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ABSTRACT: We study, in time domain, the exchange of momentum between an electromagnetic pulse and a three-dimensional, discrete, spherical invisibility cloak. We find that a discrete cloak, initially at rest, would experience an electromagnetic force due to the pulse but would acquire zero net momentum and net displacement. On the other hand, we find that while the cloak may manage to conceal an object and shroud it from the electromagnetic forces associated with the pulse, the cloak itself can experience optomechanical stress on a scale much larger than the object would in the absence of the cloak. We also consider the effects of material dispersion and losses on the electromagnetic forces experienced by the cloak and show that they lead to a transfer of momentum from the pulse to the cloak.
Phys. Rev. A. 09/2011; 84(3).
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ABSTRACT: We present a general approach, based on the discrete dipole approximation (DDA), for the computation of the exchange of momentum between light and a magnetodielectric, three-dimensional object with arbitrary geometry and linear permittivity and permeability tensors in time domain. The method can handle objects with an arbitrary shape, including objects with dispersive dielectric and/or magnetic material responses.
Optics Express 01/2011; 19(3):2466-75. · 3.59 Impact Factor
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ABSTRACT: Optical diffraction tomography (ODT) is a recent imaging technique that combines the experimental methods of phase microscopy and synthetic aperture with the mathematical tools of inverse scattering theory. We present here in detail how this technique can be applied to highly scattering samples with a nonlinear inversion algorithm taking into account multiple scattering to reconstruct their permittivity profile. The obtained resolutions are substantially improved compared with wide-field microscopy and ODT performed with standard linear inversion procedures.
Journal of Modern Optics 04/2010; 57:746-755. · 1.17 Impact Factor
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ABSTRACT: We provide a numerical study of a tomographic microscope in which the sample is deposited on a periodically nanostructured substrate and is illuminated under various incident angles. The map of permittivity of the sample is retrieved numerically from the complex data of the diffracted far-field. A single-scattering analysis shows that, with an optimized grating of period /5, the transverse resolution of the digital imager is about /10. To ameliorate the resolution further, a priori information is incorporated in the inversion procedure. Fixing the lower and upper bounds of the sample permittivity permits us to obtain a transverse resolution about /15.
Journal of Modern Optics 04/2010; 57:798-808. · 1.17 Impact Factor
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ABSTRACT: We compare the performance of a total-internal-reflection fluorescence microscope under varying illumination and substrate conditions. The samples are deposited on a standard homogeneous glass slide or on a grating and illuminated by one or two interfering beams at various incident angles. A conjugate gradient with positivity a priori information is used to reconstruct the fluorophore density from the images. Numerical studies demonstrate that when the sample lies on an optimized grating, the lateral resolution of the microscope is greatly improved, up to fourfold, the best result being obtained when the grating is illuminated by two interfering beams.
Journal of the Optical Society of America A 12/2009; 26(12):2550-7. · 1.56 Impact Factor
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ABSTRACT: Optical diffraction tomography (ODT) is a recent imaging technique that combines the experimental methods of phase microscopy and synthetic aperture with the mathematical tools of inverse scattering theory. We show experimentally that this approach permits us to obtain the map of permittivity of highly scattering samples with axial and transverse resolutions that are much better than that of a microscope with the same numerical aperture.
Physical Review Letters 06/2009; 102(21):213905. · 7.37 Impact Factor
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ABSTRACT: The aim of the present work is to validate a full vectorial electromagnetic inverse scattering algorithm against experimental data. Data were provided courtesy of Institut Fresnel, Marseille, France. These data were carried out in an anechoic chamber and correspond to different canonical targets as well as one mysterious object which is known only by experimentalists who measured the associated scattered field. The inverse algorithm was first developed in the optical domain and is adapted herein to the microwave domain. It is an iterative approach where the parameter of interest, namely the relative permittivity distribution, is updated gradually by minimizing a cost function describing the discrepancy between data and those that would be obtained via a forward solver for the best available estimate of the relative permittivity. The forward solver is based on the coupled dipole method which was introduced in the seventies to study the scattering of light by non-spherical dielectric grains. The forward and inverse schemes are briefly described and various examples are presented that demonstrate the efficiency of the inverse algorithm.
