A. Zumbusch, G. R. Holtom, and X. Sunney-xie, Three-Dimensional Vibrational Imaging by Coherent Anti-Stokes Raman Scattering, Physical Review Letters, vol.82, pp.4142-4145, 1999.

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, Electromagnetic Wave Imaging of Three-dimensional Targets Using a Hybrid Iterative Inversion Method, Inverse Probl, vol.28, p.65007, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00939212

I. Voznyuk, A. Litman, and H. Tortel, Efficient Combination of a 3d Quasi-Newton Inversion Algorithm and a Vector Dual-primal Finite Element Tearing and Interconnecting Method, Inverse Probl, p.85005, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01279541

P. C. Chaumet and K. Belkebir, Three-dimensional Reconstruction from Real Data Using a Conjugate Gradientcoupled Dipole Method, Inverse Probl, vol.25, pp.24003-24020, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00457227

J. De-zaeytijd and A. Franchois, Three-dimensional Quantitative Microwave Imaging from Measured Data with Multiplicative Smoothing and Value Picking Regularization, Inverse Probl, vol.25, p.24004, 2009.

M. Yuan, C. Yu, and Q. H. Liu, Reconstruction of 3D Objects from Multi-frequency Experimental Data with a Fast DBIM-BCGS Method, Inverse Probl, vol.25, pp.24007-24031, 2009.

E. Soubies, T. Pham, and M. Unser, Efficient Inversion of Multiple-scattering Model for Optical Diffraction Tomography, Optics Exp, vol.25, p.21786, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02428165

S. J. Norton, Iterative Inverse Scattering Algorithms: Methods Of Computing Fréchet Derivatives, J. Acoust. Soc. Amer, vol.106, pp.2653-2660, 1999.

A. Roger and . Newton-kantorovitch, Algorithm Applied to an Electromagnetic Inverse Problem, IEEE Trans. Antennas Propag, vol.29, pp.232-238, 1981.

F. M. Kahnert, Numerical Methods in Electromagnetic Scattering Theory. J. Quant. Spect. Rad. Transf, pp.775-824, 2003.

J. G. Van-bladel, Electromagnetic Fields, 2nd Edition, IEEE Press Ser. Electromagn. Wave Theory, 2007.

E. Wolf, Three-dimensional Structure Determination of Semi-transparent Objects from Holographic Data, Opt. Commun, vol.1, pp.153-156, 1969.

R. Carminati, Phase Properties of the Optical Near Field, Phys. Rev. E, vol.55, pp.4901-4904, 1997.

J. M. Liu and L. Gomelsky, Vectorial Beam Propagation Method, J. Opt. Soc. Amer. A, vol.1992, p.1574

B. T. Draine and P. J. Flatau, Discrete-dipole Approximation for Scattering Calculations, J. Opt. Soc. Am. A, vol.11, pp.1491-1499, 1994.

P. C. Chaumet, A. Sentenac, and A. Rahmani, Coupled Dipole Method for Scatterers with Large Permittivity, Phys. Rev. E, vol.70, pp.36606-36612, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00103796

P. C. Chaumet and A. Rahmani, Efficient Iterative Solution of the Discrete Dipole Approximation for Magnetodielectric Scatterers, Opt. Lett, vol.34, pp.917-919, 2009.

J. M. Geffrin and P. Sabouroux, Continuing with the Fresnel Database: Experimental Setup and Improvements in 3D Scattering Measurements, Inverse Probl, vol.25, p.24001, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00367473

C. J. Eyraud, A. .-m-geffrin, P. Litman, H. Sabouroux, and . Giovannini, Drift Correction for Scattering Measurements, Appl. Phys. Lett, p.244104, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00120448

C. Eyraud, J. M. Geffrin, P. Sabouroux, P. C. Chaumet, H. Tortel et al., Validation of 3D Bistatic Microwave Scattering Measurement Setup, Radio Sci, vol.43, p.4018, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00348506

V. Lauer, New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope, J. Microsc, vol.205, pp.165-176, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00869524

B. Simon, M. Debailleul, V. Georges, V. Lauer, and O. Haeberlé, Tomographic diffractive microscopy of transparent samples, Eur. Phys. J, vol.44, pp.29-35, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00869566

Y. Park, C. Depeursinge, and G. Popescu, Quantitative phase imaging in biomedicine, Nat. Photonics, vol.12, pp.578-589, 2018.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini et al., Far-field diffraction microscopy at ?/10 resolution, Optica, vol.3, pp.609-612, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01328835

L. Tian and L. Waller, 3d intensity and phase imaging from light field measurements in an led array microscope, vol.2, pp.104-111, 2015.

