| Re: Fourier back to real space [message #78071 is a reply to message #78067] |
Mon, 24 October 2011 20:16  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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On Oct 24, 11:46 am, Anne <anne...@gmail.com> wrote:
> Hi,
>
> I have an images with periodic stripes with various orientation which
> I would like to find the periodicity of. I've Fourier transformed the
> image and found the peak in the transform (via a radial average) so I
> have the q value (in I assume pixels^-1) corresponding to my stripe
> periodicity. I now need to get a real space value out but I'm lost as
> to where the factors of 2pi etc go. Can anyone point me in the right
> direction? I've read the help files online but I'm still horribly
> confused.
Assume your original image has a linear size of L in whatever units
you want. Let's say you have a satellite image that covers 7 km x 7
km. Then L = 7 km. Let's also say that your image has N pixels.
The FFT() produces Fourier coefficients which are a function of
"frequency" which in this case is (1/length). (in physics we would
call that a wavenumber)
The fundamental frequency is 1/L. Every fourier coefficient is an
even multiple of that frequency. So if you have N real pixels, there
are N/2 unique fourier coefficients, and they have a frequency
assignment like this:
Coeff #: 0(DC) 1 2 3 4 ... N/2
Frequency: 0 (1/L) (2/L) (3/L) (4/L) ... (N/(2*L))
Once you determine the frequency of your stripes, the linear size
corresponding to that frequency is just (1/frequency).
For example, if the stripes on our 1 km image have a fourier peak at
sample 42, that is equal to frequency of 6.0 km^(-1), and a linear
size of (1/6) km = 0.167 km.
Craig
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