Inverse Problems. 01/2009; 25:24003-17.
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ABSTRACT: We present a time-domain formulation of electrodynamics based on the self-consistent derivation of the electromagnetic field in a linear, dispersive, lossy object via the coupled dipole method.
Optics Express 01/2009; 16(25):20157-65. · 3.59 Impact Factor
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ABSTRACT: We consider in this paper the problem of the determination of the permittivity profile of an unknown buried object from measurements of the electromagnetic scattered field. The target under test is assumed to be buried in one of the two involved media while the sources and the receivers are located in the other medium (limited-aspect data configuration). This ill-posed and non-linear inverse scattering problem is reformulated as an optimization problem that is solved iteratively. This method consists in building up a sequence of the parameter of interest by minimizing, at each iteration step, a cost functional representing the discrepancy between the data and those that would be obtained with the best available estimation of the parameter. In addition, when clutter is present, the decomposition of the time reversal operator method is used to improve the signal-to-clutter ratio, since it allows us to synthesize a wave that focuses on the scatterer. The data associated with this incident field are included in the iterative minimization procedure.
The Journal of the Acoustical Society of America 06/2008; 123(5):3462. · 1.55 Impact Factor
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ABSTRACT: We propose a fluorescence surface imaging system that presents a power of resolution beyond that of the diffraction limit without resorting to saturation effects or probe scanning. This is achieved by depositing the sample on an optimized periodically nanostructured substrate in a standard total internal reflection fluorescence microscope. The grating generates a high-spatial-frequency light grid that can be moved throughout the sample by changing the incident angle. An appropriate reconstruction procedure permits one to recover the fluorescence amplitude from the images obtained for various incidences. Simulations of this imaging system show that the resolution is not limited by diffraction but by the period of the grating.
Optics Letters 03/2008; 33(3):255-7. · 3.40 Impact Factor
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ABSTRACT: Two-dimensional target characterization using inverse profiling approaches with total-field phaseless data is discussed. Two different inversion schemes are compared. In the first one, the intensity-only data are exploited in a minimization scheme, thanks to a proper definition of the cost functional. Specific normalization and starting guess are introduced to avoid the need for global optimization methods. In the second scheme [J. Opt. Soc. Am. A21, 622 (2004)], one exploits the field properties and the theoretical results on the inversion of quadratic operators to derive a two-step solution strategy, wherein the (complex) scattered fields embedded in the available data are retrieved first and then a traditional inverse scattering problem is solved. In both cases, the analytical properties of the fields allow one to properly fix the measurement setup and identify the more convenient strategy to adopt. Also, indications on the number and types of sources and receivers to be used are given. Results from experimental data show the efficiency of these approaches and the tools introduced.
Journal of the Optical Society of America A 02/2008; 25(1):271-81. · 1.56 Impact Factor
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ABSTRACT: We study the resolution of an optical diffraction tomography system in which the objects are either in an homogeneous background or deposited onto a glass prism, a prism surmounted by a thin metallic film or a prism surmounted by a metallic film covered by a periodically nanostructured dielectric layer. For all these configurations, we present an inversion procedure that yields the map of the relative permittivity of the objects from their diffracted far field. When multiple scattering can be neglected, we show that the homogeneous, prism, and metallic film configurations yield a resolution about λ∕4 while the grating substrate yields a resolution better than λ∕10. When Born approximation fails, we point out that it is possible to neglect the coupling between the object and the substrate and account solely for the multiple scattering within the objects to obtain a satisfactory reconstruction. Last, we present the robustness of our inversion procedure to noise.
Phys. Rev. A. 07/2007; 76(1).
