Fourier profilometry is a method for measuring profiles using distortions in periodic

Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...

 patterns. The method uses Fourier analysis (a 2-dimension

Dimension

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

al Fast Fourier transform

Fast Fourier transform

A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...

) to determine localized slope

Slope

In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....

s on a curving surface

Surface

In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...

.

This allows a x, y, z coordinate system

Curvilinear coordinates

Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible at each point. This means that one can convert a point given...

 of the surface to be generated from a single image which has been overlaid with the distortion pattern.

It is used specifically in measuring the shape of the human cornea

Cornea

The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Together with the lens, the cornea refracts light, with the cornea accounting for approximately two-thirds of the eye's total optical power. In humans, the refractive power of the cornea is...

 for use in contact lens

Contact lens

A contact lens, or simply contact, is a lens placed on the eye. They are considered medical devices and can be worn to correct vision, for cosmetic or therapeutic reasons. In 2004, it was estimated that 125 million people use contact lenses worldwide, including 28 to 38 million in the United...

design.