Dispersion and resolving power: prism spectrographs

Abstract

Dispersion can be achieved by refraction, diffraction or interference — that is, by prisms, gratings or interferometers. This distinction is in a way rather artificial, because all these instruments work by superposing a number of rays of varying phase, the number being infinite for the prism, 10⁵–10³ for the grating and 50-2 for the interferometer. The important properties of a disperser are its spectral range, its resolving power and dispersion, its light grasp and its ambiguity or ease of interpretation. On spectral range gratings win easily, as they can be used all the way from X-rays to microwaves. Prisms require a transparent solid, which limits the range to between 40 μm and 120 nm. Interferometers require a beam-splitter; in practice this imposes the same limit at the short-wavelength end, but thin films or grids can be used above the crystal transmission limit at long wavelengths. In respect of maximum resolving power, the order of merit is interferometer, grating, prism, with an order of magnitude between each. Light grasp is inversely related to resolving power, but a comparison of light grasp for the same resolving power favours the interferometer by one to two orders of magnitude. In ease of interpretation the order is reversed: only prisms give directly unambiguous spectra. Overlapping orders may occur with gratings and always need attention with Fabry-Perot interferometers; the Michelson interferometer used in Fourier transform spectroscopy can indeed give an unambiguous spectrum, but only after the output has been Fourier-transformed.