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Field measurements of both amplitude and phase generally are more complicated and require more expensive equipment than amplitude-only measurements. Phase retrieval from measured phaseless field data is, therefore, of interest for source modeling in dosimetry applications, electromagnetic compatibility investigations, near-field to far-field transformations and antenna diagnostics. We here present a phase-retrieval method that uses an optimization algorithm based on the phase angle gradients of a functional. Numerical test cases have shown that the method is working for different initial phase distributions as well as different placements of the source. The method also works well for a test case with measured 50 Hz magnetic flux density from a transformer. The obtained phase angles on a measurement plane in front of the transformer gave calculated field amplitudes on other measurement planes that agree well with measured field. The ratios between the largest amplitude difference and the largest measured amplitude for the three Cartesian magnetic flux density components, for one of the planes, are for example 6.62%, 9.51% and 6.40%.