Focused ultrasound (FUS) is an emerging technology, and it plays an essential role in clinical and contactless acoustic energy transfer applications. These applications have critical criteria for the acoustic pressure level, the creation of complex pressure patterns, spatial management of the complicated acoustic field, and the degree of nonlinear waveform distortion at the focal areas, which have not been met to date. This dissertation focuses on introducing experimentally validated novel numerical approaches, optimization algorithms, and experimental techniques to fill existing knowledge gaps and enhance the functionality of holographic acoustic lenses (HALs) with an emphasis on applications related to biomedical-focused ultrasound and ultrasonic energy transfer. This dissertation also aims to investigate the dynamics of nonlinear acoustic beam shaping in engineered HALs. First, We will introduce 3D-printed metallic acoustic holographic mirrors for precise spatial manipulation of reflected ultrasonic waves. Optimization algorithms and experimental validations are presented for applications like contactless acoustic energy transfer. Furthermore, a portion of the present work focuses on designing holographic lenses in strongly heterogeneous media for ultrasound focusing and skull aberration compensation in transcranial-focused ultrasound. To this end, we collaborated with the Biomedical Engineering and Mechanics Department as well as Fralin Biomedical Research Institute to implement acoustic lenses in transcranial neuromodulation, targeting to improve the quality of life for patients with brain disease by minimizing the treatment time and optimizing the ultrasonic energy into the region of interest. We will also delve into the nonlinear regime for High-Intensity Focused Ultrasound (HIFU) applications, this study is structured under three objectives: (1) establishing nonlinear acoustic-elastodynamics models to represent the dynamics of holographic lenses under low- to high-intensity acoustic fields; (2) validating and leveraging the resulting models for high-fidelity lens designs used in generating specified nonlinear ultrasonic fields of complex spatial distribution; (3) exploiting new physical phenomena in acoustic holography. The performed research in this dissertation yields experimentally proven mathematical frameworks for extending the functionality of holographic lenses, especially in transcranial-focused ultrasound and nonlinear wavefront shaping, advancing knowledge in the burgeoning field of the inverse issue of nonlinear acoustics, which has remained underdeveloped for many years. / Doctor of Philosophy / Ultrasonic waves are sound waves that have frequencies higher than the upper audible limit of human hearing. The versatility and non-invasive nature of ultrasonic waves make them a valuable tool in numerous scientific, medical, and industrial applications. In healthcare, ultrasonic waves are employed in diagnostic imaging techniques, such as ultrasound scans, to create images of internal body structures. Ultrasonic waves are also used for non-destructive testing (NDT) of materials, detecting flaws or cracks within structures without causing any damage. Furthermore, this technology finds applications in the field of material science for the manipulation of particles and in biomedical research for drug delivery systems. Focused ultrasound sound is an emerging non-invasive therapeutic modality that uses focused ultrasound waves to target tissue within the body without damaging the surrounding tissue. This technology allows for precise delivery of ultrasound energy to a specific region, where it can induce various desired therapeutic effects depending on the targeting location and parameters. Therapeutic focused ultrasound has the advantage of being non-invasive, reducing the risks and recovery time associated with traditional surgery. It can be precisely controlled and monitored in real-time with imaging techniques such as ultrasound or MRI, ensuring the targeted treatment of pathological tissues while sparing healthy ones. Applications of therapeutic are broad and include tumor ablation, facilitation of drug delivery across the blood-brain barrier, relief of chronic pain, and treatment of essential tremor and other neurological disorders. The domain of therapeutic focused ultrasound is continually advancing, driven by research that seeks to extend its applications. Recent developments in acoustic engineering and 3D printing have led to the creation of acoustic holograms, or holographic acoustic lenses, which allow for more refined control over the spatial structure of the acoustic field. These technological advancements hold the promise of enhancing FUS by improving the accuracy of acoustic field localization and providing a more cost-effective solution compared to conventional systems like phased array transducers. However, the accuracy and applicability of existing models and techniques are constrained by assumptions, including the uniformity of the propagation medium and the linearity of the acoustic field, which limits the functionality and restricts the potential applications of acoustic holograms. In this dissertation, we present novel numerical techniques, algorithms, and proof-of-concept experiments to fill those knowledge gaps and expand the functionality of acoustic holograms in crucial applications.

