The present invention discloses a method and an apparatus to compute a complex wavefield, referred to as the object wave o, by means of measuring the intensity signal resulting from the interference of the said object wave with a second wave termed the reference wave. The second wave r is assumed to have some non-vanishing mutual coherence with the said object wave o. The reference wave can be obtained from a source or from the object wave itself. The wave may be emitted from sources of variable degree of coherence and can be scattered waves, but also light-emitting molecules, matter waves such as electron beams or acoustical sources. The disclosed method relates to the said "non-linear method" (NLM). The innovation resides in the fact that the NLM improves considerably the bandwidth of the wavefront reconstructed from off-axis interferograms and holograms obtained in a single shot. The advantage is the significant improvement of the resolution of the images obtained from the reconstructed wavefront, i.e. amplitude and phase images. The said method also suppresses the artifacts resulting from the intensity recording of interferograms and holograms. The method is general in the sense that it can be used for any interferometric measurement, provided that it satisfies the simple requirement that the intensity of the reference wave is larger than the intensity of the object wave, and that the object wave modulated by the reference is confined to at least a quadrant of the spectrum. The disclosed method applies to interferometry, holography in optics, electron waves and acoustics. In particular, it can be implemented in phase, fluorescence, luminescence, electron and acoustic microscopy.