Vector analysis of astigmatism changes by flattening, steepening, and torque

Abstract

Purpose: To understand the effect of astigmatism surgery by analyzing astigmatic changes according to their component parts.

Setting: Cheltenham Eye Centre, Melbourne, Australia.

Methods: The component parts of the astigmatic changes considered were flattening, steepening, clockwise torque, and counterclockwise torque. Calculations to determine the astigmatic change were performed by vector analysis using rectangular coordinates after doubling the astigmatism and surgical vector axes. A reference axis was used for the resolution of astigmatic change to ascertain its effect along a selected meridian.

Results: When correcting astigmatism, the orientations of incisional (tissue addition) or nonincisional (tissue ablation) techniques in any cornea are at right angles to each other. Since differences exist in the measured astigmatism depending on whether it is measured topographically or by manifest refraction, an on-axis correction in one will occur with an off-axis effect in the other. The net result is a reduced flattening effect and a proportionately increased torque effect for the off-axis component.

Conclusion: When treatment is applied off one of the four primary axes, the treating vector can be resolved into its component parts of flattening, steepening, and torque. Analyzing changes in this way provides a uniform means of assessing astigmatic changes for all types of cataract and refractive surgery and quantifies the flattening effect when treatment is applied off the intended meridian.