how to convert a graph of intensity vs wavenumber into a graph of intensity vs distance in labview

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Hi,

I used inverse fourier transform (in labview) to convert a graph of intensity vs wavenumber (with a constant distance between 2 adjacent wavenumbers) into a graph of intensity vs distance.

Do you know what s the the relationship between the wavenumber and distance when I use inverse fourier transform?

I need this relationship in order to calibrate the axis of distance after inverse fourier transform
Your question seems to be about the fundamentals of Fourier transforms rather than about the use of Igor Pro to perform Fourier transforms. Briefly to the point of your direct question ...

* The units of a Fourier transform are the inverse of the original. The inverse is just going backward. So, Hz -> s with a Fourier transform, and s -> Hz with an inverse Fourier transform.

Otherwise, based on the practical undertones of your question, I might recommend that you start with your raw data and do this test ...

* Convert the raw data in Labview
* Convert the raw data in Igor Pro
* Compare the two Fourier transform results

You might be surprised to learn about the differences in what is returned by the two methods. Pay attention in particular to the two components of the return, the real part and the imaginary part. Also, pay attention to the magnitude of the return values. Finally, look at what you get for the separation between points (the "step size") in the two cases.

Finally, based on the general direction of your questions, I suggest that you might want to research a good book or book chapter on Fourier transforms and their applications.

--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAH

June 30, 2016 at 07:27 am - Permalink

I wrote the attached Igor Help File on Fourier optics a while ago for my own benefit. Perhaps it will be of value to you.

edit:
Maximus,
I just noticed that you referred to transforming an ITENSITY distribution. You should understand and appreciate the differences between coherent and incoherent imaging (or propagation) before blindly using my help file, which specifically assumed coherent propagation (and complex fields). The far-field intensity will be the magnitude squared of my FFT output, but you will have to make assumptions about the phase of your source intensity field. The lateral scaling will be common to both situations.
FFT and Fourier Optics_0.ihf (50.09 KB) FFT and Fourier Optics_0.ihf (50.09 KB) FFT and Fourier Optics_0.ihf (50.09 KB)

June 30, 2016 at 09:30 am - Permalink