L’objet de cette thèse est l’étude de la correspondance fluide/gravité, réalisation macroscopique de la dualité AdS/CFT, à la limite où la constante cosmologique tend vers zéro (limite plate). La jauge de Fefferman-Graham, habituellement utilisée dans le dictionnaire holographique, est singulière à la limite plate. Ici, en passant par la formulation hydrodynamique de la théorie dubord, nous construisons une jauge, appelée jauge du développement en série dérivatif, où cette limite est bien définie. Sur la géométrie du bord, elle correspond en fait à faire tendre vers zéro la vitesse de la lumière, situation connue comme limite carrollienne. Un fluide relativiste admet une telle lim-ite, qui donne lieu à l’hydrodynamique carrollienne, étudiée ici en dimension arbitraire, parallèlement à son homologue galiléen. Ensuite, nous montrons spécifiquement en dimensions 4 et 3 du bulk qu’il est possible de construire des solutions asymptotiquement plates des équations d’Einstein partant de systèmes hydrodynamiques conformes carrolliens du bord, qui est ici l’hypersurface degenre lumière à l’infini. En 4 dimensions nous introduisons des conditions d’intégrabilité permettant de resommer la série dérivative sous formefermée. En 3 dimensions toute configuration fluide du bord aboutit à une solution exacte des équations d’Einstein. Les solutions de Bañados sont un sous-ensemble des solutions obtenues et identifiées au moyen de leurs charges de surface. Nous accordons une attention particulière au rôle du repère hydrodynamique, trop souvent ignoré en holographie. Pour terminer, nous nous concentrons sur la formulation de la AdS/CFT dans laquelle la symétrie de Weyl est explicite. Quoique cette symétrie soit un ingrédient incontournable de la correspondance fluide/gravité, elle n’est pas codée dans la formulation habituelle de l’holographie. Nous introduisons une nouvelle jauge et analysonsses conséquences. / In this thesis we discuss the limit of vanishing cosmological constant (flat limit) of the fluid/gravity correspondence, which is a macroscopic realization of the AdS/CFT. The holographic dictionary is usually implemented in a gauge(Fefferman-Graham), which does not admit a flat limit. In the hydrodynamic formulation of the boundary theory, we introduce a gauge, dubbed derivative expansion, where such a limit turns out to be smooth. In the boundary we show that this corresponds to a Carrollian limit, i.e. a limit where the speed of light vanishes. We present Carrollian hydrodynamics, together with its dual Galilean counterpart. Then, for 4 and 3 bulk dimensions, we exhibit a resummed line element, which provides an asymptotically flat bulk solution of Einsteinequations starting only from boundary (i.e. null infinity) conformal Carrollian hydrodynamic data. In 4 dimensions we exploit specific integrability conditions, which restrict the achievable class of solutions in the bulk. In 3 dimensions every boundary fluid configuration leads to an exact solution of Einstein’s equations. Bañados solutions are a subset of the solutions reached in this way. They are rigorously identified with their surface charges and the corresponding algebra. We emphasize the choice of hydrodynamic frame, often sidesteppedin holography. Finally, we focus on the formulation of AdS/CFT to encompass Weyl symmetry. This symmetry is a key ingredient of fluid/gravity but it is not naturally encoded in the usual formulation of holography. We introduce an appropriate gauge for realizing it, and analyze its far-reaching consequences.

Diplomová práca sa zaoberá kvantitatívnym fázovým zobrazovaním objektov umiestnených za rozptyľujúcim prostredím v koherenciou riadenom holografickom mikroskope. Tento mikroskop umožnuje zobrazovať s úplne nekoherentným osvetlením vzorky, čo vyvoláva efekt koherenčnej brány. Koherenčná brána je veľmi dôležitá vlastnosť zobrazovacieho systému umožňujúca separáciu balistických a rozptýlených fotónov, jej dôkladnému vysvetleniu je venovaná značná časť práce. Ďalej sú prezentované základy teórie zobrazenia v koherenciou riadenom holografickom mikroskope. Tie sú využité v závere práce pri interpretácii experimentálnych výsledkov. Cieľom práce je navrhnúť metódu pre pozorovanie fázových objektov v rozptyľujúcich prostrediach a experimentálne túto metódu overiť. Na základe analytických výsledkov a predchádzajúceho výskumu je navrhnutá nová metóda, ktorá je ďalej overovaná pomocou rôzne komplexných vzoriek. Je založená na zázname viacerých obrazov s rôznym posunutím referenčného poľa. Každý posun korešponduje so zobrazovaním pomocou inej skupiny fotónov. Je možné vytvoriť syntetický obraz so zlepšenou kvalitou sčítaním jednotlivých obrazov získaných z interferencie balistických alebo rozptýlených fotónov. Experimenty s rôzne komplexnými vzorkami poskytujú náhľad na obmedzenia prezentovanej metódy.

This thesis deals with the problem of practical application of FDTD technique for simulation of image formation in coherence controlled holographic microscope. Various ways for obtaining scattering matrices are explored in detail and the optimal technique based on a rigorous calculation of the far field is proposed. The scattering matrix, containing information about the observed sample, is subsequently used in analytic calculation of holographic signal; two levels of approximation of pupil function are also evaluated. The results are compared with a traditional approach based on Rytov approximation resulting in specification of the parameter domain where the approximation is applicable. Based on the simulations of the microscope, the dependence of axial resolution on apertures of the objective and the condenser and sensitivity of the signal to changes of refractive index of the sample is also studied.

