Diffraction by ruled gratings with variable spacing: fundamental method of intensity calculation

Abstract

A regular diffraction grating produces intensity patterns that combine waves coming through equispaced slits, so that the waves emerging from any two neighboring slits have identical phase differences. In this paper, we calculate the degradation in the intensity pattern when the grating has irregular spacing. The model of randomness considers the grating spacing and openings as being created by a “random walk.” The resolving power of the grating is evaluated in relation to the D lines of sodium. It is shown that as the number of rulings increases, the uniformity of their spacing becomes more important in precision spectroscopic measurements, such as in astrophysical spectroscopy.