Wave field reconstruction from multiple plane intensity-only data: augmented lagrangian algorithm.

A complex-valued wave field is reconstructed from intensity-only measurements given at multiple observation planes parallel to the object plane. The phase-retrieval algorithm is obtained from the constrained maximum likelihood approach provided that the additive noise is gaussian. The forward propagation from the object plane to the measurement plane is treated as a constraint in the proposed variational setting of reconstruction. The developed iterative algorithm is based on an augmented lagrangian technique. An advanced performance of the algorithm is demonstrated by numerical simulations.

[1]  John N. Tsitsiklis,et al.  Parallel and distributed computation , 1989 .

[2]  J. Fienup,et al.  Optical wavefront measurement using phase retrieval with transverse translation diversity. , 2009, Optics express.

[3]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[4]  Anne Margarette S Maallo,et al.  Fast-convergent algorithm for speckle-based phase retrieval and a design for dynamic wavefront sensing. , 2009, Applied optics.

[5]  Jian-Feng Cai,et al.  Split Bregman Methods and Frame Based Image Restoration , 2009, Multiscale Model. Simul..

[6]  James V. Burke,et al.  Variational Analysis Applied to the Problem of Optical Phase Retrieval , 2003, SIAM J. Control. Optim..

[7]  Ross W Deming.  Phase retrieval from intensity-only data by relative entropy minimization. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  Heinz H. Bauschke,et al.  Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  M. Hestenes.  Multiplier and gradient methods , 1969 .

[10]  Anbo Wang,et al.  Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula. , 2006, Applied optics.

[11]  Jaakko Astola,et al.  Multiple Plane Phase Retrieval Based On Inverse Regularized Imaging and Discrete Diffraction Transform , 2010 .

[12]  G. Pedrini,et al.  Wave-front reconstruction from a sequence of interferograms recorded at different planes. , 2005, Optics letters.

[13]  Francesco Soldovieri,et al.  An improved version of the relative entropy minimization approach for the phase retrieval problem , 2010 .

[14]  J. Fienup,et al.  Phase retrieval with transverse translation diversity: a nonlinear optimization approach. , 2008, Optics express.

[15]  G. Pedrini,et al.  Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field. , 2006, Applied optics.

[16]  José M. Bioucas-Dias,et al.  Fast Image Recovery Using Variable Splitting and Constrained Optimization , 2009, IEEE Transactions on Image Processing.

[17]  R. Gerchberg.  A practical algorithm for the determination of phase from image and diffraction plane pictures , 1972 .

[18]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[19]  B Y Gu,et al.  Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison. , 1994, Applied optics.

[20]  James V. Burke,et al.  Optical Wavefront Reconstruction: Theory and Numerical Methods , 2002, SIAM Rev..

[21]  Mario Bertero,et al.  Introduction to Inverse Problems in Imaging , 1998 .

[22]  J. Astola,et al.  Backward discrete wave field propagation modeling as an inverse problem: toward perfect reconstruction of wave field distributions. , 2009, Applied optics.

[23]  G Ang.  On the phase retrieval problem in optical and electronic microscopy , 1981 .

[24]  J R Fienup,et al.  Phase retrieval algorithms: a comparison. , 1982, Applied optics.

[25]  T. Isernia,et al.  Role of support information and zero locations in phase retrieval by a quadratic approach , 1999 .

[26]  Robert D. Nowak,et al.  Majorization–Minimization Algorithms for Wavelet-Based Image Restoration , 2007, IEEE Transactions on Image Processing.

[27]  J. Astola,et al.  Discrete diffraction transform for propagation, reconstruction, and design of wavefield distributions. , 2008, Applied optics.

[28]  D. L. Misell.  Comment onA method for the solution of the phase problem in electron microscopy , 1973 .

[29]  Xiaojun-Hu,et al.  Resolution-enhanced subpixel phase retrieval method. , 2008, Applied optics.

[30]  M. J. D. Powell,et al.  A method for nonlinear constraints in minimization problems , 1969 .

[31]  T. Kreis.  Handbook of Holographic Interferometry: Optical and Digital Methods , 2004 .