Practical astigmatism analysis for refractive outcomes in cataract and refractive surgery

The description of sphero-cylinder lenses is approached from the viewpoint of Fourier analysis of the power profile. It is shown that the familiar sine-squared law leads naturally to a Fourier series representation with exactly three Fourier coefficients, representing the natural parameters of a thin lens. The constant term corresponds to the mean spherical equivalent (MSE) power, whereas the amplitude and phase of the harmonic correspond to the power and axis of a Jackson cross-cylinder (JCC) lens, respectively. Expressing the Fourier series in rectangular form leads to the representation of an arbitrary sphero-cylinder lens as the sum of a spherical lens and two cross-cylinders, one at axis 0 degree and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vector representation of the power profile. Advantages of this power vector representation of a sphero-cylinder lens for numerical and graphical analysis of optometric data are described for problems involving lens combinations, comparison of different lenses, and the statistical distribution of refractive errors.

This method of astigmatism analysis recognizes the need to define an astigmatism goal, thus allowing the surgeon to obtain precise, separate measures of the magnitude and the angle of surgical error. From this, the surgeon can evaluate what surgery may be required to achieve the initial preoperative goal. An index that measures surgical success is adjusted for the level of preoperative astigmatism. The resulting data allow statistical comparison of multiple surgeries and techniques. This method also assists in resolving the case when spectacle and corneal astigmatism do not coincide.