title: Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error.
abstract: 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.
authors.affiliation: School of Optometry, Indiana University, Bloomington, USA. thibos@indiana.edu
authors.forename: L N
authors.initials: LN
authors.lastname: Thibos
authors.forename: W
authors.initials: W
authors.lastname: Wheeler
authors.forename: D
authors.initials: D
authors.lastname: Horner
mesh_terms: D003196:Computer Graphics; D003627:Data Interpretation, Statistical; D005139:Eyeglasses / Q000592:standards / Q000706:statistics & numerical data; D005583:Fourier Analysis; D006801:Humans; D055095:Optics and Photonics; D009907:Optometry / Q000379:methods; D012029:Refraction, Ocular; D012030:Refractive Errors / Q000628:therapy*