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payman1-Visitor
1-Visitor
September 13, 2012
Question

Fourier transformation- rescale axis

  • September 13, 2012
  • 4 replies
  • 1774 views

Dear Friends,

My original data is in k-space (wave number domain). I want to use Fourier transformation to transfer into z-space (position domain).

After transformation, when I graph the new data, on horizontal axis I have the same number of data points as I sampled my original data. How can I express this axis in meter? what is the relation between data points and the actual position?

Could you please help me?

Thank you

Payman

4 replies

RichardJ19-Tanzanite
19-Tanzanite
September 13, 2012

The upper limit of the data should be 1/(2 x sampling interval). Is this from an FT spectrometer?

payman1-VisitorAuthor
1-Visitor
September 13, 2012

Richard: Thank you. is (1/(2 x sampling interval)) in meter ?

I am simulating the Fourier domain optical coherence tomography. To start I have defined a Gaussian spectral function. I sampled this function in wave number space and performed FT to transfer to position domain. The transfered function is the coherence function of the source with coherence length as the FWHM of the functin. However I am not sure how experess the horizontal axis in meter. What is the relation between the number of sample points in transfered space and the actual position?

RichardJ19-Tanzanite
19-Tanzanite
September 13, 2012
Richard: Thank you. is (1/(2 x sampling interval)) in meter ?

It's in 1/units of your frequency scale, so in this case cm.

OCT is a bit outside my field (I am very familiar with FT spectroscopy), but this relationship just falls out of the Nyquist criterion. The highest frequency you can measure is half the sampling frequency. If you measure in the wavenumber domain at an interval of, say, 1 cm-1, then the highest spatial frequency after the FT is 5mm.

MichaelH1-Visitor
1-Visitor
September 14, 2012

There is extensive information on using FFTs in the Mathcad help section with extensive example files included.

Your questions may be answered there.


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