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Micro-cylinders with the diameters spanning the 1-20 μm range are growing in importance, for realizing devices with new functionalities. For custom functionalities, their device-designs impose, tolerance-related constraints on their critical dimension. To meet the challenges for the associated online micro-metrology, new methods for the micro-cylinder diameter measurement, are currently receiving considerable attention. „Optical diffraction under Fraunhofer Approximation‟ is one of the most viable experimental techniques for cylinder diameter measurement, in the laboratory as well as Industrial environment. In 1-20 μm diameter range, however, the cylinder-diffraction is not well understood. The reliability of the current models/formulations for this range is far from satisfactory in respect of speed, accuracy, resolution etc., and need a re-examination. The present thesis concerns with a few investigations on the „Optical Diffraction by Micro-Cylinder‟. It highlights both the theoretical and the experimental aspects of the investigations on micro-cylinders with diameters in the range of 1-50 μm. The results of the investigation are organized into two categories. The first of them details a pair of new analytical models obtained from the principles of „Geometrical Theory of Micro-Cylinder Diffraction‟ while the second category highlights another pair of new analytical models obtained from the principles of the „Customary Fraunhofer Theory of Micro-Cylinder Diffraction‟. The model from the „geometrical theory‟ is based on the hypothesis that the ‘ray-paths relevant to the location of ‘diffraction minima’, facilitate to construct, a geometrically-equivalent triangle’. The solution of such a triangle provides the new formulation for the micro-cylinder diffraction. The model from the „customary Fraunhofer theory‟, instead, relies on the on the fact that „the diffraction pattern for a micro-cylinder is essentially, a chirped-interference pattern modulated by a diffraction envelope’. The functional form of the formulation depends upon, the type of triangle constructed for geometrical theory and the type of illumination used in the customary Fraunhofer theory. The thesis highlights, four new formulations (two from each of the approaches) to describe the micro-cylinder diffraction. The principal conclusions of the investigations are as under. - All the new formulations for the micro-cylinder diffraction facilitate, enhanced diameter inversion accuracy, in the hitherto esoteric diameter range of 1-20 μm. For the reported experimental data on 3 μm diameter micro-cylinder, the models proposed in the present investigation improve the accuracy of diameter-estimation from 16.5% known from earlier models to less than 1%. - The investigation also brings out for the first time, the hitherto unnoticed difference between slit-diffraction and the micro-cylinder diffraction: When the micro-cylinder diameter approaches the wavelength of the illumination, the first order diffraction angle approaches nearly 200. It may be noted that for a slit of same width, the corresponding diffraction angle approaches 900. When the critical dimension of the cylinder and the slit decreases from λ to 5λ, the difference in the corresponding diffraction angles reduce from nearly 700 to nearly 1.50. - The investigation also highlights that in the micro-cylinder diffraction for the said range of interest, the absolute intensity at the zero-order interference- maximum provides a new signature for the distance of separation between the diffraction minima. The consequence of this new finding is a considerable simplification in the apparatus and algorithm for diameter inversion from a diffraction experiment. The function of an array detector can be replaced by a point detector at a fixed point for all the diameters in the range of interest. - The two formulations proposed from the geometrical theory are suited for diffraction- minima search based algorithm, while those from customary Fraunhofer theory are well suited for intensity minima search based method for diameter inversion.

A novel optical diffraction based technique is proposed and demonstrated to measure deflections of the order of ~1nm in microcantilevers (MC) designed for sensing ultra-small forces of stress. The proposed method employs a double MC structure where one of the cantilevers acts as the active sensor beam, while the other as a reference. The active beam can respond to any minute change of stress, for example, molecular recognition induced surface stress, through bending (~1nm) relative to the other fixed beam. Optical diffraction patterns obtained from this double slit aperture mask with varying slit width, which is for the bending of MC due to loading, carries the deflection profile of the active beam. A significant part of the present work explores the possibility of connecting diffraction minima (or maxima) to the bending profile of the MC structure and thus the possibility to measure induced surface stress. To start with, it is also the aim to develop double MC sensors using PHDDA (Poly – Hexane diol diacrylate) because this material has the potential to achieve high mechanical deformation sensitivity in even moderately scaled down structures by virtue of its very low Young’s modulus. Moreover, the high thermal stability of PHDDA also ensures low thermally induced noise floors in microcantilever sensors. To demonstrate the proposed optical diffraction-based profiling technique, a bent microcantilever structure is designed and fabricated by an in-house developed Microstereolithography (MSL) system where, essentially one of the microcantilevers is fabricated with a bent profile by varying the gap between the two structures at each cured 2D patterned layer. The diffraction pattern obtained on transilluminating the fabricated structure by a spherical wavefront is analyzed and the possibility of obtaining the deflections at each cross section is ascertained. Since the proposed profiling technique relies on the accurate detection and measurement of shifts of intensity minima on the image plane, analysis of the minimum detectable shift in intensity minima for the employed optical interrogation setup with respect to the minimum detectable contrast and SNR of the optical measurement system is carried out, in order to justify the applicability of the proposed minima intensity shift measurement technique. The proposed novel diffraction based profiling technique can provide vital clue on the origins of surface stress at the atomic and molecular level by virtue of the entire bent profile due to adsorption induced bending thereby establishing microcantilever sensor technology as a more reliable and competitive approach for sensing ultra-low concentrations of biological and chemical agents.

