  We experimentally demonstrate how to solve the phase problem of diffraction
using multi-wave interference with standard diffraction experimental setups
without the need for taking any auxiliary data. In particular, we show that the
phases of the Fourier components of a periodic structure can be fully recovered
by deliberately choosing a probe wavelength of the diffracting radiation much
smaller than the lattice constant. In the course of the demonstration, we
accurately determine the refractive index profile of nanocomposite phase
gratings by light and neutron diffraction measurements.
