Instruction Manual Easygraph
Page 27
7.5.2.4 Fourier Analysis
Named after the French physicist Jean Baptiste
Joseph Fourier (1768-1830), this mathematical
method permits decomposition of any periodical
function in terms of trigonometric sine and cosine
functions (
Fourier analysis
). The fundamental
wave, known as the first harmonic, is a sine wave
whose period is equal to that of the wave being
analyzed. The period of the second harmonic is half
that of the first (thus giving two sine waves), the
period of the third harmonic is a third as long as that
of the first (giving three sine waves) etc. Summing up
all the constituent wave components gives the
original function (
Fourier synthesis
).
Periodic function to be analyzed
Decomposition into two sine waves and one cosine
wave
The Easygraph performs a Fourier analysis on the
topographic image by breaking it down into its
individual components as described above (To start
the Fourier analysis select “Fourier analysis” under
the menu bar function “Display”). The first step is to
divide the image into individual concentric rings.
Then the curvature on each ring is decomposed into
separate sine and cosine waves by means of Fourier
transformation. The resulting components of all rings
are regrouped and displayed in separate images
showing, respectively, zero order, first order, second
order components etc. Some interesting
characteristics are found when the individual wave
components are studied in isolation from each other
in this manner:
•
Spherical equivalent
This image consists
solely of the zero
order wave
component in the
form of the arithmetic
mean of all radii of
each individual ring.
This value can also
be interpreted as the
spherical component
of the radii of each
ring. Assuming the
cornea to have the
shape of an ellipsoid of revolution, the spherical
component permits an approximate calculation of the
eccentricity of the cornea. In a normal eye corneal
eccentricity ranges below 0.85.
•
Decentration
The first-order wave is
a regular sine wave
which achieves a
minimum and a maxi-
mum over a given
radius ring. It serves
as a measure of the
tilt between the optical
axis of the
videokeratoscope
and the optical vertex
of the cornea.
It is important to note
that this function yields relative, not absolute values,
since its arithmetic mean is zero.
The minimum and maximum values of each radius
are shown as white (minimum) and black (maximum)
circles. This makes it possible to infer the position of
the axis of decentration for each of the zones. In a
normal cornea maximum decentration rarely
exceeds
0.45 mm for sagittal curvature (1.88 for
tangential curvature)
.