APPLICATION OF FOURIER ANALYSIS TO THE DESCRIPTION OF OPTICAL LENS POWER AND THE STATISTICAL ANALYSIS OF REFRACTIVE ERROR

Title APPLICATION OF FOURIER ANALYSIS TO THE DESCRIPTION OF OPTICAL LENS POWER AND THE STATISTICAL ANALYSIS OF REFRACTIVE ERROR
Author, Co-Author Larry Thibos
Topic
Year
1992
Day
Sunday
Program Number
Poster 60
Room
Great Hall
Affiliation
Abstract A basic element of optometry is the prescribing of ophthalmic lenses to correct refractive error. In general, a combination of spherical and cylindrical lenses is required and thus the need arises for general methods of computing the optical power of such lens combinations. Several analytical tools are currently available for this task, including the power cross, Prentice's formulas, Thompson's graphical technique, optometric vectors, complex numbers, and power matrices. Because textbook descriptions sometimes give the impression that these are merely operational methods, it seemed that some useful insight might be gained by searching for a common basis. The purpose of the present study, therefore, was to investigate the validity and inter-relationship of some of these techniques by taking a fresh look at the problem from the point of view of Fourier Analysis. Starting from an analysis of the curvature of arbitrary surfaces (from which optical power is derived), it is shown why optical power varies sinusoidally with meridian and consequently is describable by a simple Fourier series with a single harmonic component. Such a series contains just three Fourier coefficients, corresponding to the three parameters of a sphero- cylinder lens. This allows for the economical representation of the complete power curve of a sphero-cylinder lens by a single point in a three dimensional space and, at the same time, provides the basis for graphical and vector methods of calculating linear combinations of lens power. We then exploit these results to show how standard statistical measures of central tendency, dispersion, and confidence intervals developed for Fourier coefficients may be applied to the statistical analysis of refractive error and to the assessment of variability in ophthalmic lenses.
Affiliation of Co-Authors
Outline