Neste trabalho desenvolvemos duas séries de EODs operando em regime simultâneo de modulação das componentes de fase e de amplitude de uma frente de luz (Modulação Complexa Completa MCC). A primeira destas séries foi constituída por Hologramas de Fourier calculados através do Algoritmo Iterativo da Transformada de Fourier (Iterative Fourier Transform Algorithm IFTA) e a segunda, por Hologramad de Fresnel cujo cálculo da propagação da luz foi obtido por filmagem linear espacial proveniente da solução da Equação de Helmholtz no domínio da frequência. Nos dois casos, a Modulação Complexa Completa foi implementada fisicamente empregando, para realizar a modulação de fase, um micro-relevo gravado em um filme de DLC (Diamond Like Carbon) depositado sobre um substrato de vidro. Sobre este relevo foi implementada a modulação de amplitude, através da deposição de um filme de alumínio, no qual foram realizadas micro-aberturas diferentes cujas áreas eram proporcionais à amplitude em cada pixel. Nos Hologramas de Fourier, uma diferente espessura do filme DLC localizada sobre cada pixel foi responsável pela modulação do valor de fase relativo àquele ponto. Nos Hologramas de Fresnel, a combinação de duas espessuras diferentes do filme de DLC em cada pixel foi responsável pela modulação do valor de fase relativo a cada ponto. Os elementos foram caracterizados física e opticamente e produziram imagens de reconstrução totalmente livres de ruídos do tipo speckle. Também em caráter de avaliação dos resultados foi efetuada a comparação entre as imagens de reconstrução óptica produzidas pelos Hologramas de Fresnel com MCC com as produzidas por Hologramas de Fresnel convencionais em regime de modulação de fase. / In this work, we developed two sets of DOESs able to modulate both phase and amplitude components of light simultaneously (Complete Complex Modulation CCM). The first set is composed of Fourier Holograms calculated by Iteractive Fourier Transform Algorithm (IFTA). The second set is composed by Fresnel Holograms, which light propagation was calculated by spatial linear filtering obtained from the solution of the Helmholtz Equation in the frequency domain. In both cases, Complete Complex Modulation was physically implemented by a micro-relief, for phase modulation, recorded on a Diamond Like Carbon (DLC) film deposited on a glass substrate. Amplitude modulation was implemented on a aluminum fim layer deposited on this relief. In this layer, micro-appertures proportional to the amplitude on each pixel, were recorded. Phase modulation in each pixel of the Fourier Holograms was achivied by different thicknesses of the DLC film. For Fresnel Holograms, phase modulation was achieved by combining two different thicknesses of DLC film inside each pixel. The elements were physically and optically characterized and produced reconstruction images completly free of speckle like noise. The optical reconstruction images produced from Fresnel Holograms working in CCM regime and convencional phase-only modulated Fourier Holograms were compared.

Neste trabalho desenvolvemos duas séries de EODs operando em regime simultâneo de modulação das componentes de fase e de amplitude de uma frente de luz (Modulação Complexa Completa MCC). A primeira destas séries foi constituída por Hologramas de Fourier calculados através do Algoritmo Iterativo da Transformada de Fourier (Iterative Fourier Transform Algorithm IFTA) e a segunda, por Hologramad de Fresnel cujo cálculo da propagação da luz foi obtido por filmagem linear espacial proveniente da solução da Equação de Helmholtz no domínio da frequência. Nos dois casos, a Modulação Complexa Completa foi implementada fisicamente empregando, para realizar a modulação de fase, um micro-relevo gravado em um filme de DLC (Diamond Like Carbon) depositado sobre um substrato de vidro. Sobre este relevo foi implementada a modulação de amplitude, através da deposição de um filme de alumínio, no qual foram realizadas micro-aberturas diferentes cujas áreas eram proporcionais à amplitude em cada pixel. Nos Hologramas de Fourier, uma diferente espessura do filme DLC localizada sobre cada pixel foi responsável pela modulação do valor de fase relativo àquele ponto. Nos Hologramas de Fresnel, a combinação de duas espessuras diferentes do filme de DLC em cada pixel foi responsável pela modulação do valor de fase relativo a cada ponto. Os elementos foram caracterizados física e opticamente e produziram imagens de reconstrução totalmente livres de ruídos do tipo speckle. Também em caráter de avaliação dos resultados foi efetuada a comparação entre as imagens de reconstrução óptica produzidas pelos Hologramas de Fresnel com MCC com as produzidas por Hologramas de Fresnel convencionais em regime de modulação de fase. / In this work, we developed two sets of DOESs able to modulate both phase and amplitude components of light simultaneously (Complete Complex Modulation CCM). The first set is composed of Fourier Holograms calculated by