The performance of optical imaging systems relies on control of aberrations that can arise from limitations in the design, manufacture, or alignment. This dissertation addresses the form of aberrations that occur for misaligned reflective systems, such as telescopes. The relationship between a characteristic set of field-dependent aberrations and the misalignments that cause them is systematically explored. A comprehensive technique that quantifies field performance for a 5-mirror system is given, using Monte Carlo analysis to provide confidence levels of image quality as functions of manufacturing and alignment errors. This analysis is an example of the "forward problem"— determining optical performance of a system if the errors are assumed. The inverse problem — determining the state of alignment based on measurements of performance — is more difficult. The solution to the inverse problem for a multiple mirror system requires an understanding of the complex coupling between many degrees of freedom (tilt, decenter, despace, shape error) of the optical elements and field-dependent aberrations.This work builds on previous treatment of field dependent optical aberrations from Tessieres, Thompson, Shack, Buchroeder and others. A basis set of field-dependent aberrations orthogonal over both field and pupil are developed here and used to describe systems with misaligned and misshapen optics. This description allows complete representation of high order and non-linear effects. The functional form of aberrations that are characteristic of mirror tilt, shift, and deformation show some useful patterns that provide insight to the fundamental effects of misalignment.The use of singular value decomposition to create orthogonal combinations of the field dependent aberrations provides a powerful tool for evaluating a system and for estimating the state of alignment using wavefront measurements. The following optical systems are evaluated to investigate the linear coupling between misalignment and the resulting field dependent aberrations:* 2-mirror telescopes, evaluating well-understood effects for an axisymmetric system and developing the relationships for an unobscured system.* 4-mirror correctors for a spherical primary telescope.The tools and methods are applied to reflective optical systems for astronomical telescopes, but the methods are general and can be useful for any optical imaging system.

Shack-Hartmann wavefront sensors are commonly used in optical alignment, ophthalmology, astronomy, adaptive optics and commercial optical testing. Wavefront error measurement yields Zernike polynomials which provide useful data for alignment correction calculations. In this thesis a practical alignment method of a helmet visor is proposed based on the wavefront error measurements. The optical system is modeled in Zemax software in order to collect the Zernike polynomial data necessary to relate the error measurements to the positioning of the visor. An artificial neural network based computer program is designed and trained with the data obtained from Zernike simulation in Zemax software and then the program is able to find how to invert the misalignments in the system. The performance of this alignment correction method is compared with the optical test setup measurements.

Topografias da córnea consistem em medir a forma da córnea, que é um fator chave para a acuidade visual. O exame é usado, por exemplo, na detecção de ceratocone, ajuste personalizado de lentes de contato, e pre e pós procedimentos associados com cirurgias refrativas e transplante de córnea. Esta dissertação apresenta, uma abordagem acessível e portátil para realizar topografias da córnea. Os resultados obtidos com o nosso protótipo mostram uma diferença média por volta de 0.02 milimetros, equivalente a 0.5% do raio médio da córnea, quando comparadas com topografias adquiridas com um topografo comercial. Nossa abordagem é baseada no disco de Plácido, a um conjunto de círculos concêntricos que são colocados na frente do olho do paciente e refletidos na córnea. Observando a deformação do padrão projetado, podemos identificar algumas condições refrativas (e.g. astigmatismo, ceratocone) e estimar a topografia da córnea do paciente. Nós construimos um dispositivo para ser utilizado com um celular para emitir os padrões, estes são então capturados pela câmera do celular. Nós usamos um sequência de procedimentos para melhor as imagens, segmentar os padrões, associar o padrão capturado com o emitido para amostrar o sinal, e finalmente estimar a superfície da córnea. A forma estimada é então decomposta, usando-se os polinômios de Zernike, em componentes com significado ótico específico. Nós avaliamos os resultados obtidos com o nosso protótipo de três maneiras: inspeção visual de ceratoscopias, detecção de ceratocone, e comparação com os resultados produzidos por um topográfo de córnea comercial. De acordo com essa análise, nosso dispositivo pode ser utilizado para o exame de indivíduos com ceratocone, e obter topografias com 0.02 milimetros de diferença em relação aos resultados obtidos com um topógrafo comercial. / Corneal topography consists of measuring the corneal shape, which is a key factor for visual acuity. The exam is used, for instance, in