Modulation patterns of astronomical imaging systems based on rotating grids

Various astronomical imaging systems use rotating grids as modulators and operate in the optical, X-ray, and gamma-ray regions. The position and strength of each measured source are encoded in a modulation pattern, produced by the imaging system. Here we present the mathematical expressions of the modulation patterns which permit efficient computer implementation and a simple approximate expression is also given which facilitates the understanding of the basic properties of the modulation patterns. Although various modulation devices strongly differ in appearance, their modulation patterns show a remarkable similarity. This suggests that a unified approach is possible by analysing the output signals of these devices.