Non-linear iterative phase retrieval based on Frechet derivative

V. Davidoiu (1) , B. Sixou (1) , M. Langer (1) , F. Peyrin (1)

1 Imagerie Tomographique et Radiothérapie

Several methods of phase retrieval for in-line phase tomog-raphy have already been investigated based on the linearization of the relation between the phase shift induced by the object and the diffracted intensity. In this work, we present a non-linear iterative approach using the Frechet derivative of the intensity recorded at a few number of propagation distances. A Landweber type iterative method with an analytic calculation of the Frechet derivative adjoint is proposed. The inverse problem is regularized with the smoothing L 2 norm of the phase gradient and evaluated for several different implementations. The evaluation of the method was performed using a simple phase map, both with and without noise. Our approach outperforms the linear methods on simulated noisy data up to high noise levels and thanks to the proposed analytical calculation is suited to the processing of large experimental image data sets.

Mots clés: Inverse problems; Phase retrieval; X-ray imaging; X-ray microscopy

Domaines: Imagerie; Traitement du signal et de l'image [eess.SP]

V. Davidoiu, B. Sixou, M. Langer, F. Peyrin. Non-linear iterative phase retrieval based on Frechet derivative. Optics Express, 2011, 19 (23), pp.22809. ⟨hal-02000438⟩