Three-dimensional (3D) cylindrically-shaped function (Its axis passes through the origin with orientation vector sin 0 cos and the intensity distribution of its cross-section has isotropic 2D Gaussian function.):
$$G(x,y,z;σ) =\frac{1}{2πσ^2}exp(-\frac{{x_a}^2+{y_a}^2}{2σ^2})$$
$$ {x_a}=xcosθ-zsinθ$$ $$ {y_a} =y$$
I try to use the method I used in 1D and 2D Fourier transformation, but it seems that it doesn't work. I can't get rid of the complex number i in this fourier transformation.