.. Géométrie-du-modulateur-et-méthodes-d, extraction de l'information de phase . 121 5.2.2 Comparaison qualitative d'images de phase en fonction des deux techniques étudiées, p.122

W. C. Röntgen, On a new kind of rays, Science, p.1896

S. Singh and M. Singh, Explosives detection systems (EDS) for aviation security, Signal Processing, vol.83, issue.1, 2003.
DOI : 10.1016/S0165-1684(02)00391-2

V. Cnudde and M. N. Boone, High-resolution X-ray computed tomography in geosciences: A review of the current technology and applications, Earth-Science Reviews, vol.123, 2013.
DOI : 10.1016/j.earscirev.2013.04.003

K. Krug, J. Dik, M. D. Leeuw, A. D. Whitson, J. Tortora et al., Visualization of pigment distributions in paintings using synchrotron K-edge imaging, Applied Physics A, vol.16, issue.2, 2006.
DOI : 10.1007/s00339-006-3519-y

K. Krug, L. Porra, P. Coan, A. Wallert, J. Dik et al., Relics in medieval altarpieces? Combining X-ray tomographic, laminographic and phase-contrast imaging to visualize thin organic objects in paintings, Journal of Synchrotron Radiation, vol.15, issue.1, 2008.
DOI : 10.1107/S0909049507045438/gf5005sup1.avi

W. Crookes, The Bakerian Lecture: On the Illumination of Lines of Molecular Pressure, and the Trajectory of Molecules, Philosophical Transactions of the Royal Society of London, vol.170, issue.0, 1879.
DOI : 10.1098/rstl.1879.0065

W. Coolidge, The development of modern roentgen-ray generating apparatus, American journal of Roentgenology, 1930.

P. K. Spiegel, The rst clinical x-ray made in america100 years, American Journal of Roentgenology, 1995.

J. Dillenseger and E. Moerschel, Guide des Technologies de L'imagerie Médicale et de la Radiotherapie : Quand la Theorie Eclaire la Pratique, 2009.

D. H. Bilderback, Review of third and next generation synchrotron light sources, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.38, issue.9, 2005.
DOI : 10.1088/0953-4075/38/9/022

J. Radon, über die bestimmung von funktionen durch ihre integralwerte längs gewisser mannigfaltigkeiten, Berichte uber die Verhandlungen der Sachsischen Akademie der Wissenschaften zu Leipzig, 1917.

A. M. Cormack, Representation of a function by its line integrals, with some radiological applications, Journal of Applied Physics, 1963.

G. N. Hounseld, Computerized transverse axial scanning (tomography) : Part 1. description of system, The British Journal of Radiology, 1973.

U. Bonse and M. Hart, AN X???RAY INTERFEROMETER, Applied Physics Letters, vol.6, issue.8, 1965.
DOI : 10.1063/1.1754212

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, Phase-contrast imaging using polychromatic hard X-rays, Nature, vol.384, issue.6607, 1996.
DOI : 10.1038/384335a0

T. Takeda, A. Momose, E. Ueno, and Y. Itai, Phase-contrast X-ray CT image of breast tumor, Journal of Synchrotron Radiation, vol.5, issue.3, 1998.
DOI : 10.1107/S0909049597020116

C. David, B. Nohammer, H. H. Solak, and E. Ziegler, Dierential x-ray contrast imaging using a shearing interferometer, Applied Physics Letters, 2002.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai et al., Demonstration of X-Ray Talbot Interferometry, Japanese Journal of Applied Physics, vol.42, issue.Part 2, No. 7B, 2003.
DOI : 10.1143/JJAP.42.L866

F. Pfeier, T. Weitkamp, O. Bunk, and C. David, Phase retrieval and dierential phase-contrast imaging with low-brilliance x-ray sources, Nature Physics, 2006.

