fft, wave number, frequency, and dispersion relation.

I have a picture of waves. Every line in the picture represents a wave. My purpose is that the determination of the dispersion relation (the angular frequency w as the function of wave number k ).

The following is the practice of references: After a background subtraction, the wave line is tracked down by an intensity threshold criterion and subjected to a one-dimensional Fourier transform. To resolve the continuous spectrum correctly, a Hamming window is applied before the fast Fourier transform. For the determination of the dispersion relation, an exponential function A(k,t)= A0(k)exp{w(k)t} is fitted to the time evolution of the lowest 30 modes, yielding a angular frequency w (k) for each of these modes.

To determine the dispersion curve experimentally, a Hann window was utilized to resolve the spectra followed by a one-dimensional Fourier transformation using the FFTPACK library from NETLIB. From the initial linear regime of the time evolution of the Fourier amplitudes, the growth rates were calculated for each mode as the slopes of the straight lines.

After fast Fourier transform, I only got amplitude and frequency. But, the dispersion relation need angular frequency and wave number. How can I do to obtain angular frequency and wave number?