Tilted component systems are known to be characterized by aberrations with unusual field dependences, such as decentered coma and binodal astigmatism. Often, a computer optimization of a tilted-component system will yield a solution having astigmatism that grows approximately linearly from a value of zero at the field center, i.e., one of the astigmatic nodes has been placed at the center of the field. For system with substantial field angles, this linear dependence is as detrimental to image quality as ordinary coma, but it is often difficult to avoid this form of solution. In this paper, the origin of binodal astigmatism in a multi-element system from the contributions of individual surfaces is explained in an intuitive manner, as a logical extension of the 'ordinary' aberrations known to all optical designers. The insight provided by this graphical model allows an understanding of why the astigmatism of any given system behaves the way it does, and what remains can be corrected by a final, rotationally symmetric subsystem. Examples of tilted component system are given in which astigmatism and coma have been reduced to 'ordinary' forms.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.