T. Pham, E. Soubies, A. Goy, J. Lim, F. Soulez et al., Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering, Opt. Express, vol.26, pp.2749-2763, 2018.
URL : https://hal.archives-ouvertes.fr/insu-01690828

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, Ptychographic transmission microscopy in three dimensions using a multi-slice approach, J. Opt. Soc. Am. A, vol.29, pp.1606-1614, 2012.

G. Zheng, R. Horstmeyer, and C. Yang, Wide-field, high-resolution Fourier ptychographic microscopy, Nat. Photonics, vol.7, pp.739-745, 2013.

K. Unger, T. Zhang, P. C. Chaumet, A. Sentenac, and K. Belkebir, Linearized inversion methods for three-dimensional electromagnetic imaging in the multiple scattering regime, J. Mod. Opt, vol.65, pp.1787-1792, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02023456

A. Sentenac and J. Mertz, Unified description of three-dimensional optical diffraction microscopy: from transmission microscopy to optical coherence tomography: tutorial, J. Opt. Soc. Am. A, vol.35, pp.748-754, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02023489

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau et al., Full-polarized tomographic diffraction microscopy achieves a resolution about one-fourth of the wavelength, Phys. Rev. Lett, vol.111, p.243904, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00931821

S. Khadir, P. C. Chaumet, G. Baffou, and A. Sentenac, Quantitative model of the image of a radiating dipole through a microscope, J. Opt. Soc. Am. A, vol.36, pp.478-484, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02059860

M. J. Nasse and J. C. Woehl, Realistic modeling of the illumination point spread function in confocal scanning optical microscopy, J. Opt. Soc. Am. A, vol.27, pp.295-302, 2010.

O. Haeberlé, Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part ii: confocal and multiphoton microscopy, Opt. Commun, vol.235, pp.1-10, 2004.

P. C. Chaumet, A. Sentenac, and A. Rahmani, Coupled dipole method for scatterers with large permittivity, Phys. Rev. E, vol.70, p.36606, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00103796

L. Novotny, D. W. Pohl, and P. Regli, Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope, J. Opt. Soc. Am. A, vol.11, pp.1768-1779, 1994.

B. Richards, E. Wolf, and D. Gabor, Electromagnetic diffraction in optical systems. ii. Structure of the image field in an aplanatic system, Proc. R. Soc. London, Ser. A, vol.253, pp.358-379, 1959.

P. C. Chaumet, A. Sentenac, and D. Sentenac, The computations were done using the free software IFDDA

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini et al., Superresolution with fullpolarized tomographic diffractive microscopy, J. Opt. Soc. Am. A, vol.32, pp.287-292, 2015.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, Tomographic diffractive microscopy: basics, techniques and perspectives, J. Mod. Opt, vol.57, pp.686-699, 2010.

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, Mirror-assisted tomographic diffractive microscopy with isotropic resolution, Opt. Lett, vol.35, pp.1857-1859, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00484543

S. Vertu, J. Delaunay, I. Yamada, and O. Haeberlé, Diffraction microtomography with sample rotation: influence of a missing apple core in the recorded frequency space, Central Eur. J. Phys, vol.7, pp.22-31, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00868388

B. Vinoth, X. Lai, Y. Lin, H. Tu, and C. Cheng, Integrated dual-tomography for refractive index analysis of free-floating single living cell with isotropic superresolution, Sci. Rep, vol.8, p.5943, 2018.

B. Simon, M. Debailleul, M. Houkal, C. Ecoffet, J. Bailleul et al., Tomographic diffractive microscopy with isotropic resolution, Optica, vol.4, p.460, 2017.

N. Streibl, Three-dimensional imaging by a microscope, J. Opt. Soc. Am. A, vol.2, pp.121-127, 1985.

M. Born and E. Wolf, Principles of Optics, 1959.

M. W. Davidson and M. Abramowitz, Optical Microscopy, 2002.

J. Lobera and J. M. Coupland, Contrast enhancing techniques in digital holographic microscopy, Meas. Sci. Technol, vol.19, p.25501, 2008.

L. Miccio, A. Finizio, R. Puglisi, D. Balduzzi, A. Galli et al., Dynamic dic by digital holography microscopy for enhancing phasecontrast visualization, Biomed. Opt. Express, vol.2, pp.331-344, 2011.

J. Bailleul, B. Simon, M. Debailleul, and O. Haeberlé, An introduction to tomographic diffractive microscopy, 2017.

X. Fan, J. J. Healy, K. O'dwyer, and B. M. Hennelly, Label-free color staining of quantitative phase images of biological cells by simulated Rheinberg illumination, Appl. Opt, vol.58, pp.3104-3114, 2019.

, Journal of the Optical Society of America A Research Article, vol.36, issue.11, 2019.

A. Zumbusch, G. R. Holtom, and X. S. Xie, Three-dimensional vibrational imaging by coherent anti-stokes raman scattering, Phys. Rev. Lett, vol.82, pp.4142-4145, 1999.

