On the Concave Grating Spectrograph, Especially at Large Angles of Incidence

Abstract

On the physical optics of the perfect concave grating. An extension of the theory of the concave grating to the fourth order approximation shows that the diffraction pattern for a spectral line is different in shape from that for a plane grating. A generalization of Rayleigh’s definition of resolving power allows the computation of the resolving power of a grating in terms of an “effective width”; i.e., the width of a plane grating having the same resolving power as the concave one in question. At grazing incidence (a case of particular interest in the spectroscopy of the extreme ultraviolet) this effective width is of the order of 1 cm.Optimum width of the grating. The optimum width of a grating (for resolving power and intensity), as a function of wave length and angle of incidence, is found. A table of values of this width shows that, in cases of large angles of incidence and short wave lengths, the gratings ordinarily used in the past have been considerably wider than the optimum.Elimination of grazing incidence ghosts. Experiments show that the reduction of the width of a grating to about the optimum eliminates the ghosts (different from Rowland ghosts) which occur in the neighborhood of strong lines in grazing incidence spectrograms.Economies in ruled area. In many cases the lengths of the rulings and of the spectrograph slit, as well as the number of rulings, may be smaller than is now customary.Inexactness of the grating condition equation. Though the intensity pattern really depends upon the value of |∫-H+Hf(η)ei(aη+η4+γη5+⋯)dη|2,usually the approximations f(η)=a constant, and γ etc.=0 are made. With the complete expression, the ordinary grating condition equation, sin θ+sin θ′=mλ/σ, becomes inexact. The error is below the threshold of importance for ordinary measurements.The spectrograph. The questions of symmetric adjustment of the grating about the point of tangency to the Rowland circle, non-uniform illumination of the grating, and finite slit width are considered. The theoretical resolving power agrees well with experimental values.