A. Olivo and R. Speller, Modelling of a novel x-ray phase contrast imaging technique based on coded apertures, Physics in Medicine and Biology, vol.52, issue.22, 2007.
DOI : 10.1088/0031-9155/52/22/001

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara et al., Cadaveric and in vivo human joint imaging based on dierential phase contrast by x-ray talbot-lau interferometry, 2013.

V. V. Lider and M. V. Kovalchuk, Xray phase contrast methods, ISSN Crystallography Reports, 2013.

O. Hemberg, M. Otendal, and H. Hertz, Liquid-metal-jet anode electron-impact x-ray source, Applied Physics Letters, vol.83, issue.7, 2003.
DOI : 10.1063/1.1292471

S. Fourmaux and J. Kieer, Laser-based K ?? X-ray emission characterization using a high contrast ratio and high-power laser system, Applied Physics B, vol.5, issue.5, 2016.
DOI : 10.1063/1.872867

S. Legoupil, A. Stolidi, and D. Tisseur, Anode structurée en multiple sites de génération de photons x, tube de rayons x et utilisation pour imagerie de source codée, p.172527, 2015.

D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation : Principles and Applications, 1999.
DOI : 10.1017/CBO9781139164429

B. Henke, X-ray interactions : photoabsorption, scattering, transmission, and reection at E=50- 30000 eV, Z=1-92, Atomic Data and Nuclear Data Tables, tech. rep., CXRO The Center for X-Ray Optics, 1993.

M. R. Teague, Deterministic phase retrieval: a Green???s function solution, Journal of the Optical Society of America, vol.73, issue.11, 1983.
DOI : 10.1364/JOSA.73.001434

E. Förster, K. Goetz, and P. Zaumseil, Double crystal diractometry for the characterization of targets for laser fusion experiments, 1980.

L. Zehnder, Ein neuer interferenzrefraktor, 1891.

Y. Shvyd-'ko and X. , Optics : High-Energy-Resolution Applications, 2004.

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. Rajewsky et al., Threedimensional imaging of nerve tissue by x-ray phase-contrast microtomography, Biophysical Journal, 1999.

A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, Wide-area phase-contrast x-ray imaging using large x-ray interferometers, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, 2001.

A. Yoneyama, T. Takeda, Y. Tsuchiya, J. Wu, A. Thet-thet-lwin et al., A phase contrast x-ray imaging system with a 60x30 mm eld of view based on a skew-symmetric two-crystal x-ray interferometer, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, 2004.

D. Chapman, W. Thomlinsonx, R. E. Johnstonk, D. Washburnk, E. Pisanok et al., Diraction enhanced x-ray imaging, Physics in Medicine and Biology, 1997.

C. Parham, Z. Zhong, D. M. Connor, L. D. Chapman, and E. D. Pisano, Design and implementation of a compact low-dose diraction enhanced medical imaging system, Academic Radiology, 2009.

M. Born and E. Wolf, Principles of optics : electromagnetic theory of propagation, interference and diraction of light, 2000.
DOI : 10.1017/CBO9781139644181

A. V. Bronnikov, Reconstruction formulas in phase-contrast tomography, Optics Communications, vol.171, issue.4-6, 1999.
DOI : 10.1016/S0030-4018(99)00575-1

A. Groso, R. Abela, and M. Stampanoni, Implementation of a fast method for high resolutionphase contrast tomography, Optics Express, 2006.

X. Wu and H. Liu, X-Ray cone-beam phase tomography formulas based on phase-attenuation duality, Optics Express, vol.13, issue.16, 2005.
DOI : 10.1364/OPEX.13.006000

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object, Journal of Microscopy, vol.206, issue.1, 2002.
DOI : 10.1046/j.1365-2818.2002.01010.x

M. Beltran, D. Paganin, K. Uesugi, and M. Kitchen, 2d and 3d x-ray phase retrieval of multimaterial objects using a single defocus distance, Optics Express, 2010.