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ABSTRACT: We propose an optical imaging system, in which both illumination and collection are done in far field, that presents a power of resolution better than one-tenth of the wavelength. This is achieved by depositing the sample on a periodically nanostructured substrate illuminated under various angles of incidence. The superresolution is due to the high spatial frequencies of the field illuminating the sample and to the use of an inversion algorithm for reconstructing the map of relative permittivity from the diffracted far field. Thus, we are able to obtain wide-field images with near-field resolution without scanning a probe in the vicinity of the sample.
Physical Review Letters 01/2007; 97(24):243901. · 7.37 Impact Factor
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ABSTRACT: We discuss the characterization of two-dimensional targets based on their diffracted intensity. The target characterization is performed by minimizing an adequate cost functional, combined with a level-set representation if the target is homogeneous. One key issue in this minimization is the choice of an updating direction, which involves the gradient of the cost functional. This gradient can be evaluated using a fictitious field, the solution of an adjoint problem in which receivers act as sources with a specific amplitude. We explore the Born approximation for the adjoint field and compare various approaches for a wide variety of objects.
Journal of the Optical Society of America A 12/2006; 23(11):2737-46. · 1.56 Impact Factor
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ABSTRACT: The present paper deals with the reconstruction of three-dimensional objects from the scattered far-field. The configuration under study is typically the one used in the Optical Diffraction Tomography (ODT), in which the sample is illuminated with various angles of incidence and the scattered field is measured for each illumination. The retrieval of the sample from the scattered field is accomplished numerically by solving the inverse scattering problem. We present herein a fast method for solving the inverse scattering problem based on the Coupled Dipole Method (CDM) and applied it for complex background configuration such as buried objects in a layered medium. Numerical experiments are reported and robustness against the presence of noise in the data is analyzed.
Optics Express 05/2006; 14(8):3415-26. · 3.59 Impact Factor
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ABSTRACT: Optical diffraction tomography is an imaging technique that permits retrieval of the map of permittivity of an object from its scattered far field. Most reconstruction procedures assume that single scattering is dominant so that the scattered far field is linearly linked to the permittivity. In this work, we present a nonlinear inversion method and apply it to complex three-dimensional samples. We show that multiple scattering permits one to obtain a power of resolution beyond the classical limit imposed by the use of propagative incident and diffracted waves. Moreover, we stress that our imaging method is robust with respect to correlated and uncorrelated noise.
Journal of the Optical Society of America A 04/2006; 23(3):586-95. · 1.56 Impact Factor
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ABSTRACT: This special section deals with the reconstruction of scattering objects from experimental data. A few years ago, inspired by the Ipswich database [1–4], we started to build an experimental database in order to validate and test inversion algorithms against experimental data. In the special section entitled 'Testing inversion algorithms against experimental data' [5], preliminary results were reported through 11 contributions from several research teams. (The experimental data are free for scientific use and can be downloaded from the web site.) The success of this previous section has encouraged us to go further and to design new challenges for the inverse scattering community. Taking into account the remarks formulated by several colleagues, the new data sets deal with inhomogeneous cylindrical targets and transverse electric (TE) polarized incident fields have also been used. Among the four inhomogeneous targets, three are purely dielectric, while the last one is a `hybrid' target mixing dielectric and metallic cylinders. Data have been collected in the anechoic chamber of the Centre Commun de Ressources Micro-ondes in Marseille. The experimental setup as well as the layout of the files containing the measurements are presented in the contribution by J-M Geffrin, P Sabouroux and C Eyraud. The antennas did not change from the ones used previously [5], namely wide-band horn antennas. However, improvements have been achieved by refining the mechanical positioning devices. In order to enlarge the scope of applications, both TE and transverse magnetic (TM) polarizations have been carried out for all targets. Special care has been taken not to move the target under test when switching from TE to TM measurements, ensuring that TE and TM data are available for the same configuration. All data correspond