Digital holographic microscopy is an interferometric imaging technique, the principle of which is the off-axis image plane holography. The principle of this technique enables to reconstruct both the image intensity and the image phase from the output interferencesignal. The reconstruction can be carried out on the basis of a single image plane hologram. This leads to the possibility of a realtime image reconstruction. The speed of the reconstruction depends on the detection and the computing process. The aim of this diploma thesis is to develop user software for the control of the detection camera and for the image plane hologram reconstruction. The effort was to achieve the highest number of image reconstructions per time unit, with the maximum utilization of the data transfer between the camera and the computer.The next aim of this thesis is the stabilization of the optical table position. The method of stabilization is based on the image phase information, which is used for the control loop feedback between reconstructed image phase and the piezoelectric actuator placed inside of the optical table. Experimental results, which prove the functionality of the stabilization, are presented.

The aim of diploma thesis are modifications in mechanical design of the coherence controlled holographic microscope which will lead to reduction of some deficiencies. In this thesis there is a brief description of the history interference microscopy and differences between each types of interference microscopes. In this work there are stated some design deficiencies of actual condition of the microscope and also several solutions are suggested and shortly described. Then the best solution is chosen which is adjusted to a final form. It is described in detail and then realized. There is a summary included in the conclusion whether the new solution is suitable and if it fulfills the required condition.

This diploma thesis deals with phase and amplitude objects observation through scattering media by means of a coherence-controlled holographic microscope (CCHM). A brief history of development and construction of the microscope, its advantages compared to the classical light microscopy and hologram processing are described. Quantitative phase imaging through scattering media by means of ballistic as well as diffuse light is verificated in the experimental part. A comparison of an image obtained through a scattering layer by means of CCHM and a classical microscopy in the light field is demonstrated.

This thesis focuses on cell tracking in image sequences acquired using a multimodal holographic microscope (MHM). The principles of holographic microscopy are described together with the application in cells acquisition. The main part of the thesis describes a complete approach for segmentation and tracking of single cells in acquired in long-term sequences. The approach is designed based on parametric active contour models with specific modifications to achieve reasonable precision and robustness. The implemented method is described in detail, including the evaluation and demonstration of results.

Within this thesis, photo-induced mechanisms of the light-matter interaction are investigated in tailored and photofunctional materials that differ significantly in their optical and structural properties. The individual coupling mechanisms in congruently melted, nominally undoped or iron doped lithium niobate crystals as well as in structurally disordered photoswitchable molecules embedded into a solid state polymer are examined in particular by the principle of holographic grating recording and transient absorption spectroscopy which provide new insight into a variety of material response properties. In case of photoswitchable ruthenium sulfoxide compounds, the underlying mechanism can be unambiguously assigned to a photochromic material response evoked by a photochemical reaction, i.e., a non-instantaneous, local ligand isomerisation. Comparable results are obtained for iron-doped, oxidized lithium niobate where holographic grating recording is related to the photophysical generation of transient excitonic states whose photochromic properties are characterized by targeted ns-pump, supercontinuum probe spectroscopy. In the event of nominally undoped lithium niobate, the holographic amplification of two sub-picosecond pulses is attached to the phenomenon of two-beam coupling on a self-induced dynamic grating. By correlating the individually obtained mechanisms of the light-matter interaction and the light-induced material response, generally accepted conclusions on a microscopic level can be achieved. A major influence of the internal structure and orientation of the excited states, i.e., an appropriate threedimensional structural arrangement, is deduced as a prerequisite for the formation of light-induced, macroscopic refractive index changes while absorption and microscopic refractive index alterations linked via the Kramers-Kronig relation are unaffected. In systems featuring a random distribution of excited states, an orientational order might be achieved as a consequence of linear polarized light, i.e., by polarization structuring. Moreover, if the photorefractive effect can be ruled out, the material response in lithium niobate can be solely assigned to a local alteration of the transient electronic states, i.e., to the photochromic properties of polarons and/or excitonic states, which is in particular comparable to the linkage isomerism of molecular photoswitchable molecules. In addition, the influence of structural parameters on the light-matter/surface interaction is studied on the μm-scale by analyzing the diffraction phenomenon arising from a relief grating. A considerable impact on the surface grating assisted coupling is determined by the transition from cw-lasers to ultrashort laser pulses which enables interference quenching. However, this phenomenon is of no consequence in case of selfinduced holographic gratings.

This thesis deals with the topic of 3D image processing for digital holographic microscopy - numerical refocusing. This method allows to perform mathematically accurate defocus correction on image of a sample captured away from the sample plane and it was applicable only for images that were made made using coherent illumination source. It has been generalized to a form in which it is also applicable to devices that use incoherent (non-monochromatic or extended) illumination sources. Another presented achievement concerns hologram processing. The advanced hologram processing method enables obtaining more data mainly concerning precision of quantities from one hologram — normally, one would have to capture multiple holograms to get those. Both methods have been verified experimentally.

Image quality metrics for several inverse scattering methods and algorithms are presented. Analytical estimates and numerical simulations provide a basis for poor image quality diagnostics. The limitations and noise behavior of reconstructed images are explored analytically and empirically using a contrast ratio. Theoretical contrast ratio estimates using the canonical PEC circular cylinder are derived. Empirical studies are conducted to confirm theoretical estimates and to provide examples of image quality vs SNR for more complex scatterer profiles. Regularized sampling is shown to be more noise sensitive than tomographic reconstructive methods.