Iteractive Fourier Transform Algorithm (IFTA). The second set is composed by Fresnel Holograms, which light propagation was calculated by spatial linear filtering obtained from the solution of the Helmholtz Equation in the frequency domain. In both cases, Complete Complex Modulation was physically implemented by a micro-relief, for phase modulation, recorded on a Diamond Like Carbon (DLC) film deposited on a glass substrate. Amplitude modulation was implemented on a aluminum fim layer deposited on this relief. In this layer, micro-appertures proportional to the amplitude on each pixel, were recorded. Phase modulation in each pixel of the Fourier Holograms was achivied by different thicknesses of the DLC film. For Fresnel Holograms, phase modulation was achieved by combining two different thicknesses of DLC film inside each pixel. The elements were physically and optically characterized and produced reconstruction images completly free of speckle like noise. The optical reconstruction images produced from Fresnel Holograms working in CCM regime and convencional phase-only modulated Fourier Holograms were compared.

Orientador: Jaime Frejlich / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-05T13:36:24Z (GMT). No. of bitstreams: 1 Oliveira_Ivande_D.pdf: 718797 bytes, checksum: 32fec7f75d9afd6a59509cc66293c0d3 (MD5) Previous issue date: 2005 / Resumo: Neste trabalho foram realizadas contribuições importantes na área de registro holográfico auto-estabilizado em niobato de lítio (LiNbO3:Fe) e do estudo da dinâmica da formação e evolução dos hologramas durante as diferentes etapas da fixação. Outras contribuições importantes neste trabalho referem-se ao desenvolvimento de técnicas mais eficientes e/ou mais simples para a fixação de hologramas. Em termos de registro auto-estabilizado, nosso trabalho permitiu o uso dessas técnicas para obtermos hologramas com alta eficiência de difração e de forma reprodutível. O registro holográfico auto-estabilizado em niobato de lítio já tinha sido utilizado anteriormente. A novidade aqui reside no estudo detalhado da dinâmica do processo, que permitiu uma melhor compreensão das possibilidades e limitações da técnica, incluindo o estudo detalhado do efeito do grau de oxidação (isto é, da relação [Fe3+]/[Fe2+]) do material sobre o comportamento do sistema de estabilização. Em função dos estudos acima referidos que permitiram uma melhor compreensão dos processos, foi possível desenvolver uma técnica de fixação para cristais oxidados que permitiu obter redes fixas com alta eficiência de difração, com valores previzíveis em função das propriedades do cristal e de forma reprodutível. O registro auto-estabilizado foi aplicado com sucesso, pela primeira vez, à técnica de fixação (registro e compensação) a alta temperatura, de forma muito mais simples do que a técnica clássica, e que permitiu obter excelentes resultados mesmo com amostras reduzidas, para as quais o processo clássico não funciona satisfatoriamente. Paralelamente mostramos teórica e experimentalmente os problemas associados à medida da eficiência de difração em hologramas espessos. Mostramos que o uso de um feixe auxiliar (frequentemente utilizado) para este tipo de medida leva a erros consideráveis e para este caso propomos uma forma muito simples de realizar essa medida / Abstract: In this work important contributions to the field and to the self stabilized holographic record in litium niobate were achieved and to the dynamic formation and hologram evolution study during different fixing stages. Other important contributions in this work refer to more efficient technique development and/or simpler ones to hologram fixing. On terms of self stabilized record our work allowed the use of these techniques to obtain some holograms with high efficiency diffractions and in a reproducible form. The self stabilized holographic record in litium niobate had already been used before. The new point here is the detailed study about the process dynamic which allowed a better understanding of the technique possibilities and limitations including the detailed study of the effect of the oxidation degree (thus the relation [Fe3+]/[Fe2+]) of the material about the stabilization system behaviour. According to the referred studies above which permitted a better understanding of the process, it was possible to develop the oxidated crystals fixing technique which permitted to get fixed nets with high diffractions efficience with predictable values according to the crystals properties and in a reproducible form. The self stabilized record was applied sucessfully to the fixing technique (recording and compensation) for the first time to high temperature in a so much simpler form than the classical one which permitted to obtain excellent results even using reduced samples to which the classical process has not worked satisfactionally. Parallel to this, we showed (theoric and experimentally) the associated problems to the diffraction efficience in thick holograms. We showed the use of an auxiliar bin (frequently used) for this kind of measure results in considerable errors and to this case we propose a so much simpler form of achieving this measure / Doutorado / Física da Matéria Condensada / Doutor em Ciências