La lithographie par double impression est une solution potentielle proposée pour l'impression des circuits des nœuds technologiques avancés (22nm et au-delà) en attendant que la lithographie Extrême Ultraviolet soit prête pour la production en masse. La technique de double impression est basée sur la décomposition en deux masques d'exposition des motifs d'un niveau donné du circuit intégré. Deux motifs voisins ayant un pas inférieur au pas minimal résolu en un procédé lithographique sont affiliés simultanément à deux masques différents. Les motifs ayant des pas supérieurs au pas critique, motifs non critiques, sont mis sur un masque ou sur un autre dans le but de générer une densité de motifs équivalente entre les deux masques d'exposition. Dans cette thèse, nous avons développé une nouvelle méthode de décomposition dite « décomposition optique ». Cette dernière est basée sur l'analyse de l'interaction des ordres de diffraction dans le plan de la pupille du système optique de projection. La décomposition optique permet d'améliorer l'affiliation des motifs non critiques à l'un des deux masques dans le but d'améliorer le contraste des deux masques lors de la double impression. Afin de valider cette nouvelle méthode de décomposition, nous l'avons appliqué au niveau contacts d'un circuit de logique du nœud 22nm. / As the lithography EUV is not yet ready to be used for semi-conductor business needs, the double patterning lithography is a promising solution to print sub 22nm node features. The principle of the double patterning is the pitch splitting also named as the coloring of a given circuit layer's features. Two adjacent features must be assigned opposite masks or opposite colors corresponding to different exposures, if their pitch is less than the minimum resolvable pitch. However, features with pitches larger than the critical one are not critical and could be assigned to one of the two masks for density balance. In this thesis, we developed a new split called “optical split” based on the diffractive orders analysis in the pupil plane. The optical split optimizes the non critical contacts affiliation to one of the two exposure masks. The goal of the optical split is to enhance the lithographic performances of the generated masks in order to improve the double patterning process printing. In order to validate the optical split, we apply it on contact layer of the 22nm node logic.

In my essay I show Fourier transform theory and applications in context with difraction theory especially Fraunhofer difraction. In part of the experiment, I set up an optical signal processing system. I take the Fourier transform of an input signal using a lens, filter the transform by placing various filters at the Fourier plane, and take the inverse transform. A simple optical bench consists of a laser, to produce a parallel, monochromatic beam which illuminates a specific area of the micrograph. Lens to focus the Fraunhofer diffraction pattern in the back focal plane of the lens. Mask transit contrived light or block out most of the noise in the diffraction pattern arising from image features. A reconstruction lens, placed behind the mask, refocuses the unobstructed rays and forms a filtered image. Optical diffraction provides useful information about the geometrical arrangement of subunits in the specimen. I make experiments for attestation on elementary objects and real images in mathematic program Matlab. From knowledge Fraunhofer difraction and organization of experiment I calculated size of circular object. I show practical using of Fraunhofer difraction and optical filtration. My essay give good introduction to the theory and techniques of optical filtration.

The primary goal of this work is to arrive at direction tomography (DT) algorithms freed from the severe linearization in the formulation, and as-assumptions on variation of the refractive index distribution (RID), involved in the earlier approaches based on Born and Royton approximations and the Fourier di reaction theorem (FDT). To start with, a direct single-step re-covery of RID from intensity measurements is demonstrated, replacing the common two-step procedure involving, rest the recovery of phase from in-density followed by the inversion of scattered led for the RID. The information loss, unavoidable in a two-step procedure is thus successfully addressed. Secondly, an iterative method which works with a forward model obtained directly from the Helmholtz equation is developed. This forward model, though has simplifying assumptions, is more general and can accommodate larger variations in RID than that allowed in the previous linear models. The iterative procedure has an update step which uses a linearization of the forward model and a re-linearization step at the updated RID. The procedure which directly employs the measured intensities is used as part of a deterministic Gauss-Newton algorithm and a stochastic optimization algorithm which uses the ensemble Kalman lter to arrive at the recursive update. The stochastic method is found to be more noise-tolerant and efficient to take care of process model inaccuracies. The proof is seen in better reconstructions from experimental data for two example objects, namely, a graded-index optical bre and a photonic-crystal bre. It is further ob-served that the reconstructions from photonic crystal bre are blurred, noisy and less accurate. Identifying the inaccurate implementation of the modemed Helmholtz equation for large k values employing the current sampling rate as the shortcoming, a new procedure, which splits the bandwidth into smaller components using short-time Fourier Transform is developed. The set of equations arrived at, each t for a narrow frequency band, is solved and the solutions are reassembled to obtain the scattered led for the original problem. The simulated di rated intensities so obtained are better matched to their measured experimental counterparts. However, the impel-mentation of the mode end procedure is computation-intensive, for which a parallel-processing machine can be a good solution. The recovery of RID with this mode cation is not attempted in this work and is left for future implementation.

