We consider the reconstruction problem for limited angle tomography using filtered backprojection (FBP). We introduce microlocal analysis and use it to explain why the well-known streak artifacts are present at the end of the limited angular range. We explain how to mitigate the streaks and prove that our modified FBP operator is a standard pseudodifferential operator, and so it does not add artifacts. We provide reconstructions to illustrate our mathematical results. This is joint work with Juergen Frikel, Helmholtz Zentrum, Muenchen.