Let $ a,\ b$ be postive real numbers. For a real number $ t$, denote by $d(t)$ the distance between the origin and the line $ (ae^t)x \plus{} (be^{ \minus{} t})y \equal{} 1$.

Let $ a,\ b$ vary with $ ab \equal{} 1$, find the minimum value of $ \int_0^1 \frac {1}{d(t)^2}\ dt$.