[ES] La tomografía por difracción surge para mejorar las técnicas de imagen al considerar la naturaleza ondulatoria de la luz. Mientras que los primeros sistemas de imagen médica se basaban únicamente en fuentes sin difracción, este enfoque consigue mejorar la reconstrucción del índice de refracción de los objetos, lo que permite, por ejemplo, el estudio de estructuras subcelulares. Del mismo modo, la demanda de redes de telecomunicaciones cada vez más rápidas y seguras ha propiciado la aparición de la fotónica. Hace dos décadas, la combinación de estos dos campos dio lugar a los primeros sistemas de tomografía por difracción óptica (ODT), los cuáles han evolucionado rápidamente durante este siglo. En esta tesis, presentamos dos nuevas aplicaciones de la ODT. La primera está relacionada con el concepto del microscopio tomográfico de fase (TPM), una versión de la ODT que permite el estudio de células aisladas, con muchas aplicaciones biomédicas, como el diagnóstico y la prognosis del cáncer. Sin embargo, los sistemas TPM actuales son caros, pesados y complejos. Para resolver estos problemas, proponemos el concepto de TPM en chip. Con este fin, diseñamos una hoja de ruta hacia el primer dispositivo tomográfico integrado en el marco de la tecnología lab-on-a-chip (LoC), y desarrollamos los primeros pasos para ello: 1) Hasta ahora, sólo se han utilizado detectores planos para obtener los mapas de índice de refracción de los objetos estudiados en TPM, basados en la detección del campo difractado hacia delante. Sin embargo, los principios físicos fundamentales indican que medir también el campo difractado hacia detrás debería mejorar la resolución de las imágenes. Además, un detector plano no es la configuración óptima para el TPM en chip. En esta línea, hemos explorado la posibilidad de usar detectores circulares en este escenario, como una técnica más adecuada para las configuraciones en chip, demostrando al mismo tiempo que este enfoque proporciona una mejor resolución que el lineal. 2) Proponemos un esquema de TPM en chip basado en el uso de nanoantenas dieléctricas como fuente de luz y píxeles detectores ODT, y caracterizamos experimentalmente su comportamiento mediante microscopía óptica de campo cercano. En cuanto a la segunda aplicación, estudiamos el potencial de la ODT como nuevo paradigma en la detección de capas de invisibilidad realistas, una de las aplicaciones más importantes de los metamateriales. Hasta ahora, el scattering cross section (SCS) se ha utilizado como modelo de referencia para diseñar y observar la eficacia de estos dispositivos para ocultar objetos. En nuestro estudio, demostramos que la ODT puede detectar las capas de invisibilidad prácticas con una sensibilidad superior a la que ofrece el SCS, incluso a las frecuencias de trabajo óptimas. Además, es posible obtener una imagen representativa del tamaño y la forma de la capa, revelando claramente su existencia. Finalmente, se discuten las conclusiones extraídas de los resultados obtenidos. Además, se detallan las futuras líneas de trabajo para abordar los retos que no se han completado en esta tesis doctoral. / [CA] La tomografia per difracció sorgeix per millorar les tècniques d'imatge anteriors en considerar la naturalesa ondulatòria de la llum. Mentre que els primers sistemes d'imatge mèdica es basaven únicament en fonts sense difracció, aquest enfocament aconsegueix millorar la reconstrucció de l'índex de refracció dels objectes, la qual cosa permet, per exemple, l'estudi d'estructures subcelulars. De la mateixa manera, la demanda de xarxes de telecomunicacions cada vegada més ràpides i segures ha propiciat l'aparició de la fotònica. Fa dues dècades, la combinació d'aquests dos camps va portar als primers sistemes de tomografia per difracció òptica (ODT), els quals han evolucionat ràpidament durant aquest segle. En aquesta tesi, presentem dues noves aplicacions de la ODT. La primera està relacionada amb el concepte del microscopi tomogràfic de fase (TPM), una versió de la ODT que permet l'estudi de cèl·lules aïllades, amb moltes aplicacions en biomedicina, com el diagnòstic i prognosi del càncer. No obstant això, els sistemes TPM actuals són cars, pesats i complexos. Per resoldre aquests problemes, proposem el concepte de TPM en xip. Per fer-ho, dissenyem un full de ruta cap al primer dispositiu tomogràfic integrat en el marc de la tecnologia lab-on-a-chip (LoC), i desenvolupem els primers passos a aquest efecte: 1) Fins ara, només s'han utilitzat detectors plans per a obtindre els mapes d'índex de refracció dels objectes estudiats en TPM, basats en la detecció del camp difractat cap avant. No obstant això, els principis físics fonamentals indiquen que mesurar també el camp difractat cap endarrere hauria de millorar la resolució de les imatges. A més, un detector pla no és la configuració òptima per al TPM en xip. En aquesta línia, hem explorat la possibilitat d'usar detectors circulars en aquest escenari, com una tècnica més adequada per a les configuracions en xip, demostrant al mateix temps que aquest enfocament proporciona una millor resolució que el lineal. 