Formulation of gauge theories on transitive Lie algebroids

In this paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration along the algebraic part of the transitive Lie algebroid (its kernel). Explicit action functionals are given in terms of global objects and in terms of their local description as well. We investigate applications of these constructions to Atiyah Lie algebroids and to derivations on a vector bundle. The obtained gauge theories are discussed with respect to ordinary and to similar non-commutative gauge theories.Comment: 30 pages. Final version. arXiv admin note: substantial text overlap with arXiv:1109.428

Local description of generalized forms on transitive Lie algebroids and applications

In this paper we study the local description of spaces of forms on transitive Lie algebroids. We use this local description to introduce global structures like metrics, $\ast$-Hodge operation and integration along the algebraic part of the transitive Lie algebroid (its kernel). We construct a \v{C}ech-de Rham bicomplex with a Leray-Serre spectral sequence. We apply the general theory to Atiyah Lie algebroids and to derivations on a vector bundle

Two-out-of-two color matching based visual cryptography schemes

International audienceVisual cryptography which consists in sharing a secret message between transparencies has been extended to color prints. In this paper, we propose a new visual cryptography scheme based on color matching. The stacked printed media reveal a uniformly colored message decoded by the human visual system. In contrast with the previous color visual cryptography schemes, the proposed one enables to share images without pixel expansion and to detect a forgery as the color of the message is kept secret. In order to correctly print the colors on the media and to increase the security of the scheme, we use spectral models developed for color reproduction describing printed colors from an optical point of view

Fourier-based automatic alignment for improved visual cryptography schemes

International audienceIn Visual Cryptography, several images, called "shadow images", that separately contain no information, are overlapped to reveal a shared secret message. We develop a method to digitally register one printed shadow image acquired by a camera with a purely digital shadow image, stored in memory. Using Fourier techniques derived from Fourier Optics concepts, the idea is to enhance and exploit the quasi periodicity of the shadow images, composed by a random distribution of black and white patterns on a periodic sampling grid. The advantage is to speed up the security control or the access time to the message, in particular in the cases of a small pixel size or of large numbers of pixels. Furthermore, the interest of visual cryptography can be increased by embedding the initial message in two shadow images that do not have identical mathematical supports, making manual registration impractical. Experimental results demonstrate the successful operation of the method, including the possibility to directly project the result onto the printed shadow image

Reconstruction of the rose of directions from a digital micro-hologram of fibers

International audienceDigital holography makes it possible to acquire quickly the interference patterns of objects spread in a volume. The digital processing of the fringes is still too slow to achieve on line analysis of the holograms. We describe a new approach to obtain information on the direction of illuminated objects. The key idea is to avoid reconstruction of the volume followed by classical three-dimensional image processing. The hologram is processed using a global analysis based on autocorrelation. A fundamental property of diffraction patterns leads to an estimate of the mean geometric-covariogram (MGC) of the objects projections. The rose of directions is connected with the MGC through an inverse problem. In the general case, only the 2D rose of the object projections can be reconstructed. The further assumption of unique-size objects gives access with the knowledge of this size to the 3D direction information. An iterative scheme is suggested to reconstruct the 3D rose in this special case. Results are provided on holograms of paper fibers

Twin-image noise reduction by phase retrieval in in-line digital holography

14 pagesInternational audienceIn-line digital holography conciles the applicative interest of a simple optical set-up with the speed, low cost and potential of digital reconstruction. We address the twin-image problem that arises in holography due to the lack of phase information in intensity measurements. This problem is of great importance in in-line holography where spatial elimination of the twin-image cannot be carried out as in off-axis holography. Applications in digital holography of particle fields greatly depend on its suppression to reach greater particle concentrations, keeping a sufficient signal to noise ratio in reconstructed images. We describe in this paper methods to improve numerically the reconstructed images by twin-image reduction. ©2005 COPYRIGHT SPI

