POWER VECTORS - AN APPLICATION OF FOURIER-ANALYSIS TO THE DESCRIPTIONAND STATISTICAL-ANALYSIS OF REFRACTIVE ERROR

The description of sphere-cylinder lenses is approached from the viewp oint of Fourier analysis of the power profile. It is shown that the fa miliar sine-squared law leads naturally to a Fourier series representa tion 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 t he harmonic correspond to the power and axis of a Jackson cross-cylind er (JCC) lens, respectively. Expressing the Fourier series in rectangu lar form leads to the representation of an arbitrary sphere-cylinder l ens as the sum of a spherical lens and two cross-cylinders, one at axi s 0 degrees and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vecto r 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 dist ribution of refractive errors.