Optical diffraction tomography

There is considerable interest in developing optical microscopes presenting a lateral resolution below the usual Rayleigh criterion, λ/(2NA), where λ is the wavelength of the illumination and NA is the numerical aperture of the imaging system, while retaining the convenience of far-field illumination and collection.
Among the various ways to ameliorate the resolution, it has been proposed to illuminate the sample with many structured illuminations, namely standing waves, and to mix the different images through simple arithmetics.This technique is very close to optical diffraction tomography (ODT) in which the sample is illuminated under various angles of incidence, the phase and intensity of the diffracted far-field is detected along several directions of observation, and a numerical procedure is used to retrieve the map of the permittivity distribution of the object from the far-field data. Experimental and theoretical studies have shown that using several illuminations permits one to exceed the classical diffraction limit by a factor of two.

In all microscopy techniques using several successive illuminations, one needs a numerical procedure to combine the different images and extract the map of the relative permittivity distribution of the object from the scattered far-field. In general, one assumes that the object is a weak scatterer so that there is a linear relationship between the scattered field and the relative permittivity of the object, namely one assumes that the Born approximation is valid. In this case, the transverse resolution limit can be inferred from simple considerations on the portion of the Ewald sphere that is covered by the experiment. It is limited by λ/2(n_i+n_d) for configurations in which the incident waves propagate in a medium of refractive index n_i, while the diffracted waves propagate in a medium of refraction index n_d.

References :
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– A. Matlock, A. Sentenac, P. C. Chaumet, J. Yi and L. Tian, Inverse scattering for reflection intensity phase microscopy, Biomedical Opt. Express 11, 911 (2020)

– K. Unger, P. C. Chaumet, G. Maire, A. Sentenac and K. Belkebir, A versatile inversion tool for phaseless optical diffraction tomography, J. Opt. Soc. Am. A 36, C1 (2019)

– T. Zhang, K. Unger, G. Maire, P. C. Chaumet, A. Talneau, C. Godavarthi, H. Giovannini, K. Belkebir and A. Sentenac, Multi-wavelength multi-angle reflection tomography, Opt. Express 26, 26093 (2018)

– 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. 65, 1787 (2018)

– G. Maire, H. Giovannini, A. Talneau, P. C. Chaumet, K. Belkebir and A. Sentenac, Phase imaging and synthetic aperture super-resolution via total internal reflection microscopy, Opt. Lett. 43, 2173 (2018)

– T. Zhang, P. C. Chaumet, A. Sentenac and K. Belkebir, Improving three-dimensional target reconstruction in the multiple scattering regime using the decomposition of the time-reversal operator, J. Appl. Phys. 120, 243101 (2016)

– T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir and A. Sentenac, Far-field diffraction microscopy at λ /10 resolution, Optica 3, 609 (2016)

– T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, C. Prada, A. Sentenac and K. Belkebir, Tomographic Diffractive Microscopy with agile illuminations for imaging targets in a noisy background, Opt. Lett. 40, 573 (2015)

– C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir and A. Sentenac, Super-resolution with full-polarized tomographic diffractive microscopy, J. Opt. Soc. Am. A 32, 287 (2015)

– T. Zhang, P. C. Chaumet, A. Sentenac and K. Belkebir, Reconstruction of three-dimensional targets using frequency-diversity data, AIP Advances 4, (2014)

– T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet and A. Sentenac, Full-polarized tomographic diffraction microscopy achieves a resolution about one fourth of the wavelength, Phys. Rev. Lett. 111, 243904, (2013)

– T. Zhang, P. C. Chaumet, A. Sentenac and K. Belkebir, Three-dimensional imaging of targets buried in a cluttered semi-infinite medium, J. Appl. Phys. 114, 143101 (2013)

– G. Maire, Y. Ruan, T. Zhang, P. C. Chaumet, H. Giovannini, D. Sentenac, A. Talneau, K. Belkebir and A. Sentenac, High resolution tomographic diffractive microscopy in reflection configuration, J. Opt. Soc. Am. A 30, 2133 (2013)

– S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. C. Chaumet, K. Belkebir and H. Giovannini, Nanometric resolution with far-field optical profilometry, Phys. Rev. Lett. 111, 053902 (2013)

– T. Zhang, P. C. Chaumet, E. Mudry, K. Belkebir and A. Sentenac,
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– Y. Ruan, P. Bon, E. Mudry, G. Maire, P. C. Chaumet, H. Giovannini, K. Belkebir, A. Talneau, B. Wattellier, S. Monneret and A. Sentenac, Tomographic diffractive microscopy with a wavefront sensor, Opt. Lett.37, 1631 (2012)

– E. Mudry, P. C. Chaumet, K. Belkebir and A. Sentenac, Electromagnetic wave imaging of three-dimensional targets using a hybrid iterative inversion method, Inv. Problems 28, 065007 (2012)

– J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet and A. Sentenac, Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime, Phys. Rev. A 82, 061801(R) (2010)

– G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet and A. Sentenac, Experimental inversion of optical diffraction tomography data with a nonlinear algorithm in the multiple scattering regime, J. of Modern Optics. 57, 746 (2010)

– P. C. Chaumet, A. Sentenac, K. Belkebir, G. Maire and H. Giovannini, Improving the resolution of grating-assisted optical diffraction tomography using a priori information in the reconstruction procedure, J. of Modern Optics 57, 798 (2010)

– E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire and A. Sentenac, Mirror-assisted optical diffraction tomography with isotropic resolution, Opt. Lett. 35, 1857 (2010)

– P. C. Chaumet, K. Belkebir and A. Sentenac, Experimental microwave imaging of three-dimensional targets with different inversion procedures, J. Appl. Phys. 109, 034901-8 (2009)

– G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet and A. Sentenac, Experimental Demonstration of Quantitative Imaging beyond Abbe’s Limit with Optical Diffraction Tomography, Phys. Rev. Lett. 102, 213905-4 (2009)

– P. C. Chaumet and Belkebir, Three-dimensional reconstruction from real data using a conjugate gradient-coupled dipole method, Inverse Problems 25, 024003 (2009)

– P. C. Chaumet, K. Belkebir and A. Sentenac, Numerical study of grating-assisted optical diffraction tomography, Phys. Rev. A 76, 013814 (2007)

– A. Sentenac, P. C. Chaumet and K. Belkebir, Beyond the Rayleigh criterion : Grating assisted far-field optical diffraction tomography, Phys. Rev. Lett. 97, 243901 (2006)

– K. Belkebir, P. C. Chaumet and A. Sentenac, Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography, J. Opt. Soc. Am. A. 23, 586 (2006)

– K. Belkebir, P. C. Chaumet and A. Sentenac, Superresolution in total-internal reflection tomography, J. Opt. Soc. Am. A. 22, 1889 (2005)