Method for obtaining a phase image from an intensity image

An apparatus for reconstructing a phase of a radiation wave field comprising:

• a means for acquisition of a representative measure of an intensity variation of the radiation wave field on a selected surface extending globally from one end to another of the radiation wave field;
• a means for acquisition of a representative measure of the intensity of the radiation wave field on the selected surface;
• a processor to sequentially perform the following steps:
• (i) transform the representative measure of the intensity variation to produce a first representation of integral transform and apply to the first representation of integral transform a first filter and produce a first representation of modified integral transform;
• (ii) apply a first function of the first representation of integral transform to the first representation of modified integral transform to produce an untransformed representation;
• (iii) apply a correction based on the measure of intensity on the selected surface to the untransformed representation;
• (iv) transform the untransformed corrected representation to produce a second representation of integral transform and to apply to the second representation of integral transform a second filter;
• and
• (v) apply a second function of the second integral transform to the second modified representation of integral transform to produce a measure of phase of the radiation wave field on the selected surface extending globally from one end to another of the radiation wave field,
• wherein the first and second filters are measure of a representation of a Green's function in a space of eigenfunctions of the Helmholtz equation with separable coordinates such that the first and second integral transforms are one-dimensional integral transforms in the space of the radiation wave field.