keratoconus detection, personalized contact lens fitting, in pre- and post-procedures associated with refractive surgery and corneal transplants. This thesis presents an accessible, inexpensive and portable approach to perform corneal topographies. The results obtained with our prototype show a mean difference of about 0.02 millimeters, equivalent to 0.5% of the mean corneal radius, when compared to topographies acquired with a commercial device. Our approach is based on Placido’s disks, a set of concentric disks that are placed in front of the patient’s eye and reflected on the cornea. Observing the deformation of the projected pattern, one can identify some refractive conditions (e.g., astigmatism, keratoconus) and estimate the patient’s corneal topography. We have built a clip-on device to be used with a cell phone to emit the patterns, which are then captured by the cell phone camera. We use a software pipeline to enhance the images, segment the patterns, associate the emitted pattern with the captured one to sample the signal, and finally estimate the corneal surface. The estimated shape is then decomposed using Zernike polynomials in components with specific optical meanings. We have evaluated the results obtained with our prototype in three ways: visual inspection of keratoscopies, keratoconus detection, and comparison with the results produced by a commercial corneal topographer. According to such analysis, our device can be used for screening of individuals with keratoconus, and to obtain corneal topographies with 0.02-millimeter differences with respect to the results obtained with a commercial corneal topographer.

Topografias da córnea consistem em medir a forma da córnea, que é um fator chave para a acuidade visual. O exame é usado, por exemplo, na detecção de ceratocone, ajuste personalizado de lentes de contato, e pre e pós procedimentos associados com cirurgias refrativas e transplante de córnea. Esta dissertação apresenta, uma abordagem acessível e portátil para realizar topografias da córnea. Os resultados obtidos com o nosso protótipo mostram uma diferença média por volta de 0.02 milimetros, equivalente a 0.5% do raio médio da córnea, quando comparadas com topografias adquiridas com um topografo comercial. Nossa abordagem é baseada no disco de Plácido, a um conjunto de círculos concêntricos que são colocados na frente do olho do paciente e refletidos na córnea. Observando a deformação do padrão projetado, podemos identificar algumas condições refrativas (e.g. astigmatismo, ceratocone) e estimar a topografia da córnea do paciente. Nós construimos um dispositivo para ser utilizado com um celular para emitir os padrões, estes são então capturados pela câmera do celular. Nós usamos um sequência de procedimentos para melhor as imagens, segmentar os padrões, associar o padrão capturado com o emitido para amostrar o sinal, e finalmente estimar a superfície da córnea. A forma estimada é então decomposta, usando-se os polinômios de Zernike, em componentes com significado ótico específico. Nós avaliamos os resultados obtidos com o nosso protótipo de três maneiras: inspeção visual de ceratoscopias, detecção de ceratocone, e comparação com os resultados produzidos por um topográfo de córnea comercial. De acordo com essa análise, nosso dispositivo pode ser utilizado para o exame de indivíduos com ceratocone, e obter topografias com 0.02 milimetros de diferença em relação aos resultados obtidos com um topógrafo comercial. / Corneal topography consists of measuring the corneal shape, which is a key factor for visual acuity. The exam is used, for instance, in keratoconus detection, personalized contact lens fitting, in pre- and post-procedures associated with refractive surgery and corneal transplants. This thesis presents an accessible, inexpensive and portable approach to perform corneal topographies. The results obtained with our prototype show a mean difference of about 0.02 millimeters, equivalent to 0.5% of the mean corneal radius, when compared to topographies acquired with a commercial device. Our approach is based on Placido’s disks, a set of concentric disks that are placed in front of the patient’s eye and reflected on the cornea. Observing the deformation of the projected pattern, one can identify some refractive conditions (e.g., astigmatism, keratoconus) and estimate the patient’s corneal topography. We have built a clip-on device to be used with a cell phone to emit the patterns, which are then captured by the cell phone camera. We use a software pipeline to enhance the images, segment the patterns, associate the emitted pattern with the captured one to sample the signal, and finally estimate the corneal surface. The estimated shape is then decomposed using Zernike polynomials in components with specific optical meanings. We have evaluated the results obtained with our prototype in three ways: visual inspection of keratoscopies, keratoconus detection, and comparison with the results produced by a commercial corneal topographer. According to such analysis, our device can be used for screening of individuals with keratoconus, and to obtain corneal topographies with 0.02-millimeter differences with respect to the results obtained with a commercial corneal topographer.

