Step-along vergence procedures in stigmatic and astigmatic systems

The traditional step-along vergence procedure applies to stigmatic systems, that is, systems that are not astigmatic. Computation is disrupted when a focus coincides with a thin lens or refracting surface. A small change to t he procedure results in a modified procedure which overcomes the computatio nal problems. The modified procedure is easier to execute than the traditio nal procedure and allows one to write down useful equations directly. Among the formulae are those for back-vertex power. A step-along vergence proced ure also exists for astigmatic systems. It makes use of the dioptric power matrix and the reduced vergence matrix. Computational problems arise when a point or line focus coincides with a thin lens or refracting surface; howe ver they are not overcome by an analogous modification to the procedure. Ne vertheless the modified procedure has some advantages including the fact th at, as for stigmatic systems, it allows one to write down useful formulae d irectly. Stepwise calculations of vergence are sometimes performed backward through a system; the advantages and disadvantages described for step-alon g procedures holds for such step-back procedures as well. (C) 2000 The Coll ege of Optometrists. Published by Elsevier Science Ltd. All rights reserved .