S. Zabler, P. Cloetens, J. Guigay, J. Baruchel, and M. Schlenker, Optimization of phase contrast imaging using hard x rays, Review of Scientic Instruments, 2005.

L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent et al., Peele, X-ray phase imaging : Demonstration of extended conditions for homogeneous objects, Optics Express, 2004.

T. E. Gureyev, T. J. Davis, A. Pogany, S. C. Mayo, and S. W. Wilkins, Optical phase retrieval by use of rst born-and rytov-type approximations, Applied Optics, 2004.

A. Burvall, U. Lundström, P. A. Takman, D. H. Larsson, and H. M. Hertz, Phase retrieval in X-ray phase-contrast imaging suitable for tomography, Optics Express, vol.19, issue.11, 2011.
DOI : 10.1364/OE.19.010359

P. Cloetens, Principles current status ans recent results of propagation based x-ray phase imaging, International workshop on x ray and neutron phase imaging (XNPIG), 2014.

J. Hartmann, Investigations on the spectrum and orbit of delta Orionis., The Astrophysical Journal, vol.19, 1904.
DOI : 10.1086/141112

F. J. Roddier, Variations on a Hartmann theme, Optical Engineering, vol.29, issue.10, 1990.
DOI : 10.1117/12.55721

K. S. Morgan, D. M. Paganin, and K. K. Siu, Quantitative x-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size, Optics Letters, vol.36, issue.1, 2011.
DOI : 10.1364/OL.36.000055

K. S. Morgan, D. M. Paganin, and K. K. Siu, Quantitative single-exposure x-ray phase contrast imaging using a single attenuation grid, Optics Express, vol.19, issue.20, 2011.
DOI : 10.1364/OE.19.019781

K. S. Morgan, P. Modregger, S. C. Irvine, S. Rutishauser, V. A. Guzenko et al., A sensitive x-ray phase contrast technique for rapid imaging using a single phase grid analyzer, Optics Letters, vol.38, issue.22, 2013.
DOI : 10.1364/OL.38.004605

H. H. Wen, E. E. Bennett, R. Kopace, A. F. Stein, and V. Pai, Single-shot x-ray dierential phasecontrast and diraction imaging using two-dimensional transmission gratings, Optics Letters, 2010.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. Rapacchi, Fourier X-ray Scattering Radiography Yields Bone Structural Information, Radiology, vol.251, issue.3, 2009.
DOI : 10.1148/radiol.2521081903

URL : http://europepmc.org/articles/pmc2687535?pdf=render

E. E. Bennett, R. Kopace, A. F. Stein, and H. Wen, A grating-based single-shot x-ray phase contrast and diraction method for in vivo imaging, Medical Physics, 2010.

H. Lim, Y. Park, H. Cho, U. Je, D. Hong et al., Experimental setup and the system performance for single-grid-based phase-contrast x-ray imaging (PCXI) with a microfocus x-ray tube, Optics Communications, vol.348, 2015.
DOI : 10.1016/j.optcom.2015.03.028

Y. Park, T. Woo, H. Cho, D. Hong, U. Je et al., Detection analysis of phase-contrast X-ray imaging (PCXI) with single grid for nano-scopic applications, Optik - International Journal for Light and Electron Optics, vol.127, issue.2, 2016.
DOI : 10.1016/j.ijleo.2015.10.175

V. Zverev, S. Rodionov, M. Sokolskii, and V. Usoskin, Mathematical principles of hartmann test of the primary mirror of the large azimuthal telescope/lat, 1977.

Y. Carmon and E. N. Ribak, Phase retrieval by demodulation of a hartmannshack sensor, Optics Communications, 2003.

V. Ronchi, Forty Years of History of a Grating Interferometer, Applied Optics, vol.3, issue.4, 1964.
DOI : 10.1364/AO.3.000437

H. F. Talbot, Facts relating to optical science, The London and Edinburgh Philosophical Magazine and, Journal of Science, 1836.