In mainstream media and entertainment, holography is often misrepresented as single perspective non-stereoscopic imagery suggesting three-dimensionality. Traditional holographic artists, however, utilize a laser setup to record and reconstruct wavefronts to describe a scene in multi-perspective natural parallax vision ("auto-stereoscopic"). Although these approaches are mutually exclusive in practice, they share a similar goal of staging three-dimensional (3D) imagery for a window-like viewing experience. This thesis presents a non-waveform digital computer approach for recording, reconstructing, and experiencing holographic visualizations in a cinematic context. By recording 3D information from a scene using the structured light method, a custom computer program performs stereoscopic reconstruction in real-time during presentation. Artists and computer users could then use a hardware device, such as the Microsoft Kinect, to explore the holographic cinematic form interactively.

As visual display technologies move closer to producing true three dimensional displays, pixel technologies need to be ever smaller and more functional to keep pushing the boundaries. Plasmonic metasurfaces have been shown to control the phase, amplitude and/or polarisation of incoming electromagnetic radiation. Nano-fabrication advancements have resulted in the fabrication of the building blocks of such metasurfaces at nano-scale dimensions, allowing the surfaces to interact with visible light, opening up applications in visual displays. As pixel sizes shrink, smaller colour filters will be required. The excitation of plasmonic resonances in metallic nano-structure arrays have resulted in colour filters an order of magnitude smaller than what is currently commercially available. As colour filters, plasmonic metasurfaces offer numerous advantages over pigment-based colour filters used in modern commercial liquid crystal (LC) displays, including environmental, size and longevity factors. Furthermore, exploiting the wavelength and polarisation dependant scattering of nano-structures, optical components, including lenses, waveplates and holograms containing sub-wavelength pixels have been demonstrated in the visible wavelength spectrum. The metasurfaces are able to mould optical wavefronts into arbitrary shapes with sub-wavelength resolution by introducing spatial variations in the optical response of the light scatterers. The applications demonstrated so far are, on the whole, static devices, that is to say their optical properties may not be altered post fabrication. To realise the full potential of plasmonic metasurfaces to visual applications the devices must be made active. By activating structural colour surfaces, not only may pixel densities potentially be increased simply by removing the need for separate red, green and blue filters, but a new class of high definition ultra-thin display devices may be accessible, whilst the dynamic manipulation of the wavelength and polarisation properties of nano-scattering elements would open up the possibilities to create sub-wavelength holographic pixels. This thesis investigates ways to activate static metasurfaces for colour, flat optic, and holographic applications. First, methods of dynamic control of the structural colour of plasmonic nano-hole arrays are investigated. By combining nano-hole arrays with liquid crystals, transmissive electrically tunable LC-nanohole pixels operating across the visible spectrum with un-polarised input light are experimentally demonstrated. An output analyser in combination with a nematic LC layer enables pixel colour to be electronically controlled through an applied voltage across the device, where LC re-orientation leads to tunable mixing of the relative contributions from the plasmonic colour input. Furthermore, exploiting the strong surface anchoring effects between an aluminium surface and LC molecules a twisted nematic LC cell, using a metallic grating as a combined colour filter, electrode and alignment layer, was shown to act a variable amplitude colour filter. The colour of these pixels was improved greatly utilising a grating-insulator-grating structure unique to this work. Second, a new process for fabricating aluminium nano-rod structures embedded in an elastomeric medium, with high spatial accuracy, is presented. The process is used to create nano-rod plasmonic resonator arrays whose optical properties may be altered by mechanical deformation. The pattern transfer process is further utilised to create dynamic optical elements, including nano-rod arrays for colour filters, tunable focal length Fresnel zone plates and photon sieves, and stretchable holograms with dynamic replay fields.

