Rotational Symmetry

A television image is rectangular and uses two independent variables in its representation of a three-dimensional scene. However, the television camera has an optical system with component parts, such as the aperture containing the objective lens, which, while distinctly multidimensional, possess circular symmetry. Only one independent variable, namely radius, may be needed to specify the instrumental properties across such an aperture, because the properties may be independent of the second variable, in this case angle. Circular symmetry also occurs in objects that are under study (some astronomical objects, for example) or in objects that influence imaging (rain drops), and is a property of many artifacts. Because of the prevalence of circular symmetry, particularly in instruments, special attention to circularly symmetrical transforms is warranted. This chapter also deals briefly with objects having rotational symmetry, which are of less frequent occurrence, but related.