Stability in diffraction tomography and a nonlinear “basic theorem”

The stability problem is studied for reconstruction of the refraction coefficient from boundary measurements of solutions of the Helmholtz equation at a fixed time-frequency. An answer is given in terms of Gabor means of the coefficient. A domain in the phase space is shown where the Gabor means can be stably reconstructed. As a corollary, a rigorous form is given to the basic theorem of diffraction tomography.[PUBLICATION ABSTRACT]