to electric field measurements. In TE polarization the measured component is orthogonal to the axis of invariance. Contributions A Abubakar, P M van den Berg and T M Habashy, Application of the multiplicative regularized contrast source inversion method TM- and TE-polarized experimental Fresnel data, present results of profile inversions obtained using the contrast source inversion (CSI) method, in which a multiplicative regularization is plugged in. The authors successfully inverted both TM- and TE-polarized fields. Note that this paper is one of only two contributions which address the inversion of TE-polarized data. A Baussard, Inversion of multi-frequency experimental data using an adaptive multiscale approach, reports results of reconstructions using the modified gradient method (MGM). It suggests that a coarse-to-fine iterative strategy based on spline pyramids. In this iterative technique, the number of degrees of freedom is reduced, which improves robustness. The introduction, during the iterative process, of finer scales inside areas of interest leads to an accurate representation of the object under test. The efficiency of this technique is shown via comparisons between the results obtained with the standard MGM and those from an adaptive approach. L Crocco, M D'Urso and T Isernia, Testing the contrast source extended Born inversion method against real data: the case of TM data, assume that the main contribution in the domain integral formulation comes from the singularity of Green's function, even though the media involved are lossless. A Fourier–Bessel analysis of the incident and scattered measured fields is used to derive a model of the incident field and an estimate of the location and size of the target. The iterative procedure lies on a conjugate gradient method associated with Tikhonov regularization, and the multi-frequency data are dealt with using a frequency-hopping approach. In many cases, it is difficult to reconstruct accurately both real and imaginary parts of the permittivity if no prior information is included. M Donelli, D Franceschini, A Massa, M Pastorino and A Zanetti, Multi-resolution iterative inversion of real inhomogeneous targets, adopt a multi-resolution strategy, which, at each step, adaptive discretization of the integral equation is performed over an irregular mesh, with a coarser grid outside the regions of interest and tighter sampling where better resolution is required. Here, this procedure is achieved while keeping the number of unknowns constant. The way such a strategy could be combined with multi-frequency data, edge preserving regularization, or any technique also devoted to improve resolution, remains to be studied. As done by some other contributors, the model of incident field is chosen to fit the Fourier–Bessel expansion of the measured one. A Dubois, K Belkebir and M Saillard, Retrieval of inhomogeneous targets from experimental frequency diversity data, present results of the reconstruction of targets using three different non-regularized techniques. It is suggested to minimize a frequency weighted cost function rather than a standard one. The different approaches are compared and discussed. C Estatico, G Bozza, A Massa, M Pastorino and A Randazzo, A two-step iterative inexact-Newton method for electromagnetic imaging of dielectric structures from real data, use a two nested iterative methods scheme, based on the second-order Born approximation, which is nonlinear in terms of contrast but does not involve the total field. At each step of the outer iteration, the problem is linearized and solved iteratively using the Landweber method. Better reconstructions than with the Born approximation are obtained at low numerical cost. O Feron, B Duchêne and A Mohammad-Djafari, Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data, adopt a Bayesian framework based on a hidden Markov model, built to take into account, as prior knowledge, that the target is composed of a finite number of homogeneous regions. It has been applied to diffraction tomography and to a rigorous formulation of the inverse problem. The latter can be viewed as a Bayesian adaptation of the contrast source method such that prior information about the contrast can be introduced in the prior law distribution, and it results in estimating the posterior mean instead of minimizing a cost functional. The accuracy of the result is thus closely linked to the prior knowledge of the contrast, making this approach well suited for non-destructive testing. J-M Geffrin, P Sabouroux and C Eyraud, Free space experimental scattering database continuation: experimental set-up and measurement precision, describe the experimental set-up used to carry out the data for the inversions. They report the modifications of the experimental system used previously in order to improve the precision of the measurements. Reliability of data is demonstrated through comparisons between measurements and computed scattered field with both fundamental polarizations. In addition, the reader interested in using the database will find the relevant information needed to perform inversions as well as the description of the targets under