Correlation between polar values and vector analysis

Abstract

PURPOSE: To evaluate the possible correlation between polar value and vector analysis assessment of surgically induced astigmatism. SETTING: Department of Ophthalmology, Aalborg Sygehus Syd, Denmark. METHODS: The correlation between polar values and vector analysis was evaluated by simple mathematical and optical methods using accepted principles of trigonometry and first-order optics. RESULTS: Vector analysis and polar values report different aspects of surgically induced astigmatism. Vector analysis describes the total astigmatic change, characterized by both astigmatic magnitude and direction, while the polar value method produces a single, reduced figure that reports flattening or steepening in preselected directions, usually the plane of the surgical meridian. There is a simple Pythagorean correlation between vector analysis and two polar values separated by an arch of 45 degrees. CONCLUSION: The polar value calculated in the surgical meridian indicates the power or the efficacy of the surgical procedure. The polar value calculated in a plane inclined 45 degrees to the surgical meridian indicates the degree of cylinder rotation induced by surgery. These two polar values can be used to obtain other relevant data such as magnitude, direction, and sphere of an induced cylinder. Consistent use of these methods will enable surgeons to control and in many cases reduce preoperative astigmatism.