How to plot wavelength and wavenumber FFT from intensity data

Halo.

I have a problem with FFT data, i cant fine correct wavenumber domain and wavelength domain for FFT from my data.

my data base on 3648 pixel array with 8 nm between each pixel.

i want to fine wavelength domain and filter the noise of intensity.

Answer 1

[David Goodmanson]

Hi Arwi,

n = 3648, dpix = 8e-9;   % 8nm seems small for a pixel width

The x array has spacing delx = dpix and is

x = delx*(0:n-1)

The conjugate variable to x is 1/lambda which I shall denote by ilam, since there does not seem to be a generally accepted symbol for this. For an n-point fft, the golden rule for array spacings [delx for array x and dilam for array ilam] is

delx*dilam = 1/n  

which results in the array for inverse wavelength

dilam = 1/(delx*n);      ilam = (1/(delx*n))*(0:n-1)    % m^-1

Wave number is 2pi/lamda, so the k array is

k = (2*pi/(delx*n))*(0:n-1)   % m^-1

In terms of pixels, in that case dpix = delx = 1 and

x = 0:n-1
ilam = (1/n)*(0:n-1)       % pixel^-1
k = (2*pi/n)*(0:n-1)       % pixel^-1

This makes sense since the first nonzero value of k (second point n the array) is k1 = 2*pi/n and

exp(i*k1*x) = exp( (2*pi*i/n)*(0:n-1) )   

is one complete oscillation across the array. That's the lowest allowable nonzero periodic frquency.

[Arwi Rinaldo]

and how about the fft?

[David Goodmanson]

The data in the frequency domain is fft(your data)/3648, and the k or ilam array that goes with it is shown above.