2) Proposem un esquema de TPM en xip basat en l'ús de nanoantenes dielèctriques com a font de llum i píxels detectors ODT, i caracteritzem experimentalment el seu comportament en camp pròxim mitjançant microscòpia òptica de camp pròxim. Pel que fa a la segona aplicació, estudiem el potencial de la ODT com a nou paradigma en la detecció de capes d'invisibilitat realistes, una de les aplicacions més importants dels metamaterials. Fins ara, el scattering cross section (SCS) s'ha utilitzat com a model de referència per a dissenyar i observar l'eficàcia d'aquests dispositius per a ocultar objectes. En el nostre estudi, vam demostrar que la ODT pot detectar les capes d'invisibilitat pràctiques amb una sensibilitat superior a la que ofereix el SCS, fins i tot a les freqüències de treball òptimes. A més, és possible obtindre una imatge representativa de la grandària i la forma de la capa, revelant clarament la seua existència. Finalment, es discuteixen les conclusions extretes dels resultats obtinguts i es detallen les futures línies de treball per a abordar els reptes que no s'han completat en aquesta tesi doctoral. / [EN] Diffraction Tomography arises to improve previous imaging techniques by considering the wave nature of light. Whereas the first medical imaging systems relied only on non-diffracting sources, this approach results in an enhanced reconstruction of the object's refractive index distribution, allowing, for example, the study of subcellular structures. Likewise, the demand for increasingly faster and secure telecommunication networks led to the advent of photonics. Two decades ago, the combination of these two fields gave rise to the first optical diffraction tomography (ODT) systems, which have rapidly evolved during this century. In this thesis, we present two novel applications of ODT. The first one is related to the concept of tomographic phase microscopy (TPM), a version of ODT that enables the study of isolated cells, with many applications in biomedicine, such as the diagnosis and prognosis of cancer. Nevertheless, current TPM systems are expensive, heavy, and cumbersome. To solve these issues we propose the concept of on-chip TPM. For this purpose, we design a roadmap towards the first integrated tomographic device in the frame of lab-on-a-chip (LoC) technology and develop the first steps to this end: 1) Until now, only flat detectors have been used to obtain the refractive index maps of the objects studied in TPM, based on the detection of the forward scattering. However, fundamental physical principles indicate that measuring also the backscattered field should improve the resolution of the images. Moreover, a flat detector is not the optimal configuration for on-chip TPM. In this vein, we have explored the possibility of using circular detectors in this scenario as a more suitable technique for on-chip configurations, demonstrating at the same time that this approach provides a better resolution than the linear one. 2) We propose a TPM on-chip scheme based on the use of dielectric nanoantennas as the ODT light source and detector pixels, and experimentally characterize their near-field behavior via scanning near-field optical microscopy. As for the second application, we study the potential of ODT as a new paradigm in the detection of realistic invisibility cloaks, one of the most important applications of metamaterials. Up to now, the scattering cross section (SCS) has been used as the gold standard to design and observe the effectiveness of these devices in hiding objects. In our study, we show that ODT can detect practical invisibility cloaks with a higher sensitivity than that offered by the SCS, even at the optimal working frequencies. Moreover, it is possible to obtain an image depicting the size and shape of the cloak, clearly revealing their existence. Finally, the conclusions drawn from the obtained results are discussed. In addition, future lines of action to address the challenges that have not been completed in this doctoral thesis are detailed. / Díaz Fernández, FJ. (2021). Novel Applications of Optical Diffraction Tomography: On-chip Microscopy and Detection of Invisibility Cloaks [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/180125