Short-distance digital communication links, between chips on a circuit board, or between different circuit boards for example, have traditionally been built by using electrical interconnects -- metallic tracks and wires. Recent technological advances have resulted in improvements in the speed of information processing, but have left electrical interconnects intact, thus creating a serious communication problem. Free-space optical interconnects, made up of arrays of vertical-cavity surface-emitting lasers, microlenses, and photodetectors, could be used to solve this problem. If free-space optical interconnects are to successfully replace electrical interconnects, they have to be able to support large rates of information transfer with high channel densities. The biggest obstacle in the way of reaching these requirements is laser beam diffraction. There are three approaches commonly used to model the effects of laser beam diffraction in optical interconnects: one could pursue the path of solving the diffraction integral directly, one could apply stronger approximations with some loss of accuracy of the results, or one could cleverly reinterpret the diffraction problem altogether. None of the representatives of the three categories of existing solutions qualified for our purposes. The main contribution of this dissertation consist of, first, formulating the mode expansion method, and, second, showing that it outperforms all other methods previously used for modelling diffraction in optical interconnects. The mode expansion method allows us to obtain the optical field produced by the diffraction of arbitrary laser beams at empty apertures, phase-shifting optical elements, or any combinations thereof, regardless of the size, shape, position, or any other parameters either of the incident optical field or the observation plane. The mode expansion method enables us to perform all this without any reference or use of the traditional Huygens-Kirchhoff-Fresnel diffraction integrals. When using the mode expansion method, one replaces the incident optical field and the diffracting optical element by an effective beam, possibly containing higher-order transverse modes, so that the ultimate effects of diffraction are equivalently expressed through the complex-valued modal weights. By using the mode expansion method, one represents both the incident and the resultant optical fields in terms of an orthogonal set of functions, and finds the unknown parameters from the condition that the two fields have to be matched at each surface on their propagation paths. Even though essentially a numerical process, the mode expansion method can produce very accurate effective representations of the diffraction fields quickly and efficiently, usually by using no more than about a dozen expanding modes. The second tier of contributions contained in this dissertation is on the subject of the analysis and design of microchannel free-space optical interconnects. In addition to the proper characterisation of the design model, we have formulated several optical interconnect performance parameters, most notably the signal-to-noise ratio, optical carrier-to-noise ratio, and the space-bandwidth product, in a thorough and insightful way that has not been published previously. The proper calculation of those performance parameters, made possible by the mode expansion method, was then performed by using experimentally-measured fields of the incident vertical-cavity surface-emitting laser beams. After illustrating the importance of the proper way of modelling diffraction in optical interconnects, we have shown how to improve the optical interconnect performance by changing either the interconnect optical design, or by careful selection of the design parameter values. We have also suggested a change from the usual `square' to a novel `hexagonal' packing of the optical interconnect channels, in order to alleviate the negative diffraction effects. Finally, the optical interconnect tolerance to lateral misalignment, in the presence of multimodal incident laser beams was studied for the first time, and it was shown to be acceptable only as long as most of the incident optical power is emitted in the fundamental Gaussian mode.