Dans cette thèse, l'holographie numérique dans l'axe (DIH) est la principale méthode optique utilisée pour analyser des inclusions dans une gouttelette. L'holographie numérique dans l'axe est utilisée pour caractériser des inclusions du point de vue de leur taille, leur position 3D et leur trajectoire à l'intérieur de la gouttelette. Comme les particules sont situées à l'intérieur d'une gouttelette, le front d'onde incident sur l'inclusion est modifié avant qu'il l'illumine. Le défi de ce travail est double : premièrement de prendre en compte la forme de la gouttelette dans le modèle d'holographie et deuxièmement d'étendre l'analyse aux inclusions transparentes (type objet de phase). Pour décrire l'hologramme enregistré par le capteur CCD, l'intégrale d'Huygens-Fresnel et le formalisme des matrices ABCD ont été utilisés. Dans ce modèle, nous introduisons les polynômes de Zernike pour décrire la fonction de transmission d'une particule. Pour l'analyse des hologrammes, l'outil mathématique de la transformation de Fourier fractionnaire 2D (2D-FRFT) est utilisé pour restituer l'image des inclusions et dans ce cas une mesure la taille de l'inclusion et de sa position 3D sont réalisées. Les trajectoires des inclusions dans la goutte est possible avec un long temps de pose de l'obturateur du capteur CCD. Nous avons également proposé un nouveau modèle pour décrire des objets de phases quelconque et des particules opaques. Pour ce nouveau modèle, les mêmes procédés ont été utilisés. Dans le cas d'inclusions filiformes à l'intérieur d'une géométrie cylindrique comme un canal, une méthode de simulation d'imagerie interférométrique multi-coeurs est proposée. Dans ce cas, une somme de distributions de Dirac, localisées le long d'une droite, introduite dans l'intégrale de Fresnel généralisée (c'est-à-dire le formalisme des matrices ABCD et l'intégrale de Fresnel) permet d'obtenir un bon degré de similitude entre l'expérience et la simulation. / In this thesis, the digital in-line holography (DIH) is the main optical method used to analyze inclusions in a droplet. The digital in-line holography is used to characterize the inclusions in terms of of their size, their 3D position, and their trajectories inside the droplet. Since the particles are located within a droplet, the incident wavefront is changed before it illuminates the inclusions. The challenge of this work has two points : first to take into account the shape of the droplet in the holographic model and secondly to extend the analysis to the transparent inclusions (phase object). To describe the hologram recorded by the CCD sensor, the Huygens-Fresnel integral and the ABCD matrix formalism were used. In this model, we introduce the Zernike polynomials to describe the transmission function of a particle. For the analysis of holograms, the2D fractional Fourier transformation (2D-FRFT) is used to reconstruct the image of inclusions and in this case the size and their 3D position of the inclusions are performed.The trajectories of the inclusions in the drop are possible tracked with a long exposure shutter speed of the CCD. We also proposed a new simulation to describe objects of any phases and opaque particles. For this simulation, the same methods of reconstruction were used. In the case of micro-channel inclusions inside a cylindrical geometry such as a pipe, the interferometric imaging of multi-core pipe is proposed. In this case, summation of Dirac delta distribution, located along a line, introduced into the generalized Fresnel integral allows us to get a good agreement between the experiment and the simulation.

