How to measure the wave-function absolute squared of a moving particle by using mirrors

We consider a slow particle with wave function $\psi_t(\vec{x})$, moving freely in some direction. A mirror is briefly switched on around a time $T$ and its position is scanned. It is shown that the measured reflection probability then allows the determination of $|\psi_T(\vec{x})|^2$. Experimentally available atomic mirrors should make this method applicable to the center-of-mass wave function of atoms with velocities in the cm/s range.