In the phase screen theory of ionospheric scintillations the ionospheric irregularities are considered as pure phase objects, and the diffraction pattern produced on the ground, by radio waves propagating through this phase screen, is obtained from conventional Fresnel diffraction theory. In the present paper the inverse problem of retrieving phase variations in the screen from the diffraction pattern on the ground is treated by using the transport-of-intensity equation (TIE), which is derived from the Fresnel diffraction theory result. An approximate version of the TIE is solved to obtain the phase variation in the screen from the intensity distribution on the ground. It is seen that when the phase variations involve spatial scale lengths ~400 m, phase fluctuations of ~5 rad can be recovered from intensity variations on the ground, for a 300-MHz signal. For larger spatial scale lengths and higher frequencies this method can be used to retrieve larger phase variations in the screen. ¿ 1999 American Geophysical Union