Topografias da córnea consistem em medir a forma da córnea, que é um fator chave para a acuidade visual. O exame é usado, por exemplo, na detecção de ceratocone, ajuste personalizado de lentes de contato, e pre e pós procedimentos associados com cirurgias refrativas e transplante de córnea. Esta dissertação apresenta, uma abordagem acessível e portátil para realizar topografias da córnea. Os resultados obtidos com o nosso protótipo mostram uma diferença média por volta de 0.02 milimetros, equivalente a 0.5% do raio médio da córnea, quando comparadas com topografias adquiridas com um topografo comercial. Nossa abordagem é baseada no disco de Plácido, a um conjunto de círculos concêntricos que são colocados na frente do olho do paciente e refletidos na córnea. Observando a deformação do padrão projetado, podemos identificar algumas condições refrativas (e.g. astigmatismo, ceratocone) e estimar a topografia da córnea do paciente. Nós construimos um dispositivo para ser utilizado com um celular para emitir os padrões, estes são então capturados pela câmera do celular. Nós usamos um sequência de procedimentos para melhor as imagens, segmentar os padrões, associar o padrão capturado com o emitido para amostrar o sinal, e finalmente estimar a superfície da córnea. A forma estimada é então decomposta, usando-se os polinômios de Zernike, em componentes com significado ótico específico. Nós avaliamos os resultados obtidos com o nosso protótipo de três maneiras: inspeção visual de ceratoscopias, detecção de ceratocone, e comparação com os resultados produzidos por um topográfo de córnea comercial. De acordo com essa análise, nosso dispositivo pode ser utilizado para o exame de indivíduos com ceratocone, e obter topografias com 0.02 milimetros de diferença em relação aos resultados obtidos com um topógrafo comercial. / Corneal topography consists of measuring the corneal shape, which is a key factor for visual acuity. The exam is used, for instance, in keratoconus detection, personalized contact lens fitting, in pre- and post-procedures associated with refractive surgery and corneal transplants. This thesis presents an accessible, inexpensive and portable approach to perform corneal topographies. The results obtained with our prototype show a mean difference of about 0.02 millimeters, equivalent to 0.5% of the mean corneal radius, when compared to topographies acquired with a commercial device. Our approach is based on Placido’s disks, a set of concentric disks that are placed in front of the patient’s eye and reflected on the cornea. Observing the deformation of the projected pattern, one can identify some refractive conditions (e.g., astigmatism, keratoconus) and estimate the patient’s corneal topography. We have built a clip-on device to be used with a cell phone to emit the patterns, which are then captured by the cell phone camera. We use a software pipeline to enhance the images, segment the patterns, associate the emitted pattern with the captured one to sample the signal, and finally estimate the corneal surface. The estimated shape is then decomposed using Zernike polynomials in components with specific optical meanings. We have evaluated the results obtained with our prototype in three ways: visual inspection of keratoscopies, keratoconus detection, and comparison with the results produced by a commercial corneal topographer. According to such analysis, our device can be used for screening of individuals with keratoconus, and to obtain corneal topographies with 0.02-millimeter differences with respect to the results obtained with a commercial corneal topographer.

No description available.

Erros de alinhamento em sistemas ópticos não criam novas aberrações, mas alteram a dependência com o campo das aberrações já conhecidas. Neste trabalho, a sensibilidade teórica ao alinhamento, de sistemas ópticos reflexivos compostos por dois elementos, foi avaliada em função das constantes cônicas dos espelhos. Dentre as diferentes configurações consideradas nesta análise, uma específica apresenta menor sensibilidade à descentralização do espelho secundário. A utilização da teoria de aberração de onda aplicável a sistemas plano-simétricos revelou que a escolha apropriada da constante cônica do espelho secundário faz com que coma uniforme de terceira ordem seja compensado quando esse elemento encontra-se descentralizado, fazendo com que esse sistema seja livre da aberração mais importante causada a ele por desalinhamentos, tornando-o menos sensível. Este trabalho apresenta uma metodologia de alinhamento baseada na análise da frente de onda transmitida por sistemas ópticos, que utiliza redes neurais artificiais para a estimativa dos erros de alinhamento. A frente de onda transmitida por um sistema óptico carrega informações das aberrações desse sistema, que podem ser descritas em termos dos polinômios de Zernike. Esses polinômios podem ser usados para a análise dos efeitos de erros de alinhamento nas aberrações do sistema. Redes neurais artificiais são empregadas na análise dos coeficientes dos polinômios de Zernike visando avaliar o tipo de desalinhamento e a sua magnitude. As estimativas teóricas dos desalinhamentos tanto em sistemas reflexivos como em sistemas refrativos são satisfatórias quando o sistema é considerado perfeito, ou seja, as superfícies ópticas de seus elementos não apresentam erros de forma e não há ruído nos dados avaliados. Na presença de defeitos de fabricação ocorre degradação no desempenho do estimador. Além de descentralização e inclinação, redes neurais artificiais são capazes de fornecer uma estimativa de erros de posicionamento axial dos elementos do sistema. Com base nos estudos realizados, acredita-se que redes neurais artificiais constituem uma alternativa promissora no alinhamento de sistemas ópticos complexos. / Although misalignments in optical systems do not generate new aberration forms, they change the field-dependence of the known ones. In this research, the sensitivity