Cross-talk compensation of a spatial light modulator for iterative phase retrieval applications.

Beam-propagation-based phase recovery approaches, also known as phase retrieval methods, retrieve the amplitude and the phase of arbitrary complex-valued fields. We present and experimentally demonstrate a simple and robust iterative method using a liquid crystal spatial light modulator located at an object diffraction plane. M random phase masks are applied between the object and the image sensor using the modulator, and then M diffraction patterns are collected in the Fourier plane. An iterative algorithm using these patterns and simulating the propagation of the light between the two planes allow us to recover the object wavefront. The use of this type of dynamic modulator makes the experimental setup simpler and more flexible. We need no a priori knowledge about the object field, and the convergence rate is high. Simulation results show that the method exhibits high immunity to noise and does not suffer any stagnation problem. However, experimental results have shown that the technique is sensitive to the cross talk of the modulator. We propose a method for compensating these modulator defects that are validated by experimental results.

[1]  B. Dong,et al.  Numerical investigation of phase retrieval in a fractional Fourier transform , 1997 .

[2]  James R. Fienup,et al.  Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint , 1987 .

[3]  J. Miao,et al.  Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects , 1998 .

[4]  G. Pedrini,et al.  Phase retrieval using multiple illumination wavelengths. , 2008, Optics letters.

[5]  James R. Fienup,et al.  Phase retrieval using boundary conditions , 1986 .

[6]  Eldad Bahat Treidel,et al.  On the fringing-field effect in liquid-crystal beam-steering devices. , 2004, Applied optics.

[7]  J. Miao,et al.  Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens , 1999, Nature.

[8]  G. Pedrini,et al.  Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation , 2007 .

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

[10]  S. Eisebitt,et al.  Lensless imaging of magnetic nanostructures by X-ray spectro-holography , 2004, Nature.

[11]  J. Rodenburg,et al.  Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm. , 2004, Physical review letters.

[12]  A. M. Kowalczyk,et al.  Phase Retrieval for a Complex-Valued Object Using a Low-Resolution Image , 1990, Signal Recovery and Synthesis III.

[13]  Wen Chen,et al.  Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain. , 2010, Optics express.

[14]  T. Martin,et al.  Polarization properties of a nematic liquid-crystal spatial light modulator for phase modulation. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[15]  M. Vorontsov,et al.  Phase retrieval from a set of intensity measurements: theory and experiment , 1992 .

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

[17]  M. Goksör,et al.  Reducing the effect of pixel crosstalk in phase only spatial light modulators. , 2012, Optics express.

[18]  W. Osten,et al.  Characterization of a spatial light modulator and its application in phase retrieval. , 2009, Applied optics.

[19]  N George,et al.  Image reconstruction from partial Fresnel zone information. , 1986, Applied optics.

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

[21]  Aharon Levi,et al.  Image restoration by the method of generalized projections with application to restoration from magnitude , 1984 .

[22]  J. Zuo,et al.  Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities , 2003, Science.

[23]  K. Nugent,et al.  Diffraction with wavefront curvature: a path to unique phase recovery. , 2005, Acta crystallographica. Section A, Foundations of crystallography.

[24]  J R Fienup,et al.  Reconstruction of an object from the modulus of its Fourier transform. , 1978, Optics letters.

[25]  W. Crossland,et al.  Modeling of the diffraction efficiency and polarization sensitivity for a liquid crystal 2D spatial light modulator for reconfigurable beam steering. , 2007, Journal of the Optical Society of America. A, Optics, image science, and vision.

[26]  M. Yzuel,et al.  Anamorphic and spatial frequency dependent phase modulation on liquid crystal displays. Optimization of the modulation diffraction efficiency. , 2005, Optics express.

[27]  D. Gabor.  A New Microscopic Principle , 1948, Nature.

[28]  Wolfgang Osten,et al.  A benchmark system for the evaluation of selected phase retrieval methods , 2014, Photonics Europe.

[29]  G. Pedrini,et al.  Interferometric evaluation of angular displacements using phase retrieval. , 2008, Optics letters.

[30]  K. Nugent,et al.  Unique phase recovery for nonperiodic objects. , 2003, Physical review letters.

[31]  J. Rodenburg,et al.  A phase retrieval algorithm for shifting illumination , 2004 .

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

[33]  Claas Falldorf,et al.  Investigation of smooth wave fronts using SLM-based phase retrieval and a phase diffuser , 2012 .

[34]  James R. Fienup,et al.  Phase-retrieval stagnation problems and solutions , 1986 .

[35]  Wen Chen,et al.  Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging. , 2011, Applied optics.

[36]  Wolfgang Osten,et al.  Examination and optimizing of a liquid crystal display used as spatial light modulator concerning the fringing field effect , 2012, Other Conferences.

[37]  J. Kirz,et al.  High-Resolution Imaging by Fourier Transform X-ray Holography , 1992, Science.