def two_point_correlation_fft(im):
    r"""
    Calculates the two-point correlation function using fourier transforms

    Parameters
    ----------
    im : ND-array
        The image of the void space on which the 2-point correlation is desired

    Returns
    -------
    result : named_tuple
        A tuple containing the x and y data for plotting the two-point
        correlation function, using the *args feature of matplotlib's plot
        function.  The x array is the distances between points and the y array
        is corresponding probabilities that points of a given distance both
        lie in the void space.

    Notes
    -----
    The fourier transform approach utilizes the fact that the autocorrelation
    function is the inverse FT of the power spectrum density.
    For background read the Scipy fftpack docs and for a good explanation see:
    http://www.ucl.ac.uk/~ucapikr/projects/KamilaSuankulova_BSc_Project.pdf
    """
    # Calculate half lengths of the image
    hls = (np.ceil(np.shape(im))/2).astype(int)
    # Fourier Transform and shift image
    F = sp_ft.ifftshift(sp_ft.fftn(sp_ft.fftshift(im)))
    # Compute Power Spectrum
    P = sp.absolute(F**2)
    # Auto-correlation is inverse of Power Spectrum
    autoc = sp.absolute(sp_ft.ifftshift(sp_ft.ifftn(sp_ft.fftshift(P))))
    tpcf = _radial_profile(autoc, r_max=np.min(hls))
    return tpcf
r"""
    Calculates the two-point correlation function using fourier transforms

    Parameters
    ----------
    im : ND-array
        The image of the void space on which the 2-point correlation is desired

    Returns
    -------
    result : named_tuple
        A tuple containing the x and y data for plotting the two-point
        correlation function, using the *args feature of matplotlib's plot
        function.  The x array is the distances between points and the y array
        is corresponding probabilities that points of a given distance both
        lie in the void space.

    Notes
    -----
    The fourier transform approach utilizes the fact that the autocorrelation
    function is the inverse FT of the power spectrum density.
    For background read the Scipy fftpack docs and for a good explanation see:
    http://www.ucl.ac.uk/~ucapikr/projects/KamilaSuankulova_BSc_Project.pdf