Localização e Mapeamento Simultâneos (SLAM), fundamental para robôs dotados de verdadeira autonomia, é um dos problemas mais difíceis na Robótica e consiste em estimar a posição de um robô que está se movendo em um ambiente desconhecido, enquanto incrementalmente constrói-se o mapa de tal ambiente. Provavelmente o requisito mais importante para localização e mapeamento adequados seja um preciso reconhecimento de local, isto é, determinar se um robô estava no mesmo lugar em diferentes ocasiões apenas analizando as observações feitas pelo robô em cada ocasião. A maioria das abordagens da literatura são boas quando se utilizam sensores altamente expressivos, como câmeras, ou quando o robô está situado em ambientes com pouco ambiguidade. No entanto, este não é o caso, por exemplo, quando o robô equipado apenas com sensores de alcance está em ambientes internos estruturados altamente ambíguos. Uma boa estratégia deve ser capaz de lidar com tais ambientes, lidar com ruídos e erros nas observações e, especialmente, ser capaz de modelar o ambiente e estimar o estado do robô de forma eficiente. Nossa proposta consiste em traduzir sequências de medições de laser em uma representação de texto eficiente e compacta, para então lidar com o problema de reconhecimento de local usando técnicas de processamento lingüísticos. Nós traduzimos as medições dos sensores em valores simples computados através de um novo modelo de observação baseado em estimativas de densidade de kernel chamado de Densidade de Espaço Livre (FSD). Estes valores são quantificados permitindo a divisão do ambiente em regiões contíguas de densidade homogênea, como corredores e cantos. Regiões são representadas de forma compacta por simples palavras descrevendo o valor de densidade espacial, o tamanho e a variação da orientação daquela região. No final, as cadeias de palavras compõem um texto, no qual se buscam casamentos de n-gramas (isto é, sequências de palavras). Nossa técnica também é aplicada com sucesso em alguns cenários de operação de longo-prazo, onde devemos lidar com objetos semi-estáticos (i.e. que se movem ocasionalmente, como portas e mobílias). Todas as abordagens foram avaliadas em cenários simulados e reais obtendo-se bons resultados. / Simultaneous Localization and Mapping (SLAM), fundamental for building robots with true autonomy, is one of the most difficult problems in Robotics and consists of estimating the position of a robot that is moving in an unknown environment while incrementally building the map of such environment. Arguably the most crucial requirement to obtain proper localization and mapping is precise place recognition, that is, determining if the robot is at the same place in different occasions just by looking at the observations taken by the robot. Most approaches in literature are good when using highly expressive sensors such as cameras or when the robot is situated in low ambiguous environments. However this is not the case, for instance, using robots equipped only with range-finder sensors in highly ambiguous indoor structured environments. A good SLAM strategy must be able to handle these scenarios, deal with noise and observation errors, and, especially, model the environment and estimate the robot state in an efficient way. Our proposal in this work is to translate sequences of raw laser measurements into an efficient and compact text representation and deal with the place recognition problem using linguistic processing techniques. First, we translate raw sensor measurements into simple observation values computed through a novel observation model based on kernel-density estimation called Free-Space Density (FSD). These values are quantized into significant classes allowing the division of the environment into contiguous regions of homogeneous spatial density, such as corridors and corners. Regions are represented in a compact form by simple words composed of three syllables – the value of spatial density, the size and the variation of orientation of that region. At the end, the chains of words associated to all observations made by the robot compose a text, in which we search for matches of n-grams (i.e. sequences of words), which is a popular technique from shallow linguistic processing. The technique is also successfully applied in some scenarios of long-term operation, where we must deal with semi-static objects (i.e. that can move occasionally, such as doors and furniture). All approaches were evaluated in simulated and real scenarios obtaining good results.

This thesis describes work on the theoretical modelling and experimental measurement of the complex permittivity of dielectrics. The main focus of research has been into the characterisation of permittivity of planar and layered samples within the millimetre wave band. The measurement method is based on the free-space measurement of the transmission and reflection coefficients of samples. A novel analytical method of determining the transmission and reflection coefficients as functions of frequency arising from a generalised structure of planar dielectric layers is also described and validated. The analytical method is based on signal flow techniques. The measurement and analytical techniques have been applied in two main areas: firstly, the acquisition of new data on human skin in the band 57 to 100GHz and secondly, the detection and location of defects in composite materials for which a band of 90 to 100GHz was used. Measurements have been made on the complex permittivity of a single sample of excised human skin fixed in formaldehyde. The experimental results have been corrected to account for the fixing process in formaldehyde and are projected to body temperature. This data is, to the best of the author’s knowledge, the first of its kind to be published. Predicted skin permittivity based on various relaxation models varies widely and only partially fits the measured data. The experimental results have been used to determine the parameters of a Cole-Cole function which gives the best fit to the measured data. The measured skin data has also been used to calculate power deposition in skin exposed to millimetre wave radiation. This work concludes that a skin surface temperature rise of only 0.20C results from a thirty second exposure to signals of 100W/m2. Experimental work with fibreglass composite samples has shown that defects such as delaminations, voids, matrix cracks and improper cure result in resolvable differences in the dielectric properties of the samples at 90 – 100GHz. The measurement technique is particularly sensitive to the detection of cracks and its spatial resolution is 20mm or better. Whilst confirming the general conclusions of previously published work, the specific findings of this study are novel.