of two-mirror optical systems due to misalignments is evaluated in function of the conic constants of the mirrors. Among the different configurations considered in this study, a specific one has shown low sensitivity due to decenter misalignments. The application of the wave aberration theory for plane-symmetric optical systems has revealed that the proper choice of the secondary mirror conic constant allows third-order uniform coma to be compensated, leading to a less sensitive system, free from the most important misalignment-induced aberration. This thesis also presents an alignment methodology based on the analysis of the transmitted wavefront utilizing artificial neural networks to estimate alignment errors in the components of the system. The transmitted wavefront carries information about the aberrations in the optical system, which can be described in terms of Zernike polynomials. Such polynomials are used for the analysis of the effects of misalignments on the aberrations of the system. Artificial neural networks are employed in the analysis of the coefficients of Zernike polynomials and used to evaluate both type and magnitude of the misalignments. Theoretical misalignments estimated in reflexive and refractive optical systems are satisfactory for perfect systems, i.e., systems with no surface errors, and noiseless data. When surface imperfections are considered, the performance of the estimator is reduced. Besides decenter and tilt misalignments, artificial neural networks can estimate axial positioning errors of the elements in the system, therefore they are believed to be a promising alternative for the alignment of complex optical systems.

Inspection of optical components is essential to assure the quality and performance of optical systems. Evaluation of optical components includes metrology measurements of surface topography. It also requires optical measurements including refractive index, thin film thickness, reflectivity and transmission. The dispersion characteristics of optical constants including refractive index are also required. Hence, various instruments are used to make these measurements in research laboratories and for quality assurance. Clearly, it would be a significant advantage and cost saving if a technique was developed that could combine surface metrology with optical measurements. {Coherence Scanning Interferometry} (CSI) (also referred to as {Scanning White Light Interferometry} (SWLI)) has been used widely to measure surface topography with sub-nanometre vertical resolution. One of the benefits of the CSI is that the technique is non-contacting and hence non-destructive. Thus the test surfaces are not affected by the measurement using a CSI instrument whereas damage to the surfaces can occur when using traditional contact methods such as stylus profilometry. However use of CSI is geometrically limited to small areas ($\lesssim 10 \times 10$ mm) with gentle slopes ($\lesssim \ang{40}$) because of the numerical aperture of objective lens whereas stylus profilometry works well with larger areas and higher slopes due to the range of motion of the gauge and the traverse unit. Since the CSI technique is optical and involves light reflection and interference it is possible to extend the technique for the measurement of the thickness of transparent films, the roughness of surfaces buried beneath thin films or interfacial surfaces. It may also be used to determine spectral complex refractive index. This thesis provides an analytical framework of new methods to obtain complex refractive index in a visible light domain and interfacial surface roughness (ISR). It also provides experimental verification of these new capabilities using actual thin film model systems. The original Helical Complex Field (HCF) function theory is presented followed by its existing extensions that enable determination of complex refractive index and interfacial surface roughness. Further theoretical extensions of the HCF theory are also provided: A novel theory to determine the refractive index of a (semi-)transparent film is developed to address the constraint of the current HCF theory that restricted its use to opaque materials; Another novel theory is provided to measure ISR with noise compensation, which avoids erroneous surface roughness caused by the numerical optimisation affected by the existence of noise. The effectiveness of the ISR measurement with noise compensation has been verified using a number of computer simulations. Stylus profilometry is a well established method to provide a profile and has been used extensively as a 'reference' for other techniques. It normally provides a profile on which the roughness and the waviness are computed. Extension of the stylus profilometry technique to areal measurement of asymmetrical surfaces, namely raster scan measurement, requires a system to include error compensation between each traverse. The system errors and the random errors need to be separately understood particular when the measurement of a surface with nanometre-order accuracy is required. In this thesis a mathematical model to locate a stylus tip considering five mechanical errors occurring in a common raster scan profilometer is provided. Based on the model, the simulator which provides an areal measurement of a sphere was developed. The simulator clarified the relationship between the Zernike coefficients obtained from the form residual and the size of the errors in the form of partial derivatives of Zernike coefficients with respect to the errors. This provides theoretical support to the empirical knowledge of the relationship between the coefficients and the errors. Furthermore, a method to determine the size of errors directly from Zernike coefficients is proposed supported by simulations. Some of the error parameters were accurately determined avoiding iterative computation with this method whereas the errors are currently being determined by iterative computation.

