Ordinary wave reflectometry in a plasma containing a localized density perturbation is studied with a one-dimensional (1D) model. The phase response is studied as a function of the wavenumber and position of the perturbation. It is shown that it strongly depends upon the perturbation shape and size. For a small perturbation wavenumber, the response is due to the oscillation of the cut-off layer. For larger wavenumbers, two regimes of resonant Bragg scattering are found: for a broad perturbation, the phase response is an image of the perturbation itself; for a narrow perturbation, it is an image of the Fourier transform. These features are enhanced for a broadband perturbation (modulated square wave) and scattering can occur over the whole region up to the cut-off. Furthermore, in that case there is a specific behaviour at the cut-off due to the sharp boundary effects of this perturbation. Because of this peculiarity, the phase response obtained for a damped square perturbation reproduces the results of an earlier experiment (Rhodes et al, Rev. Sci. Instrum. 1992).

The phase shift due to the resonant Bragg scattering of an ordinary wave in a fluctuating plasma is numerically computed for large amplitude density fluctuations, i.e. well beyond the Born approximation. The phase response (the phase shift against the perturbation position in the density gradient) is strongly distorted with respect to the small amplitude case, and 2π phase jumps occur. For localized quasi-monochromatic fluctuations, the results are explained by an analytical model where the Helmholtz equation is approximated by a Mathieu equation. The maximum phase shift and the phase jumps are well predicted by the model. It turns out that the theoretical predictions also apply to moderate amplitudes. For an actual phase measurement where the number of different frequencies (i.e. the number of perturbation positions) is finite, most phase jumps are missed, due to the steepness of the phase jumps, and the measured phase shift increases continuously.