Chapter 18: Polar vs Double Angle Displays in Astigmatism

Polar plots - representing the eye, Double-angle (Cartesian) plots - a mathematical construct, Astigmatism analysis What are polar and double angle diagrams and they and how can they be used clinically? Well that is a really interesting subject and there has been some conjecture about it. How I like to understand it is a polar diagram is a representation of astigmatism as it appears on an eye, whether it be cylinder or corneal astigmatism. The polar diagram is displayed as a semi-circle that goes from 0 – 180 degrees. Horizontally is against the rule and the vertical direction is with the rule. A double angle diagram is an absolutely essential tool that allows the calculation of vectors using Cartesian co-ordinates. It’s a mathematical construct and does not represent the eye. So how does one construct a double angle vector diagram from a polar diagram? The axis of the astigmatism represented on a polar diagram is doubled but the magnitude remains the same to convert to a double angle vector diagram. So 90 degrees becomes 180 degrees and 180 degrees becomes 360 degrees. What essentially needs to be displayed as part of any astigmatic analysis are polar diagrams depicting the astigmatic treatment or the TIA, the surgically induced astigmatism, the difference vector and the correction index to determine any over or under correction of astigmatism. Display of preoperative or postoperative astigmatism is NOT a vectorial analysis.