Two-flux transfer matrix model for predicting the reflectance and transmittance of duplex halftone prints

International audienceWe introduce a model allowing convenient calculation of the spectral reflectance and transmittance of duplex prints. It is based on flux transfer matrices and enables retrieving classical Kubelka-Munk formulas, as well as extended formulas for non-symmetric layers. By making different assumptions on the flux transfers, we obtain two predictive models for the duplex halftone prints: The "duplex Clapper-Yule model" which is an extension of the classical Clapper-Yule model, and the "duplex primary reflectance-transmittance model". The two models can be calibrated from either reflectance or transmittance measurements; only the second model can be calibrated from both measurements, thus giving optimal accuracy for both reflectance and transmittance predictions. The conceptual differences between the two models are deeply analyzed, as well as their advantages and drawbacks in terms of calibration. According to the test carried out in this study with paper printed in inkjet, their predictive performances are good provided appropriate calibration options are selected

Co-design of an in-line holographic microscope with enhanced axial resolution: selective filtering digital holography

International audienceCommon-path digital in-line holography is considered as a valuable 3D diagnostic techniques for a wide range of applications. This configuration is cost effective and relatively immune to variation in the experimental environment. Nevertheless, due to its common-path geometry, the signal to noise-ratio of the acquired hologram is weak as most of the detector (i.e. CCD/CMOS sensor) dynamics is occupied by the reference field signal, whose energy is orders of magnitude higher than the field scattered by the imaged object. As it is intrinsically impossible to modify the ratio of energy of reference to the object field, we propose a co-design approach (Optics/Data Processing) to tackle this issue. The reference to object field ratio is adjusted by adding a 4-f device to a conventional in-line holographic setup , making it possible to reduce the weight of the reference field while keeping the object field almost constant. Theoretical analysis of the Cràmer-Rao lower bounds of the corresponding imaging model illustrate the advantages of this approach. These lower bounds can be asymptotically reached using a parametric inverse problems reconstruction. This implementation results in a 60 % gain in axial localization accuracy (for of 100 µm diameter spherical objects) compared to a classical in-line holography setup

In-line particle holography with an astigmatic beam: set-up self-calibration using an "inverse problems" approach

11 pagesInternational audienceThe use of digital in-line holography for the characterization of confined flows in cylindrical geometry confinements (e.g. cylindrical pipe or cylindrical capillaries) is discussed. Due to cylindrical geometry of the walls, the illuminating laser wave can be strongly astigmatic, which renders the use of classical reconstruction techniques impossible. Contrary to plane wave holography set-up, the diffraction pattern of the particles strongly depends on the axial distance of the latter to the entry face of the confinement structure. To address this reconstruction issue, we propose to use an "inverse problems" approach. This approach amounts to finding the best match (least squares solution) between a diffraction pattern model and the captured hologram. For this purpose, a direct imaging model for astigmatic holograms, based on the use of transfer matrices is presented and validated by comparing experimental and simulated holograms. The accuracy of the "inverse problems" reconstruction is then used to calibrate the experimental set-up adjustable parameters. Finally, the approach is tested through experimental astigmatic hologram reconstruction, thus paving the way to its use in pipe flow studies

Numerical suppression of the twin-image in in-line holography of a volume of micro-objects

This paper was published in Measurement Science and Technology and is made available as an electronic reprint with the permission of IOP. The paper can be found at the following URL on the IOP website: http://www.iop.org/EJ/journal/MSTInternational audienceWe address the twin-image problem that arises in holography due to the lack of phase information in intensity measurements. This problem is of great importance in in-line holography where spatial elimination of the twin image cannot be carried out as in off-axis holography. A unifying description of existing digital suppression methods is given in the light of deconvolution techniques. Holograms of objects spread in 3D cannot be processed through available approaches. We suggest an iterative algorithm and demonstrate its efficacy on both simulated and real data. This method is suitable to enhance the reconstructed images from a digital hologram of small objects