Astigmatism

The quantitative representation and analysis of astigmatism present difficu lties for the researcher. The case is made that the difficulties arise beca use of the way astigmatism is conceived and defined. In most cases astigmat ism is regarded as cylinder. Cylinder, however, is not invariant under sphe rocylindrical transposition and, hence, cannot strictly be regarded as mean ingful. The purpose of the paper is to find a rational, context-free, invar iant and universally-applicable definition of astigmatism for all quantitat ive analyses. One is led to definitions of astigmatism and its components s ome of which have already appeared in the literature but which are not in u se in analyses of astigmatism. Astigmatism is defined with respect to pure sphere. In the case of thin systems (including keratometric measurements an d refraction) astigmatism turns out to be Jacksonian power, that is, the po wer of a Jackson crossed cylinder. The power of every thin system can be re garded as consisting of two orthogonal components, sphere and astigmatism. The astigmatism of thin systems itself further decomposes naturally into tw o orthogonal components called ortho- and oblique astigmatism. In the case of thick systems, like the eye itself, astigmatism decomposes naturally int o three orthogonal components, ortho-, oblique and antisymmetric astigmatis m. The approach is based on the general definition of power in paraxial opt ics, the dioptric power matrix, and leads to useful graphical representatio ns. Because of its mathematical foundation the analysis can claim completen ess and contextual independence. Furthermore it is also directly applicable to the four fundamental paraxial properties of optical systems. (C) 1999 T he College of Optometrists. Published by Elsevier Science Ltd.