J. Guigay, On fresnel diraction by one-dimensional periodic objects, with application to structure determination of phase objects, Journal of Modern Optics, 1971.

K. Creath, V Phase-Measurement Interferometry Techniques, Progress in Optics, 1988.
DOI : 10.1016/S0079-6638(08)70178-1

T. Weitkamp, A. Diaz, C. David, F. Pfeier, M. Stampanoni et al., X-ray phase imaging with a grating interferometer, Optics Express, vol.13, issue.16, 2005.
DOI : 10.1364/OPEX.13.006296

F. Pfeier, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry et al., Hard-x-ray dark-eld imaging using a grating interferometer, Nature Materials, 2008.

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation, Optics Express, vol.17, issue.15, 2009.
DOI : 10.1364/OE.17.012540.m005

H. Itoh, Two dimentional grating-based x-ray phase contrast imaging using fourier transform phase retrieval, Optics Express, 2011.

M. Bech, Advanced contrast modalities for x-ray radiology-phase contrast and dark-eld imaging using a grating interferometer, 2010.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster et al., Beam hardening eects in grating-based x-ray phase-contrast imaging, Medical physics, 2011.

G. K. Kallon, M. Wesolowski, F. A. Vittoria, M. Endrizzi, D. Basta et al., A laboratory based edge-illumination x-ray phase-contrast imaging setup with twodirectional sensitivity, Applied Physics Letters, 2015.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk et al., An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical eld, Medical Physics, 2001.

A. Olivo and R. Speller, A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources, Applied Physics Letters, 2007.

P. Diemoz, C. Hagen, M. Endrizzi, and A. Olivo, Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging, Applied Physics Letters, vol.103, issue.24, 2013.
DOI : 10.1063/1.4816827

P. C. Diemoz and A. Olivo, On the origin of contrast in edge illumination X-ray phase-contrast imaging, Optics Express, vol.22, issue.23, 2014.
DOI : 10.1364/OE.22.028199

M. Endrizzi, D. Basta, and A. Olivo, Laboratory-based X-ray phase-contrast imaging with misaligned optical elements, Applied Physics Letters, vol.107, issue.12, 2015.
DOI : 10.1063/1.3606442

S. Mahaut, M. Darmon, S. Chatillon, F. Jenson, and P. Calmon, Recent advances and current trends of ultrasonic modelling in civa, Insight-Non-Destructive Testing and Condition Monitoring, 2009.

R. Miorelli, C. Reboud, T. Theodoulidis, J. Martinos, N. Poulakis et al., Coupled approach vimbem for ecient modeling of ect signal due to narrow cracks and volumetric aws in planar layered media, Non Destructive Testing & Evaluation International, 2014.

C. Welnak, G. Chen, and F. Cerrina, Shadow : a synchrotron radiation and x-ray optics simulation tool, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers , Detectors and Associated Equipment, 1994.

P. Monnin, S. Bulling, J. Hoszowska, J. Valley, R. Meuli et al., Quantitative characterization of edge enhancement in phase contrast x-ray imaging, Medical Physics, 2004.

A. Ishisaka, H. Ohara, and C. Honda, A new method of analyzing edge eect in phase contrast imaging with incoherent x-rays, Optical Review, 2000.

E. J. Buis and G. Vacanti, X-ray tracing using geant4, Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment, 2009.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, The eects of the imaging system on the validity limits of the ray-optical approach to phase contrast imaging, Medical Physics, 2005.