Localização e Mapeamento Simultâneos (SLAM), fundamental para robôs dotados de verdadeira autonomia, é um dos problemas mais difíceis na Robótica e consiste em estimar a posição de um robô que está se movendo em um ambiente desconhecido, enquanto incrementalmente constrói-se o mapa de tal ambiente. Provavelmente o requisito mais importante para localização e mapeamento adequados seja um preciso reconhecimento de local, isto é, determinar se um robô estava no mesmo lugar em diferentes ocasiões apenas analizando as observações feitas pelo robô em cada ocasião. A maioria das abordagens da literatura são boas quando se utilizam sensores altamente expressivos, como câmeras, ou quando o robô está situado em ambientes com pouco ambiguidade. No entanto, este não é o caso, por exemplo, quando o robô equipado apenas com sensores de alcance está em ambientes internos estruturados altamente ambíguos. Uma boa estratégia deve ser capaz de lidar com tais ambientes, lidar com ruídos e erros nas observações e, especialmente, ser capaz de modelar o ambiente e estimar o estado do robô de forma eficiente. Nossa proposta consiste em traduzir sequências de medições de laser em uma representação de texto eficiente e compacta, para então lidar com o problema de reconhecimento de local usando técnicas de processamento lingüísticos. Nós traduzimos as medições dos sensores em valores simples computados através de um novo modelo de observação baseado em estimativas de densidade de kernel chamado de Densidade de Espaço Livre (FSD). Estes valores são quantificados permitindo a divisão do ambiente em regiões contíguas de densidade homogênea, como corredores e cantos. Regiões são representadas de forma compacta por simples palavras descrevendo o valor de densidade espacial, o tamanho e a variação da orientação daquela região. No final, as cadeias de palavras compõem um texto, no qual se buscam casamentos de n-gramas (isto é, sequências de palavras). Nossa técnica também é aplicada com sucesso em alguns cenários de operação de longo-prazo, onde devemos lidar com objetos semi-estáticos (i.e. que se movem ocasionalmente, como portas e mobílias). Todas as abordagens foram avaliadas em cenários simulados e reais obtendo-se bons resultados. / Simultaneous Localization and Mapping (SLAM), fundamental for building robots with true autonomy, is one of the most difficult problems in Robotics and consists of estimating the position of a robot that is moving in an unknown environment while incrementally building the map of such environment. Arguably the most crucial requirement to obtain proper localization and mapping is precise place recognition, that is, determining if the robot is at the same place in different occasions just by looking at the observations taken by the robot. Most approaches in literature are good when using highly expressive sensors such as cameras or when the robot is situated in low ambiguous environments. However this is not the case, for instance, using robots equipped only with range-finder sensors in highly ambiguous indoor structured environments. A good SLAM strategy must be able to handle these scenarios, deal with noise and observation errors, and, especially, model the environment and estimate the robot state in an efficient way. Our proposal in this work is to translate sequences of raw laser measurements into an efficient and compact text representation and deal with the place recognition problem using linguistic processing techniques. First, we translate raw sensor measurements into simple observation values computed through a novel observation model based on kernel-density estimation called Free-Space Density (FSD). These values are quantized into significant classes allowing the division of the environment into contiguous regions of homogeneous spatial density, such as corridors and corners. Regions are represented in a compact form by simple words composed of three syllables – the value of spatial density, the size and the variation of orientation of that region. At the end, the chains of words associated to all observations made by the robot compose a text, in which we search for matches of n-grams (i.e. sequences of words), which is a popular technique from shallow linguistic processing. The technique is also successfully applied in some scenarios of long-term operation, where we must deal with semi-static objects (i.e. that can move occasionally, such as doors and furniture). All approaches were evaluated in simulated and real scenarios obtaining good results.