Erros de alinhamento em sistemas ópticos não criam novas aberrações, mas alteram a dependência com o campo das aberrações já conhecidas. Neste trabalho, a sensibilidade teórica ao alinhamento, de sistemas ópticos reflexivos compostos por dois elementos, foi avaliada em função das constantes cônicas dos espelhos. Dentre as diferentes configurações consideradas nesta análise, uma específica apresenta menor sensibilidade à descentralização do espelho secundário. A utilização da teoria de aberração de onda aplicável a sistemas plano-simétricos revelou que a escolha apropriada da constante cônica do espelho secundário faz com que coma uniforme de terceira ordem seja compensado quando esse elemento encontra-se descentralizado, fazendo com que esse sistema seja livre da aberração mais importante causada a ele por desalinhamentos, tornando-o menos sensível. Este trabalho apresenta uma metodologia de alinhamento baseada na análise da frente de onda transmitida por sistemas ópticos, que utiliza redes neurais artificiais para a estimativa dos erros de alinhamento. A frente de onda transmitida por um sistema óptico carrega informações das aberrações desse sistema, que podem ser descritas em termos dos polinômios de Zernike. Esses polinômios podem ser usados para a análise dos efeitos de erros de alinhamento nas aberrações do sistema. Redes neurais artificiais são empregadas na análise dos coeficientes dos polinômios de Zernike visando avaliar o tipo de desalinhamento e a sua magnitude. As estimativas teóricas dos desalinhamentos tanto em sistemas reflexivos como em sistemas refrativos são satisfatórias quando o sistema é considerado perfeito, ou seja, as superfícies ópticas de seus elementos não apresentam erros de forma e não há ruído nos dados avaliados. Na presença de defeitos de fabricação ocorre degradação no desempenho do estimador. Além de descentralização e inclinação, redes neurais artificiais são capazes de fornecer uma estimativa de erros de posicionamento axial dos elementos do sistema. Com base nos estudos realizados, acredita-se que redes neurais artificiais constituem uma alternativa promissora no alinhamento de sistemas ópticos complexos. / Although misalignments in optical systems do not generate new aberration forms, they change the field-dependence of the known ones. In this research, the sensitivity of two-mirror optical systems due to misalignments is evaluated in function of the conic constants of the mirrors. Among the different configurations considered in this study, a specific one has shown low sensitivity due to decenter misalignments. The application of the wave aberration theory for plane-symmetric optical systems has revealed that the proper choice of the secondary mirror conic constant allows third-order uniform coma to be compensated, leading to a less sensitive system, free from the most important misalignment-induced aberration. This thesis also presents an alignment methodology based on the analysis of the transmitted wavefront utilizing artificial neural networks to estimate alignment errors in the components of the system. The transmitted wavefront carries information about the aberrations in the optical system, which can be described in terms of Zernike polynomials. Such polynomials are used for the analysis of the effects of misalignments on the aberrations of the system. Artificial neural networks are employed in the analysis of the coefficients of Zernike polynomials and used to evaluate both type and magnitude of the misalignments. Theoretical misalignments estimated in reflexive and refractive optical systems are satisfactory for perfect systems, i.e., systems with no surface errors, and noiseless data. When surface imperfections are considered, the performance of the estimator is reduced. Besides decenter and tilt misalignments, artificial neural networks can estimate axial positioning errors of the elements in the system, therefore they are believed to be a promising alternative for the alignment of complex optical systems.