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We present a variational approach to obtain a reconstruction of module and phase of a 3D wave field from intensity-only measurements on two or more sensor planes at different axial positions. The objective functional consists of a data fidelity term and a regularizer. The fidelity term corresponds to the likelihood function derived for the Gaussian noisy observations of the wave field intensities (powers). The wave field reconstruction is framed as a constrained nonlinear optimization with respect to a 2D object wave field and is based on the augmented Lagrangian technique. The main goal is to design an algorithm which is more efficient and accurate than the conventional ones such as the well-known Gerchberg-Saxton algorithms and their multiple modifications. As a further development we discuss a variational approach using a transform domain prior on phase and module of the 2D object wave field.