Neste trabalho analisamos o movimento de carga espacial monopolar livre em dielétricos, procurando fornecer subsídios para a interpretação de resultados experimentais. São mostradas as soluções para diversos tipos de distribuições iniciais de carga. A partir daí são encontradas relações que nos levam a algumas conclusões a respeito da relação entre distribuição e corrente externa produzida. São propostos métodos para a determinação da mobilidade dos portadores de carga no dielétrico e da concavidade de uma distribuição desconhecida. Analisamos também as condições para o aparecimento de inversão de corrente / On this work, we study the monopolar space charge motion in dielectrics in the aim of providing general information about it to the experimentalist. The electric current is obtained for many initial charge distributions and some relations are derived linking the behavior of the current to the initial charge distribution. We propose methods for obtaining the mobility of the carriers from experimental results. Finally the conditions for observation of current reversals are analyzed

Este trabalho versa sobre a verticalização em São Paulo e seus impactos sobre a qualidade ambiental dos espaços livres. Parte-se do pressuposto de que a não compreensão, por parte do corpo técnico e da população em geral, dos problemas resultantes da verticalização (tais como: sombreamentos, canalização de ventos, alteração da umidade do ar, maior aquecimento e agravamento da poluição) piora a qualidade ambiental dos espaços livres. No corpo do trabalho são introduzidos os procedimentos básicos para o aprimoramento da qualidade ambiental, que devem ser conhecidos e aplicados normalmente no projeto dos espaços livres. Os espaços livres públicos, como as vias, praças e parques, assim como os espaços privados, que são os espaços livres existentes nos lotes, em torno das edificações; têm perdido sua habitabilidade em conseqüência da verticalização e do adensamento urbano, mesmo com a aplicação da atual legislação de uso e ocupação do solo. Implantada em 1972, ela gera espaços livres mais generosos do que anteriormente, com a obrigatoriedade de novos recuos e menores taxas de ocupação. Esta legislação ao determinar espaços livres um pouco maiores, cria condições para que os incorporadores agreguem, aos seus empreendimentos, equipamentos para o lazer, mesmo que essas áreas sejam ambientalmente inadequadas. A qualidade ambiental resultante é analisada sob o aspecto perceptivo-sensorial, considerando-se a influência que o Meio Urbano Verticalizado (malha viária, espaços livres, quadras, lotes e edificações) tem sobre as variáveis ambientais do Meio Natural (radiação solar, ar, água, solo, vegetação e fauna). As variáveis ambientais são analisadas em cinco regiões com bairros densamente verticalizados: a) Centro: Higienópolis; b) Norte: Freguesia do Ó; c) Sul: Moema; d) Leste: Vila Gomes Cardim; e) Oeste: Perdizes. Como resultado, são apresentadas recomendações, implementáveis no processo de projeto, para melhorar a qualidade ambiental nos espaços livres urbanos de áreas verticalizadas. / This thesis turns on the verticalization in São Paulo and its impacts on the environmental quality of free spaces. It breaks of the presupposition that the nonunderstanding, on the part of the technical body and of the population in general, of the resulting problems of the verticalization (such as shadows, canalization of winds, alteration of the humidity of the air, larger heating and worsening of the pollution) worsens the environmental quality of free spaces. In the body of the work the basic procedures are introduced to increase the environmental quality that should be known and usually applied in the project of such spaces. The public free spaces, as roads, squares and parks; as well as the private spaces, that are the existent free spaces in the lots, around the constructions; they have been losing its inhabitability in consequence of the verticalization and the increase of the urban areas, even with the application of the current legislation on use and occupation of the soil. Implanted in 1972, it generates more generous free spaces than previously, with the obligation of new recoils and smaller occupation rates. This legislation when establishing free spaces a little larger, it creates conditions so that the incorporators joins, to its enterprises, equipments for leisure, even if those areas are functionally inadequate for such, even if they never receive sun light or that make funnel-shaped and accelerate the winds. The resulting environmental quality is analyzed under the perceptive-sensorial aspect, considering the influence that the Verticalized Urban Way (its street ensemble, free spaces, blocks, lots and constructions) has on the environmental variables of the Natural Way (solar radiation, air, water, soil, vegetation and fauna). The analysis are applied to five areas with neighborhoods densely verticalized: a) Center: Higienópolis; b) North: Freguesia do Ó; c) South: Moema; d) East: Vila Gomes Cardim; e) West: Perdizes. As result, recommendations presented, to be used in the project process, to improve the environmental quality in the urban free spaces of verticalized areas.