J. Keller, Geometrical theory of diraction, Journal of the Optical Society of America, 1961.

C. Huygens, Traité de la lumière, 1912.

A. Prodi, E. Knudsen, P. Willendrup, S. Schmitt, C. Ferrero et al., A Monte Carlo approach for simulating the propagation of partially coherent x-ray beams, Advances in Computational Methods for X-Ray Optics II, 2011.
DOI : 10.1117/12.894520

E. Bergbäck-knudsen, A. Prodi, J. Baltser, M. Thomsen, P. Kjaer-willendrup et al., : a Monte Carlo software package for simulating X-ray optics, beamlines and experiments, Journal of Applied Crystallography, vol.13, issue.4, 2013.
DOI : 10.1107/S0021889813007991/he5585sup2.txt

S. Cipiccia, F. A. Vittoria, M. Weikum, A. Olivo, and D. A. Jaroszynski, Inclusion of coherence in Monte Carlo models for simulation of x-ray phase contrast imaging, Optics Express, vol.22, issue.19, 2014.
DOI : 10.1364/OE.22.023480

A. Kavanagh, A. Olivo, R. Speller, and B. Vojnovic, Feasibility testing of a pre-clinical coded aperture phase contrast imaging conguration using a simple fast monte carlo simulator, Biomedical Optics Express, 2014.

J. Bahrdt, Wave-front propagation: design code for synchrotron radiation beam lines, Applied Optics, vol.36, issue.19, 1997.
DOI : 10.1364/AO.36.004367

X. Shi, R. Reininger, M. Sanchez-del-rio, and L. Assoud, A hybrid method for X-ray optics simulation: combining geometric ray-tracing and wavefront propagation, Journal of Synchrotron Radiation, vol.95, issue.103, 2014.
DOI : 10.1103/PhysRevLett.95.043904

URL : https://hal.archives-ouvertes.fr/hal-01573008

A. Pogany, D. Gao, and S. Wilkins, Contrast and resolution in imaging with a microfocus x-ray source, Review of Scientic Instruments, 1997.

K. Morgan, K. Siu, and D. Paganin, The projection approximation and edge contrast for x-ray propagation-based phase contrast imaging of a cylindrical edge, Optics Express, vol.18, issue.10, 2010.
DOI : 10.1364/OE.18.009865

J. Wolf, A. Malecki, J. Sperl, M. Chabior, M. Schüttler et al., Fast one-dimensional wave-front propagation for x-ray dierential phase-contrast imaging, Biomedical Optics Express, 2014.

X. Wu and H. Liu, A general theoretical formalism for x-ray phase contrast imaging, Journal of X-ray Science and Technology, 2003.

X. Wu and H. Liu, A new theory of phase-contrast x-ray imaging based on wigner distributions, Medical Physics, 2004.

A. Hare and G. Morrison, Near-eld soft x-ray diraction modelled by the multislice method, Journal of Modern Optics, 1994.

B. Wªodarczyk and J. Pietrzak, Analytical reconstructions of intensity modulated x-ray phasecontrast imaging of human scale phantoms, Biomedical Optics Express, 2015.

Y. Sung, C. J. Sheppard, G. Barbastathis, M. Ando, and R. Gupta, Full-wave approach for x-ray phase imaging, Optics Express, vol.21, issue.15, 2013.
DOI : 10.1364/OE.21.017547

Y. Sung and G. Barbastathis, Rytov approximation for x-ray phase imaging, Optics Express, vol.21, issue.3, 2013.
DOI : 10.1364/OE.21.002674

Y. Sung, W. P. Segars, A. Pan, M. Ando, C. J. Sheppard et al., Realistic wave-optics simulation of X-ray phase-contrast imaging at a human scale, Scientific Reports, vol.25, issue.1, 2015.
DOI : 10.1007/978-3-642-59223-2

A. Peterzol, J. Berthier, P. Duvauchelle, C. Ferrero, and D. Babot, X-ray phase contrast image simulation, Nuclear Instruments and Methods in Physics Research Section B : Beam Interactions with Materials and Atoms, 2007.

J. M. Cowley, Diraction Physics, 1995.

P. Cloetens, Contribution to Phase Contrast Imaging, Reconstruction and Tomography with Hard Synchrotron Radiation, p.39, 1999.