Orientador: Prof. Dr. Marcos Roberto da Rocha Gesualdi / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Elétrica, 2016. / A holografia permite o registro e a reconstrução óptica de imagens 3D de objetos, pois um holograma carrega as informações de intensidade e fase da função da onda óptica espalhada pelo objeto. Com a evolução do armazenamento e da velocidade de processamento de dados em computadores, a viabilidade dos hologramas gerados por computador tem evoluído no decorrer dos anos. Na atualidade, a implementação experimental dos CGHs tem sido realizada por meio de novos dispositivos opto-eletrônicos, como os moduladores espaciais de luz, câmeras CMOS, e CCDs de alta resolução, além dos novos materiais fotossensíveis, permitindo o registro e reconstrução óptica de objetos tridimensionais e de feixes ópticos especiais. Por outro lado, as possibilidades do FPGA, um dispositivo lógico programável capaz de criar diferentes tipos de circuitos digitais, permite desenvolver um hardware capaz de melhorar os tempos de processamentos para a geração dos hologramas sintéticos. O objetivo deste trabalho é estudar a holografia gerada por computador a partir de algoritmos (software), a realização da reconstrução óptica destes hologramas usando dispositivos SLMs, bem como as possibilidades de implementação dos CGHs via FPGA (hardware) de cenas 3D virtuais. Desta forma, foram obtidos resultados de construção (gravação) numérica de CGHs de imagens estáticas e dinâmicas, 2D e 3D, via MATLAB e de reconstrução (reprodução) óptica usando dispositivos SLMs destas imagens estáticas e dinâmicas (cenas). / Holography allows three-dimensional recording and optical reconstruction of objects, as a hologram carries the information of the intensity and the optic wave¿s phase function spread over the object. With the evolution of data storage and processing speed in computers, the viability of creating holograms by computer has advance through the years. Today, the CGHs¿s experimental implementation has been performed by new optoelectronic devices, as special light modulators, CMOS cameras, e high resolution CCDs, besides new photosensitive materials, allowing recording and optical reconstruction of 3D objects and special optic beams. On the other hand, FPGA possibilities, a logic programmable device able to create different kind of digital circuits, enables the development of hardware to improve processing time when creating synthetic holograms. The main objective of this work is to study holography created by computer using algorithms (software), moreover the optical reconstruction of holograms utilizing SLMs devices, as the possibility of implementing CGHs by FPGA (hardware), of virtual 3D scenes. Therefore, results of numeric construction (recording) of CGHs of static and dynamic images were obtained, 2D and 3D, using MATLAB, and the optical reconstruction (reproduction) using SLMs devices of these images (scenes).

Orientador: Prof. Dr. Marcos Roberto da Rocha Gesualdi / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Elétrica, 2017. / Estudos da aplicação de moduladores espaciais de luz do tipo LCoS (Liquid Cristal on Silicon) e técnicas holográficas em substituição às máscaras no processo de fotolitografia são apresentados. Hologramas Gerados por Computador (HGC) a partir de duas imagens com dimensões conhecidas, simulando uma máscara de campo claro e uma máscara de campo escuro, foram aplicados a um modulador espacial de luz LCoS conectado a um arranjo óptico capaz de reduzir as imagens reconstruídas, permitindo o levantamento dos parâmetros de maior relevância no processo de fotolitografia para fabricação de estruturas micrométricas e, a partir da sua caracterização, identificar os limites impostos pelo modulador espacial de luz LCoS nesse processo. Registro das imagens, com diferentes dimensões, adquiridas à partir da reconstrução dos HGC provenientes das máscaras de campo claro e campo escuro, foram realizados através de uma câmera CCD e filmes de alta resolução. Os resultados permitiram a visualização e medição de estruturas com até 13 Pm e representam uma base de estudo na busca de alternativas para substituição das máscaras em processos de fotolitografia / Application studies of the Spatial Light Modulators LCoS type (Liquid Crystal on Silicon) and holographic techniques to replace the masks in the photolithography process are presented. Computer-generated Holograms (HGC) from two images with known dimensions, simulating a clear field mask and a dark field mask, were applied to a Spatial Light Modulators LCoS connected to an optical arrangement capable of reducing the reconstructed images, allowing the survey of the parameters of greater relevance in the process of photolithography to fabricate micrometric structures and from its characterization to identify the limits imposed by the Spatial Light Modulators LCoS in this process. Recording of the images, with different dimensions, acquired from the reconstruction of the HGC from clear field and dark field masks, were performed through a CCD camera and high resolution films. The results allowed the visualization and measurement of structures up to 13 ìm and represent a base of study in the search of alternatives for replacing the masks in photolithography processes.