O teste de raios X é um teste rápido, simples, não destrutivo e de alta precisão, que possibilita examinar com detalhes, a morfologia interna da semente, identificar áreas danificadas, sua localização e tipos de danos. Uma das abordagens atuais da pesquisa sobre análise de imagens de sementes radiografadas é verificar até que ponto a relação entre o grau de desenvolvimento embrionário e o espaço disponível na cavidade interna da semente está associada ao desempenho da semente. Na literatura há diversos trabalhos com resultados promissores para diferentes espécies; porém, para sementes de citros são escassas estas informações. Neste sentido, os objetivos desta pesquisa foram: a) avaliar a eficiência do teste de raios X em relacionar a morfologia interna das sementes com a germinação das sementes de citrumelo \'Swingle\'; b) verificar a possibilidade de utilização do teste de raios X para avaliar a poliembrionia das sementes de citrumelo \'Swingle\'; c) verificar se há relação do espaço livre na cavidade interna com o desempenho das sementes de citrumelo \'Swingle\'. Foram utilizados sete lotes de sementes tratadas de citrumelo \'Swingle\'. A pesquisa foi dividida em três experimentos: experimento I - avaliação da morfologia interna das sementes de por meio de raios X; experimento II - avaliação da poliembrionia das sementes por meio do teste de raios X; experimento III - avaliação do potencial fisiológico das sementes por meio dos testes tradicionais de vigor e avaliação do espaço livre da cavidade interna das sementes por meio do software ImageJ. O primeiro e o segundo experimento foram conduzidos em uma época de avaliação, porém, o terceiro experimento foi conduzido em duas épocas, espaçada em oito meses de armazenamento (0 e 8 meses), durante esse período as sementes foram armazenadas em câmara fria com a temperatura de 5°C e umidade relativa do ar de 75 %. O teste de raios X foi realizado nos três experimentos e relacionado com a germinação, porém no experimento II foi relacionado também com o metódo direto (contagem dos embriões) e no experimento III as imagens radiográficas foram analisadas por meio do software ImageJ para determinar o espaço livre das sementes. Para determinar o potencial fisiológico, os lotes de sementes foram submetidos a testes de germinação e de vigor (primeira contagem de germinação, velocidade de germinação, tempo médio de germinação, emergência de plântulas em areia, comprimento e massa de matéria seca da parte aérea e raiz de plântulas), foi avaliado também número médio de plântulas por sementes e a taxa de poliembrionia de cada lote. Verificou-se que a análise de imagens de raios X permite indentificar danos internos na semente com efeitos negativos na germinação; é um método eficiente para avaliar a poliembrionia das sementes; e a alta porcentagem de sementes com espaço livre interno superior a 22,1% prejudica o potencial germinativo de sementes de citrumelo \'Swingle\'. / X-ray test is a fast, simple, non-destructive, high-precision test that allows you to examine in detail the internal morphology of the seed, identify damaged areas, their location and types of damage. One of the current approaches to X-ray seed imaging research is to ascertain the extent to which the relationship between the degree of embryonic development and the available space in the internal cavity of the seeds is associated with seed performance. In the literature there are several works with promising results for different species; however, this information is scarce for citrus seeds. In this sense, the objectives of this research were: a) to evaluate the efficiency of the X-ray test in relation to the internal morphology of the seeds with the germination of \'Swingle\' citrumelo seeds; b) to verify the possibility of using the X-ray test to evaluate the polyembryony of the \'Swingle\' citrumelo seeds; c) to verify if there is a relation of free space in the internal cavity with the performance of \'Swingle\' citrumelo seeds. Seven lots of treated \'Swingle\' citrumelo seeds were used, the research was divided into three experiments: experiment I - evaluation of the internal morphology of seeds by X-ray; experiment II - evaluation of seed polyembryony by X-ray test; experiment III - evaluation of the physiological potential of the seeds by traditional tests of vigor and evaluation of the free space of the internal cavity of the seeds by of ImageJ software. The first and second experiments were conducted at a time of evaluation, but the third experiment was conducted in two seasons, spaced in eight months of storage (0 and 8 months), during which time the seeds were stored cold chamber with temperature of 5 °C and relative humidity of 75 %. The X-ray test was performed in the three experiments and related to germination, but in experiment II it was also related to the direct method (counting of the embryos) and in experiment III the radiographic images were analyzed by of the ImageJ software to determine the space of the seeds. In order to determine the physiological potential, seed lots were submitted to germination and vigor tests (first germination count, speed of germination, mean time germination, emergence of seedlings in sand, length and dry mass of aerial part and root of seedlings), we also evaluated the average number of seedlings per seed and the polyembryony rate of each lot. It was verified that X-ray image analysis allows identification of internal damage in the seed with negative effects on germination; is an efficient method to evaluate the polyembryony of the seeds; and the high percentage of seeds with internal free space greater than 22.1% impairs the germination potential of \'Swingle\' citrumelo seeds.

