrations of other components of the spectrograph, which affect the limit of resolution.Uniqueness of interpretation of the interferograms can be ascertained by taking interferograms of the same grating area in two suitably selected orders, with a graduated reference scale placed directly on the grating surface showing in both.

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