Converting principal meridional representation of power to the coordinates of the power matrix using the matrix similarity transform.

General or local variations of the refractive elements in the eye, called irregular astigmatism, may manifest as non-orthogonal meridians when each principal meridian on the front surface of a cornea is independently aligned with the focussed mires of a keratometer. These are examples of astigmatic systems that are thick. The representation of power along the principal meridians is not suitable for quantitative work. The purpose of this research note is to convert power along principal meridians that can be non-orthogonal, to the coordinates of the power matrix that are suitable for quantitative analysis.