Fourier Transforms
Joseph Fourier
-
Fourier transforms takes image in x-space
and converts it to k-space
(momentum space)
-
Any function can be made up of a linear
superposition of sine functions of suitable
phases
-
The fourier transform calculates the
amount of each of the sine functions of different wavelengths that is required
to make the original function
-
Simply a different representation of
the same function
-
Here transform assumes array has periodic
boundary conditions
-
We can extrapolate
the field at the surface of the sun to different heights above the surface
and know the components of the field in x, y, and z
-
The fourier transform of a fourier
transform takes us back to the initial function