, Coherent Raman Scattering Microscopy (Series in Cellular and Clinical Imaging) (Chemical Rubber Company, 2013)

H. Rigneault and P. Berto, Tutorial: Coherent raman light matter interaction processes, APL Photonics, vol.3, p.91101, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01850264

, OPTICS EXPRESS, vol.27, issue.16, p.23512, 2019.

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, Coherent nonlinear optical imaging: Beyond fluorescence microscopy, Annu. Rev. Phys. Chem, vol.62, pp.507-530, 2011.

J. P. Day, K. F. Domke, G. Rago, H. Kano, H. Hamaguchi et al., Quantitative coherent anti-stokes raman scattering (CARS) microscopy, J. Phys. Chem. B, vol.115, pp.7713-7725, 2011.

M. T. Cicerone and C. H. Camp, Histological coherent raman imaging: a prognostic review, Analyst, vol.143, pp.33-59, 2018.

T. W. Bocklitz, F. S. Salah, N. Vogler, S. Heuke, O. Chernavskaia et al., Pseudo-HE images derived from CARS/TPEF/SHG multimodal imaging in combination with raman-spectroscopy as a pathological screening tool, BMC Cancer, vol.16, p.534, 2016.

O. Chernavskaia, S. Heuke, M. Vieth, O. Friedrich, S. Schürmann et al., Beyond endoscopic assessment in inflammatory bowel disease: real-time histology of disease activity by non-linear multimodal imaging, Sci. Rep, vol.6, p.29239, 2016.

S. Heuke, O. Chernavskaia, T. Bocklitz, F. B. Legesse, T. Meyer et al., Multimodal nonlinear microscopy of head and neck carcinoma -toward surgery assisting frozen section analysis, Head Neck, vol.38, pp.1545-1552, 2016.

J. Zheng, D. Akimov, S. Heuke, M. Schmitt, B. Yao et al., Vibrational phase imaging in wide-field CARS for nonresonant background suppression, Opt. Express, vol.23, p.10756, 2015.

P. Berto, A. Jesacher, C. Roider, S. Monneret, H. Rigneault et al., Wide-field vibrational phase imaging in an extremely folded box-CARS geometry, Opt. Lett, vol.38, p.709, 2013.

P. Berto, D. Gachet, P. Bon, S. Monneret, and H. Rigneault, Wide-field vibrational phase imaging, Phys. Rev. Lett, vol.109, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00727832

Y. Shen, J. Wang, K. Wang, A. V. Sokolov, and M. O. Scully, Wide-field coherent anti-stokes raman scattering microscopy based on picosecond supercontinuum source, APL Photonics, vol.3, p.116104, 2018.

C. Heinrich, S. Bernet, and M. Ritsch-marte, Wide-field coherent anti-stokes raman scattering microscopy, Appl. Phys. Lett, vol.84, pp.816-818, 2004.

C. Heinrich, C. Meusburger, S. Bernet, and M. Ritsch-marte, CARS microscopy in a wide-field geometry with nanosecond pulses, J. Raman Spectrosc, vol.37, pp.675-679, 2006.

C. Heinrich, A. Hofer, S. Bernet, and M. Ritsch-marte, Coherent anti-stokes raman scattering microscopy with dynamic speckle illumination, New J. Phys, vol.10, p.23029, 2008.

A. Jesacher, C. Roider, S. Khan, G. Thalhammer, S. Bernet et al., Contrast enhancement in widefield CARS microscopy by tailored phase matching using a spatial light modulator, Opt. Lett, vol.36, p.2245, 2011.

I. Toytman, K. Cohn, T. Smith, D. Simanovskii, and D. Palanker, Wide-field coherent anti-stokes raman scattering microscopy with non-phase-matching illumination, Opt. Lett, vol.32, p.1941, 2007.

I. Toytman, D. Simanovskii, and D. Palanker, On illumination schemes for wide-field CARS microscopy, Opt. Express, vol.17, p.7339, 2009.

K. Wicker and R. Heintzmann, Resolving a misconception about structured illumination, Nat. Photonics, vol.8, pp.342-344, 2014.

M. Lei, Video-rate wide-field coherent anti-stokes raman scattering microscopy with collinear nonphase-matching illumination, J. Biomed. Opt, vol.16, p.21102, 2011.

K. M. Hajek, B. Littleton, D. Turk, T. J. Mcintyre, and H. Rubinsztein-dunlop, A method for achieving super-resolved widefield cars microscopy, Opt. Express, vol.18, p.19263, 2010.

K. Shi, P. S. Edwards, J. Hu, Q. Xu, Y. Wang et al., Holographic coherent anti-stokes raman scattering bio-imaging, Biomed. Opt. Express, vol.3, p.1744, 2012.

A. S. Duarte, C. Schnedermann, and P. Kukura, Wide-field detected fourier transform CARS microscopy, Sci. Rep, vol.6, p.37516, 2016.

