If one has a 2-D array and would like to take the 1-D Fourier transform along a direction $\theta$ degrees off the horizontal, is there a better/faster way to do this rather than rotating the image by $-\theta$ degrees, taking the 1-D FT across the columns, and then rotating the result back by $\theta$ degrees?
You can take the 1D IFFT using a pseudo-polar grid. Fig. 2 in this paper shows an example of such grid.
Possible choices for the angle $\theta$ are going to be limited. but the transform will be free from interpolation artifacts introduced by the rotation algorithm.