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Fourier transformation- rescale axis

payman
13-Aquamarine

Fourier transformation- rescale axis

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 4
RichardJ
19-Tanzanite
(To:payman)

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

payman
13-Aquamarine
(To:RichardJ)

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?

RichardJ
19-Tanzanite
(To:payman)

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.

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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