|Both the data and the Fourier transform can be complex. The
magnitude is represented by brightness and color by phase as shown in the complex plane
to the left and in the applet's color picker. Pure positive real is bluish-cyan and negative imaginary is red.
The display setting tools under the images (shown highlited to the left) don't
modify the data, just how it is displayed. If you wanted to display only the real part
of the image, click on the appropriate button under it.
Because Fourier transforms often have data spanning by many orders of
magnitude, the Brightness slider lets you smoothly change the brightness
over orders of magnitude in a "tangent function" way.
||Clicking on the image button on the bottom or by typing in the URL of an
image on the web -- it will automatically be converted to a pure-positive-real
image at the resolution selected (default is 128x128.)
By using the square tool and using the selector to draw zero you can
remove the high spatial frequency components and see the image get blurry.
(If you're within a few pixels of the origin, the program will use exactly
||Which is more important in the Fourier transform, magnitude of
phase? When we think of Fourier analysis on sound, for example,
we're almost exclusively interested in the magnitude information, but it's
the phase of each component that determines how much that sin wave will be
To investigate, pull up an image and click on the "Discard
Phase" or "Discard Magnitude" buttons. Unlike the
display buttons, these actually change the underlying data.
At the left
I have discarded magnitude information and kept only phase. It still looks
recognizable. When phase information is discarded, it's a blurry
jumble. Unfortunately in x-ray crystallography, only the magnitude
information is measurable.