Properties of elementary astigmatic pencils of rays in a decentered optical system

Properties of elementary astigmatic pencils of rays of an optical system with small decentering are formulated using the technique based on translating astigmatism from the intermediate space of the optical system to the space of images. The results obtained are not limited by the approximations based on expansions in series and are valid for decentering-caused astigmatism of an arbitrary order. The necessity of calculating at least two elementary pencils of rays when analyzing the effect of decenterings on the astigmatism is proved. 5 refs., 3 figs