test. A Litman, Reconstruction by level sets of n-ary scattering obstacles, presents the reconstruction of targets using a level sets representation. It is assumed that the constitutive materials of the obstacles under test are known and the shape is retrieved. Two approaches are reported. In the first one the obstacles of different constitutive materials are represented in a single level set, while in the second approach several level sets are combined. The approaches are applied to the experimental data and compared. U Shahid, M Testorf and M A Fiddy, Minimum-phase-based inverse scattering algorithm applied to Institut Fresnel data, suggest a way of extending the use of minimum phase functions to 2D problems. In the kind of inverse problems we are concerned with, it consists of separating the contributions from the field and from the contrast in the so-called contrast source term, through homomorphic filtering. Images of the targets are obtained by combination with diffraction tomography. Both pre-processing and imaging are thus based on the use of Fourier transforms, making the algorithm very fast compared to classical iterative approaches. It is also pointed out that the design of appropriate filters remains an open topic. C Yu, L-P Song and Q H Liu, Inversion of multi-frequency experimental data for imaging complex objects by a DTA–CSI method, use the contrast source inversion (CSI) method for the reconstruction of the targets, in which the initial guess is a solution deduced from another iterative technique based on the diagonal tensor approximation (DTA). In so doing, the authors combine the fast convergence of the DTA method for generating an accurate initial estimate for the CSI method. Note that this paper is one of only two contributions which address the inversion of TE-polarized data. Conclusion In this special section various inverse scattering techniques were used to successfully reconstruct inhomogeneous targets from multi-frequency multi-static measurements. This shows that the database is reliable and can be useful for researchers wanting to test and validate inversion algorithms. From the database, it is also possible to extract subsets to study particular inverse problems, for instance from phaseless data or from `aspect-limited' configurations. Our future efforts will be directed towards extending the database in order to explore inversions from transient fields and the full three-dimensional problem. Acknowledgments The authors would like to thank the Inverse Problems board for opening the journal to us, and offer profound thanks to Elaine Longden-Chapman and Kate Hooper for their help in organizing this special section.
Inverse Problems 11/2005; 21(6):S1. · 1.88 Impact Factor
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ABSTRACT: We simulate a total internal reflection tomography experiment in which an unknown object is illuminated by evanescent waves and the scattered field is detected along several directions. We propose a full-vectorial three-dimensional nonlinear inversion scheme to retrieve the map of the permittivity of the object from the scattered far-field data. We study the role of the solid angle of illumination, the incident polarization, and the position of the prism interface on the resolution of the images. We compare our algorithm with a linear inversion scheme based on the renormalized Born approximation and stress the importance of multiple scattering in this particular configuration. We analyze the sensitivity to noise and point out that using incident propagative waves together with evanescent waves improves the robustness of the reconstruction.
Journal of the Optical Society of America A 10/2005; 22(9):1889-97. · 1.56 Impact Factor
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ABSTRACT: We simulate a three-dimensional optical diffraction tomography experiment in which superresolution is achieved by illuminating the object with evanescent waves generated by a prism. We show that accounting for multiple scattering between the object and the prism interface is mandatory to obtain superresolved images. Because the Born approximation leads to poor results, we propose a nonlinear inversion method for retrieving the map of permittivity of the object from the scattered far field. We analyze the sensitivity to noise of our algorithm and point out the importance of using incident propagative waves together with evanescent waves to improve the robustness of the reconstruction without losing the superresolution.
Optics Letters 01/2005; 29(23):2740-2. · 3.40 Impact Factor
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ABSTRACT: In an optical diffraction microscopy experiment, one measures the phase and amplitude of the field diffracted by the sample and uses an inversion algorithm to reconstruct its map of permittivity. We show that with an iterative procedure accounting for multiple scattering, it is possible to visualize details smaller than lambda/4 with relatively few illumination and observation angles. The roles of incident evanescent waves and noise are also investigated.
Journal of the Optical Society of America A 08/2003; 20(7):1223-9. · 1.56 Impact Factor