L. Roscoe, Stereolithography interface specication, America-3D Systems Inc, 1988.

N. Freud, Modélisation et simulation de systemes d'imagerie par rayon X ou ?, 2003.

F. Salvat, J. M. Fernández-varea, and J. Sempau, A code system for monte carlo simulation of electron and photon transport, Workshop Proceedings, 2006.

J. H. Hubbell, Tables of x-ray mass attenuation coecients and mass energy-absorption coecients from 1 kev to 20 mev for elements z = 1 to 92 and 48 additional substances of dosimetric interest, tech. rep, NIST National Institute of Standards and Technology, 2010.

M. Frigo and S. G. Johnson, The Design and Implementation of FFTW3, Proceedings of the IEEE, 2005.
DOI : 10.1109/JPROC.2004.840301

A. Beer, Bestimmung der absorption des rothen lichts in farbigen üssigkeiten, Annalen der Physik und Chemie, p.1852

J. Lambert, Photometria, sive de mensura et gradibus luminis, colorum et umbrae Sumptibus Vidae Eberhardi Klett, 1760.

J. Plagnard, Comparison of measured and calculated spectra emitted by the x-ray tube used at the gustave roussy radiobiological service, X-Ray Spectrometry, 2014.

A. Stolidi, D. Tisseur, and J. Primot, Multi-lateral shearing interferometry : Principle and application on x-ray laboratory sources, International Symposium on Digital Industrial Radiology and Computed Tomography, 2015.

J. Primot, Three-wave lateral shearing interferometry, Applied Optics, 1993.
DOI : 10.1364/ao.32.006242

M. Murty, Modication of michelson interferometer using only one cube-corner prism, Journal of the Optical Society of America, 1960.

J. Kitabayashi, Method of and apparatus for measuring the shape of a wavefront, United States Patent, vol.4, pp.744-659, 1988.

J. Wyant, White Light Extended Source Shearing Interferometer, Applied Optics, vol.13, issue.1, 1974.
DOI : 10.1364/AO.13.000200

C. L. Koliopoulos, Radial grating lateral shear heterodyne interferometer, Applied Optics, vol.19, issue.9, 1980.
DOI : 10.1364/AO.19.001523

J. Primot and L. Sogno, Achromatic three-wave (or more) lateral shearing interferometer, Journal of the Optical Society of America A, vol.12, issue.12, 1995.
DOI : 10.1364/JOSAA.12.002679

J. Primot and N. Guérineau, Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard, Applied Optics, vol.39, issue.31, 2000.
DOI : 10.1364/AO.39.005715

R. V. Shack and B. Platt, Production and use of a lenticular hartmann screen, Journal of the Optical Society of America, 1971.

J. Primot, Theoretical description of shack-hartmann wave-front sensor, Optics Communication, 2003.

K. Patorski, I The Self-Imaging Phenomenon and its Applications, 1989.
DOI : 10.1016/S0079-6638(08)70084-2

B. Toulon, J. Primot, N. Guérineau, R. Haïdar, S. Velghe et al., Step-selective measurement by grating-based lateral shearing interferometry for segmented telescopes, Optics Communications, vol.279, issue.2, 2007.
DOI : 10.1016/j.optcom.2007.07.037

URL : https://hal.archives-ouvertes.fr/hal-00577721

C. Bellanger, B. Toulon, J. Primot, L. Lombard, J. Bourderionnet et al., Collective phase measurement of an array of ber lasers by quadriwave lateral shearing interferometry for coherent beam combining, Optics Letters, 2010.

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells, Optics Express, vol.17, issue.15, 2009.
DOI : 10.1364/OE.17.013080.m002

URL : https://hal.archives-ouvertes.fr/hal-00424664

J. Rizzi, T. Weitkamp, N. Guérineauu, M. Idir, P. Mercère et al., Quadriwave lateral shearing interferometry in an achromatic and continuously selfimaging regime for future x-ray phase imaging, Optics Letters, 2011.