This thesis describes work on the theoretical modelling and experimental measurement of the complex permittivity of dielectrics. The main focus of research has been into the characterisation of permittivity of planar and layered samples within the millimetre wave band. The measurement method is based on the free-space measurement of the transmission and reflection coefficients of samples. A novel analytical method of determining the transmission and reflection coefficients as functions of frequency arising from a generalised structure of planar dielectric layers is also described and validated. The analytical method is based on signal flow techniques. The measurement and analytical techniques have been applied in two main areas: firstly, the acquisition of new data on human skin in the band 57 to 100GHz and secondly, the detection and location of defects in composite materials for which a band of 90 to 100GHz was used. Measurements have been made on the complex permittivity of a single sample of excised human skin fixed in formaldehyde. The experimental results have been corrected to account for the fixing process in formaldehyde and are projected to body temperature. This data is, to the best of the author’s knowledge, the first of its kind to be published. Predicted skin permittivity based on various relaxation models varies widely and only partially fits the measured data. The experimental results have been used to determine the parameters of a Cole-Cole function which gives the best fit to the measured data. The measured skin data has also been used to calculate power deposition in skin exposed to millimetre wave radiation. This work concludes that a skin surface temperature rise of only 0.20C results from a thirty second exposure to signals of 100W/m2. Experimental work with fibreglass composite samples has shown that defects such as delaminations, voids, matrix cracks and improper cure result in resolvable differences in the dielectric properties of the samples at 90 – 100GHz. The measurement technique is particularly sensitive to the detection of cracks and its spatial resolution is 20mm or better. Whilst confirming the general conclusions of previously published work, the specific findings of this study are novel.

We experimentally demonstrate an eight-state continuous-variable quantum key distribution (CV-QKD) over atmospheric turbulence channels. The high secret key rate (SKR) is enabled by 4-D multiplexing of 96 channels, i.e., six-channel wavelength-division multiplexing, four-channel orbital angular momentum multiplexing, two-channel polarization multiplexing, and two-channel spatial-position multiplexing. The atmospheric turbulence channel is emulated by a spatial light modulator on which a series of azimuthal phase patterns yielding Andrews' spectrum are recorded. A commercial coherent receiver is implemented at Bob's side, followed by a phase noise cancellation stage, where channel transmittance can be monitored accurately and phase noise can be effectively eliminated. Compared to four-state CV-QKD, eight-state CV-QKD protocol potentially provides a better performance by offering higher SKR, better excess noise tolerance, and longer secure transmission distance. In our proposed CV-QKD system, the minimum transmittances of 0.24 and 0.26 are required for OAM states of 2 (or -2) and 6 (or -6), respectively, to guarantee the secure transmission. A maximum SKR of 3.744 Gb/s is experimentally achievable, while a total SKR of 960 Mb/s can be obtained in case of mean channel transmittances.

When using quantum key distribution (QKD), one of the trade-offs for security is that the generation rate of a secret key is typically very low. Recent works have shown that using a weak coherent source allows for higher secret key generation rates compared to an entangled photon source, when a channel with low loss is considered. In most cases, the system that is being studied is over a fiber-optic communication channel. Here a theoretical QKD system using the BB92 protocol and entangled photons over a free-space maritime channel with multiple spatial modes is presented. The entangled photons are generated from a spontaneous parametric down conversion (SPDC) source of type II. To employ multiple spatial modes, the transmit apparatus will contain multiple SPDC sources, all driven by the pump lasers assumed to have the same intensity. The receive apparatuses will contain avalanche photo diodes (APD), modeled based on the NuCrypt CPDS-1000 detector, and located at the focal point of the receive aperture lens. The transmitter is assumed to be located at Alice and Bob will be located 30 km away, implying no channel crosstalk will be introduced in the measurements at Alices side due to turbulence. To help mitigate the effects of atmospheric turbulence, adaptive optics will be considered at the transmitter and the receiver. An eavesdropper, Eve, is located 15 km from Alice and has no control over the devices at Alice or Bob. Eve is performing the intercept resend attack and listening to the communication over the public channel. Additionally, it is assumed that Eve can correct any aberrations caused by the atmospheric turbulence to determine which source the photon was transmitted from. One, four and nine spatial modes are considered with and without applying adaptive optics and compared to one another.