This is kind-of-difficult in practice. Your fft has low-wavenumber components at [0,0], [1,0], [-1, 0], [0,1], [0,-1] and if we include the components with norm 2^(1/2) at [1,1], [-1,1], [-1,-1] and [1,-1]. The non-DC components are at 0, 90, 180 and 270 degrees angle, and then 45, 135, 225, and 315 degrees. It is not at all clear to me that you can trivially interpolate between these Fourier-components. What I suggest is that you rotate your image with imrotate, and then do the fft and extract the horizontal and vertical components from those ffts to get the angular variation. By doing that it is at least clear what interpolation-effects are introduced.