I know what it means for a pseudodifferential operator $A\in\Psi(\mathbb{R}^n)$ to be elliptic at a point $(x,\xi)\in T^*\mathbb{R}^n$: the principal symbol of $A$ is non-vanishing at the point.
But what does it mean for a Fourier Integral Operator to be elliptic? Is there an analogous notion of principal symbol for an FIO?