J. Rizzi, P. Mercère, M. Idir, P. D. Silva, G. Vincent et al., X-ray phase contrast imaging and noise evaluation using a single phase grating interferometer, Optics Express, vol.21, issue.14, 2013.
DOI : 10.1364/OE.21.017340

M. Takeda, H. Ina, and S. Kobayashi, Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry, Journal of the Optical Society of America, vol.72, issue.1, 1982.
DOI : 10.1364/JOSA.72.000156

S. Velghe, Les nouvelles dimensions de l'interférométrie á décalage quadri-latéral : l'infrarouge et les surfaces morcelées, 2007.

J. W. Gibbs, Fourier's series, Nature, p.1898

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping : theory, algorithms, and software, 1998.

P. Bon, S. Monneret, and B. Wattellier, Noniterative boundary-artifact-free wavefront reconstruction from its derivatives, Applied Optics, vol.51, issue.23, 2012.
DOI : 10.1364/AO.51.005698

URL : https://hal.archives-ouvertes.fr/hal-00728198

A. Montaux-lambert, P. Mercère, and J. Primot, Interferogram conditioning for improved Fourier analysis and application to X-ray phase imaging by grating interferometry, Optics Express, vol.23, issue.22, 2015.
DOI : 10.1364/OE.23.028479

M. P. Rimmer, Method for Evaluating Lateral Shearing Interferograms, Applied Optics, vol.13, issue.3, 1974.
DOI : 10.1364/AO.13.000623

W. H. Southwell, Wave-front estimation from wave-front slope measurements, Journal of the Optical Society of America, vol.70, issue.8, 1980.
DOI : 10.1364/JOSA.70.000998

R. Bracewell, The fourier transform and iis applications, McGraw-Hill Electrical and Electronic Engineering Series, 1965.

C. Kottler, C. David, F. Pfeier, and O. Bunk, A two-directional approach for grating based dierential phase contrast imaging using hard x-rays, Optics Express, 2007.

J. Rizzi, Imagerie de phase quantitative par interférométrie à décalage quadri-latéral. Application au domaine des rayons x durs, 2013.

R. Jennison, A Phase Sensitive Interferometer Technique for the Measurement of the Fourier Transforms of Spatial Brightness Distributions of Small Angular Extent, Monthly Notices of the Royal Astronomical Society, vol.118, issue.3, 1958.
DOI : 10.1093/mnras/118.3.276

D. L. Fried, Least-square tting a wave-front distortion estimate to an array of phase-dierence measurements, Journal of the Optical Society of America A, 1977.

K. R. Freischlad and C. L. Koliopoulos, Modal estimation of a wave front from dierence measurements using the discrete fourier transform, Journal of the Optical Society of America A, 1986.

N. Guérineau, B. Harchaoui, and J. Primot, Talbot experiment re-examined: demonstration of an achromatic and continuous self-imaging regime, Optics Communications, vol.180, issue.4-6, 2000.
DOI : 10.1016/S0030-4018(00)00717-3

J. W. Goodman, Some fundamental properties of speckle*, Journal of the Optical Society of America, vol.66, issue.11, 1976.
DOI : 10.1364/JOSA.66.001145

I. Freund, M. Rosenbluh, and S. Feng, Memory eects in propagation of optical waves through disordered media, Physical Review Letters, 1988.

D. A. Boas and A. K. Dunn, Laser speckle contrast imaging in biomedical optics, Journal of Biomedical Optics, vol.15, issue.1, 2010.
DOI : 10.1117/1.3285504

O. Katz, P. Heidmann, M. Fink, and S. Gigan, Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations, Nature Photonics, vol.6701, issue.10, 2014.
DOI : 10.1103/PhysRevLett.87.134301

C. Halford, W. Gamble, and N. George, Experimental Investigation Of The Longitudinal Characteristics Of Laser Speckle, Optical Engineering, vol.26, issue.12, 1987.
DOI : 10.1117/12.7977166

L. Leushacke and M. Kirchner, Three-dimensional correlation coecient of speckle intensity for rectangular and circular apertures, Journal of the Optical Society of America A, 1990.

