As far as I understand you're taking a Fourier Transform of an image. In your case, that image corresponds to that of a microstructure alloy. So basically in 2D-Fourier transforms we are trying to model the intensity levels of the image and represent it in terms of a frequency plot. This is analogous to the 1D Fourier transform.
Is there a relationship between the angle of these bands in the
Fourier image and the orientation of the grain boundaries in the real
This can only be answered if there was an image provided. But still one could say that there is a relationship between the bands and the orientation of the grain boundaries. In the image of simple patters given below you can see the relation between the Spatial and Fourier domains. For an image of an alloy microstructure we cannot explicitly see the realtionship due to the immense detail in the spatial domain.
Another observation is that if high frequencies are removed, and the
inverse Fourier transform is taken, a significant amount of noise is
removed, and I am mostly left with the grain boundaries of the
microstructure. Is there any other kind of useful information that can
be extracted from the Fourier image?
This disappearence of noise takes place because the noise being a sharply varying intensity value is modelled by high frequencies in the Frequency domain. Removing those will in face reveal the boundaries which are represented by smoothly varing intensity values.
Hope this helps. :)