Orientation Device is a tool for understanding the other towards recognizing alternative possibilities, for care and compassion, for expanding our culturally and politically bounded mindset, a tool of vital nausea and questioning compulsory heterosexuality. The work is a series of augmented reality (AR) experiences for mobile device that allow the audience to participate in documentary queer performances in any private or public setting. These immersive experiences challenge our perception of space. The LGBTQIA+ community is often disoriented within heteronormative spaces, and this work reverses that dichotomy by disorienting the audience. As a cisgender creator, I invite queer performers, artists, poets, and thinkers who express their identity in their creative practices. As the AR medium is widely distributable, I want to give the participants the potential opportunity to present themselves to a wide international audience through the poetics of augmented reality and documentary video holograms. / Master of Fine Arts / ORIENTATION DEVICE: poiesis of documentary volumetric video for augmented reality; location-aware interactive mise-en-scène; applied queer phenomenology; the potential of procedural worldmaking in the future

On présente une modélisation tout-analytique d’hologrammes épais uni- ou bidimensionnels (1D/2D), passifs ou actifs, pouvant être photo-inscrits dans des matrices de polymère éventuellement dopées, par exemple en vue de réaliser à faible coût des lasers DFB. Les outils et hypothèses de la modélisation (formalismes des ondes couplées et des matrices de transfert, régime de diffraction de Bragg, hypothèse des enveloppes lentement variables, approche perturbative) sont d’abord introduits et appliqués au cas d’un hologramme épais 1D (réseau en transmission) placé dans une cavité Fabry-Pérot. On montre que la matrice de transfert et la réponse de la structure sont entièrement gouvernées par quelques paramètres réduits : désaccord de phase des ondes co-propagatives avec la condition de Bragg du réseau et coefficients de couplage entre ces ondes. L’étude est ensuite étendue au cas d’un hologramme épais 2D, superposition de réseaux en transmission et en réflexion distribuée placés dans une cavité Fabry-Pérot. On montre que l’approche tout-analytique reste valide au prix de changements judicieux de base de décomposition des champs. Quelques paramètres suffisent à nouveau à décrire le système : désaccord avec la condition de Bragg de chaque réseau et coefficients de couplage entre ondes respectivement co- et contra-propagatives. Enfin, les bases d’une extension du traitement tout-analytique à un hologramme 2D actif sont posées. La présence d’une source localisée d’émission spontanée est prise en compte via une extension du formalisme des matrices de transfert. On montre que l’émission de la source est filtrée angulairement et spectralement par la cavité que forme l’H2D passif. / This work is devoted to an analytical modelling of thick, one- or two-dimensional (1D/2D), passive or active holograms. Such devices can be obtained by photoinscription of diffraction gratings in polymer matrices, e.g. for the fabrication of low-cost DFB lasers. First we introduce the tools and hypotheses (coupled-mode theory, transfer matrix formalism, Bragg diffraction regime, slowly-varying envelopes, perturbative approach) of our model and apply them to the case of a thick 1D hologram (transmission grating) in a Fabry-Pérot cavity. We show that its transfer matrix and optical response are entirely governed by a small set of adimensional parameters that quantify the phase mismatch with the Bragg condition of the grating and coupling constants between co-directional waves. We then extend our study to the case of a thick 2D hologram resulting from the crossed superposition of a transmission grating and a distributed Bragg reflector in a Fabry-Pérot cavity. We establish that our all-analytical approach remains valid, provided fields are expressed in a well-chosen basis. Again, a small set of physical parameters (phase mismatch with each grating’s Bragg condition, co- and contra-directional coupling constants) is shown to completely describe the behaviour of the device. Finally, we lay the foundations of an extension of our analytical treatment to the case of an active 2D hologram containing a single localized point source, whose isotropic spontaneous emission is readily taken into account through an extension of the transfer matrix formalism. We show that the emission is angularly and spectrally filtered by the response of the passive 2D hologram previously described.