  Let $\mathcal{M}$ be a holonomic algebraic $\mathcal{D}$-module on the affine
line. Its exponential factors are Puiseux germs describing the growth of
holomorphic solutions to $\mathcal{M}$ at irregular points. The stationary
phase formula states that the exponential factors of the Fourier transform of
$\mathcal{M}$ are obtained by Legendre transform from the exponential factors
of $\mathcal{M}$. We give a microlocal proof of this fact, by translating it in
terms of enhanced ind-sheaves through the Riemann-Hilbert correspondence.