G. Zheng, R. Horstmeyer, and C. Yang, Wide-field, high-resolution fourier ptychographic microscopy, Nat. Photonics, vol.7, pp.739-745, 2013.

J. Cheng, A. Volkmer, and X. S. Xie, Theoretical and experimental characterization of coherent anti-stokes raman scattering microscopy, J. Opt. Soc. Am. B, vol.19, p.1363, 2002.

N. Streibl, Three-dimensional imaging by a microscope, J. Opt. Soc. Am. A, vol.2, p.121, 1985.

S. Heuke, F. B. Legesse, A. Lorenz, T. Pascher, D. Akimov et al., Fiber-based dual-focus time-demultiplexed second harmonic generation microscopy, Opt. Lett, vol.40, p.2505, 2015.

M. Schrader, S. W. Hell, H. T. Van-der, and . Voort, Three-dimensional super-resolution with a 4pi-confocal microscope using image restoration, J. Appl. Phys, vol.84, pp.4033-4042, 1998.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, Tomographic diffractive microscopy: basics, techniques and perspectives, J. Mod. Opt, vol.57, pp.686-699, 2010.

S. Khadir, P. C. Chaumet, G. Baffou, and A. Sentenac, Quantitative model of the image of a radiating dipole through a microscope, J. Opt. Soc. Am. A, vol.36, p.478, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02059860

D. Gachet, N. Sandeau, and H. Rigneault, Influence of the raman depolarisation ratio on far-field radiation patterns in coherent anti-stokes raman scattering (CARS) microscopy, J. Eur. Opt. Soc. Rapid Publ, issue.1, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00093144

L. Novotny and B. Hecht, Preface, Principles of Nano-Optics, pp.xv-xviii, 2006.

D. A. Smunev, P. C. Chaumet, and M. A. Yurkin, Rectangular dipoles in the discrete dipole approximation, J. Quant. Spectrosc. Radiat. Transf, vol.156, pp.67-79, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01120340

, OPTICS EXPRESS, vol.27, issue.16, p.23513, 2019.

M. J. Huttunen, A. Abbas, J. Upham, and R. W. Boyd, Label-free super-resolution with coherent nonlinear structured-illumination microscopy, J. Opt, vol.19, p.85504, 2017.

Z. Wen, C. Yang, X. Liu, and S. Marchesini, Alternating direction methods for classical and ptychographic phase retrieval, Inverse Probl, vol.28, p.115010, 2012.

L. Bian, J. Suo, J. Chung, X. Ou, C. Yang et al., Fourier ptychographic reconstruction using poisson maximum likelihood and truncated wirtinger gradient, Sci. Rep, vol.6, p.27384, 2016.

A. P. Konijnenberg, W. M. Coene, and H. P. Urbach, Model-independent noise-robust extension of ptychography, Opt. Express, vol.26, p.5857, 2018.

C. Zuo, J. Sun, and Q. Chen, Adaptive step-size strategy for noise-robust fourier ptychographic microscopy, Opt. Express, vol.24, p.20724, 2016.

X. Ou, G. Zheng, and C. Yang, Embedded pupil function recovery for fourier ptychographic microscopy, Opt. Express, vol.22, p.4960, 2014.

L. Tian and L. Waller, 3d intensity and phase imaging from light field measurements in an LED array microscope, Optica, vol.2, p.104, 2015.

K. Unger, T. Zhang, P. C. Chaumet, A. Sentenac, and K. Belkebir, Linearized inversion methods for three-dimensional electromagnetic imaging in the multiple scattering regime, J. Mod. Opt, vol.65, pp.1787-1792, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02023456

E. Polak and G. Ribière, Note sur la convergence de méthodes directions conjuguées, Revue française d'informatique et de recherche opérationelle, vol.3, pp.35-43, 2017.

D. B. Murphy and M. W. Davidson, Fundamentals of Light Microscopy and Electronic Imaging, 2012.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, Standardizing the resolution claims for coherent microscopy, Nat. Photonics, vol.10, pp.68-71, 2016.

G. Eckhardt, R. W. Hellwarth, F. J. Mcclung, S. E. Schwarz, D. Weiner et al., Stimulated raman scattering from organic liquids, Phys. Rev. Lett, vol.9, pp.455-457, 1962.

S. Heuke, B. Sarri, X. Audier, and H. Rigneault, Simultaneous dual-channel stimulated raman scattering microscopy demultiplexed at distinct modulation frequencies, Opt. Lett, vol.43, p.3582, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01846763

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, Wide-field fourier ptychographic microscopy using laser illumination source, Biomed. Opt. Express, vol.7, p.4787, 2016.

R. W. Boyd, Nonlinear Optics, 2003.

, OPTICS EXPRESS, vol.27, issue.16, p.23514, 2019.