M. Giglio, M. Carpineti, and A. Vailati, Space intensity correlations in the near eld of the scattered light : a direct measurement of the density correlation function g (r), Physical Review Letters, 2000.

M. Giglio, M. Carpineti, A. Vailati, and D. Brogioli, Near-eld intensity correlations of scattered light, Applied Optics, 2001.

R. Cerbino, Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem, Physical Review A, vol.297, issue.5, 2007.
DOI : 10.1088/1009-1963/14/10/012

R. Cerbino, L. Peverini, M. Potenza, A. Robert, P. Bösecke et al., X-ray-scattering information obtained from near-eld speckle, Nature Physics, 2008.
DOI : 10.1038/nphys837

J. P. Lewis, Fast template matching, in Vision interface, 1995.

K. S. Morgan, D. M. Paganin, and K. K. Siu, X-ray phase imaging with a paper analyzer, Applied Physics Letters, vol.61, issue.12, 2012.
DOI : 10.1063/1.3694918.1

K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan et al., Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging, Journal of Physics D: Applied Physics, vol.37, issue.19, 2004.
DOI : 10.1088/0022-3727/37/19/021

S. Bérujon, E. Ziegler, R. Cerbino, and L. Peverini, Two-dimensional x-ray beam phase sensing, Physical Review Letters, 2012.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson et al., Speckle-based x-ray phase-contrast and dark-eld imaging with a laboratory source, Physical Review Letters, 2014.

S. Berujon, H. Wang, and K. Sawhney, X-ray multimodal imaging using a random-phase object, Physical Review A, vol.86, issue.6, 2012.
DOI : 10.1063/1.3665063

H. Wang, Y. Kashyap, and K. Sawhney, Hard-x-ray directional dark-eld imaging using the speckle scanning technique, Physical Review Letters, 2015.

T. Zhou, I. Zanette, M. Zdora, U. Lundström, D. H. Larsson et al., Speckle-based x-ray phase-contrast imaging with a laboratory source and the scanning technique, Optics Letters, vol.40, issue.12, 2015.
DOI : 10.1364/OL.40.002822

H. Wang, Y. Kashyap, and K. Sawhney, From synchrotron radiation to lab source: advanced speckle-based X-ray imaging using abrasive paper, Scientific Reports, vol.25, issue.1, 2016.
DOI : 10.1093/bioinformatics/btp184

Y. Takeda, W. Yashiro, Y. Suzuki, S. Aoki, T. Hattori et al., X-Ray Phase Imaging with Single Phase Grating, Japanese Journal of Applied Physics, vol.46, issue.No. 3, 2007.
DOI : 10.1143/JJAP.46.L89

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, Hard-x-ray phase-dierence microscopy using a fresnel zone plate and a transmission grating, Physical Review Letters, 2009.

N. Morimoto, S. Fujino, A. Yamazaki, Y. Ito, T. Hosoi et al., Two dimensional x-ray phase imaging using single grating interferometer with embedded x-ray targets, Optics Express, vol.23, issue.13, 2015.
DOI : 10.1364/OE.23.016582

. Hooper, X-ray specks : low dose in vivo imaging of lung structure and function, Physics in Medicine and Biology, 2015.

G. Sato, T. Kondoh, H. Itoh, S. Handa, K. Yamaguchi et al., Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube, Optics Letters, vol.36, issue.18, 2011.
DOI : 10.1364/OL.36.003551

]. P. Bon, Imagerie microscopique de champs électromagnétiques par interférométrie à décalage quadri-latéral. Applications à la biologie, 2011.

. Titre, Développement de méthodes d'imagerie par contraste de phase sur source X de laboratoire Mots clés : Imagerie par rayons X