Modeling diffraction and imaging of laser beams by the mode-expansion method

We present a new method of modeling imaging of laser beams in the presence of diffraction. Our method is based on the concept of first orthogonally expanding the resultant diffraction field (that would have otherwise been obtained by the laborious application of the Huygens diffraction principle) and then representing it by an effective multimodal laser beam with different beam parameters. We show not only that the process of obtaining the new beam parameters is straightforward but also that it permits a different interpretation of the diffraction-caused focal shift in laser beams. All of the criteria that we have used to determine the minimum number of higher-order modes needed to accurately represent the diffraction field show that the mode-expansion method is numerically efficient. Finally, the characteristics of the mode-expansion method are such that it allows modeling of a vast array of diffraction problems, regardless of the characteristics of the incident laser beam, the diffracting element, or the observation plane. (C) 2005 Optical Society of America.

Integrated System Technologies for Modular Trapped Ion Quantum Information Processing

Although trapped ion technology is well-suited for quantum information science, scalability of the system remains one of the main challenges. One of the challenges associated with scaling the ion trap quantum computer is the ability to individually manipulate the increasing number of qubits. Using micro-mirrors fabricated with micro-electromechanical systems (MEMS) technology, laser beams are focused on individual ions in a linear chain and steer the focal point in two dimensions. Multiple single qubit gates are demonstrated on trapped 171Yb+ qubits and the gate performance is characterized using quantum state tomography. The system features negligible crosstalk to neighboring ions (< 3e-4), and switching speeds comparable to typical single qubit gate times (< 2 us). In a separate experiment, photons scattered from the 171Yb+ ion are coupled into an optical fiber with 63% efficiency using a high numerical aperture lens (0.6 NA). The coupled photons are directed to superconducting nanowire single photon detectors (SNSPD), which provide a higher detector efficiency (69%) compared to traditional photomultiplier tubes (35%). The total system photon collection efficiency is increased from 2.2% to 3.4%, which allows for fast state detection of the qubit. For a detection beam intensity of 11 mW/cm2, the average detection time is 23.7 us with 99.885(7)% detection fidelity. The technologies demonstrated in this thesis can be integrated to form a single quantum register with all of the necessary resources to perform local gates as well as high fidelity readout and provide a photon link to other systems.

Optimized aperture shapes for depth estimation

The finite depth of field of a real camera can be used to estimate the depth structure of a scene. The distance of an object from the plane in focus determines the defocus blur size. The shape of the blur depends on the shape of the aperture. The blur shape can be designed by masking the main lens aperture. In fact, aperture shapes different from the standard circular aperture give improved accuracy of depth estimation from defocus blur. We introduce an intuitive criterion to design aperture patterns for depth from defocus. The criterion is independent of a specific depth estimation algorithm. We formulate our design criterion by imposing constraints directly in the data domain and optimize the amount of depth information carried by blurred images. Our criterion is a quadratic function of the aperture transmission values. As such, it can be numerically evaluated to estimate optimized aperture patterns quickly. The proposed mask optimization procedure is applicable to different depth estimation scenarios. We use it for depth estimation from two images with different focus settings, for depth estimation from two images with different aperture shapes as well as for depth estimation from a single coded aperture image. In this work we show masks obtained with this new evaluation criterion and test their depth discrimination capability using a state-of-the-art depth estimation algorithm.

A sensitivity study of the human crystalline lens using finite element analysis

Finite element analysis is a useful tool in understanding how the accommodation system of the eye works. Further to simpler FEA models that have been used hitherto, this paper describes a sensitivity study which aims to understand which parameters of the crystalline lens are key to developing an accurate model of the accommodation system. A number of lens models were created, allowing the mechanical properties, internal structure and outer geometry to be varied. These models were then spun about their axes, and the deformations determined. The results showed the mechanical properties are the critical parameters, with the internal structure secondary. Further research is needed to fully understand how the internal structure and properties interact to affect lens deformation.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Progressive power lens measurement by low coherence speckle interferometry

This work proposes a method for dioptric power mapping of progressive lenses through dual wavelength, low-coherence digital speckle pattern interferometry. Lens characterization finds several applications and is extremely useful in the fields of ophthalmology and astronomy, among others. The optical setup employs two red diode lasers which are conveniently aligned and tuned in order to generate a synthetic wavelength. The resulting speckle image formed onto a diffusive glass plate positioned behind the test lens appears covered of contour interference fringes describing the deformation on the light wavefront due to the analyzed lens. By employing phase stepping and phase unwrapping methods the wavefront phase was retrieved and then expressed in terms of a Zernike series. From this series, expressions for the dioptric power and astigmatic power were derived as a function of the x- and y-coordinates of the lens aperture. One spherical and two progressive lenses were measured. The experimental results presented a good agreement with those obtained through a commercial lensometer, showing the potentialities of the method. © 2013 Elsevier Ltd.

Knots and links in lens spaces

The aim of this dissertation is to improve the knowledge of knots and links in lens spaces. If the lens space L(p,q) is defined as a 3-ball with suitable boundary identifications, then a link in L(p,q) can be represented by a disk diagram, i.e. a regular projection of the link on a disk. In this contest, we obtain a complete finite set of Reidemeister-type moves establishing equivalence, up to ambient isotopy. Moreover, the connections of this new diagram with both grid and band diagrams for links in lens spaces are shown. A Wirtinger-type presentation for the group of the link and a diagrammatic method giving the first homology group are described. A class of twisted Alexander polynomials for links in lens spaces is computed, showing its correlation with Reidemeister torsion. One of the most important geometric invariants of links in lens spaces is the lift in 3-sphere of a link L in L(p,q), that is the counterimage of L under the universal covering of L(p,q). Starting from the disk diagram of the link, we obtain a diagram of the lift in the 3-sphere. Using this construction it is possible to find different knots and links in L(p,q) having equivalent lifts, hence we cannot distinguish different links in lens spaces only from their lift. The two final chapters investigate whether several existing invariants for links in lens spaces are essential, i.e. whether they may assume different values on links with equivalent lift. Namely, we consider the fundamental quandle, the group of the link, the twisted Alexander polynomials, the Kauffman Bracket Skein Module and an HOMFLY-PT-type invariant.

Extraordinary transmission through a single coaxial aperture in a thin metal film

We investigate experimentally the transmission properties of single sub-wavelength coaxial apertures in thin metal films (t = 110 nm). Enhanced transmission through a single sub-wavelength coaxial aperture illuminated with a strongly focused radially polarized light beam is reported. In our experiments we achieved up to four times enhanced transmission through a single coaxial aperture as compared to a (hollow) circular aperture with the same outer diameter.We attribute this enhancement of transmission to the excitation of a TEM-mode for illumination with radially polarized light inside the single coaxial aperture. A strong polarization contrast is observed between the transmission for radially and azimuthally polarized illumination. Furthermore, the observed transmission through a single coaxial aperture can be strongly reduced if surface plasmons are excited. The experimental results are in good agreement with finite difference time domain (FDTD) simulations.

Solid catadioptric telephoto lens design with SMS method

Two new optical structures are designed using the Simultaneous Multiple Surfaces (SMS) method, comprised of 2 reflecting surfaces and 2 refracting surfaces, 800mm focal length, f/8 (aperture diameter 100 mm) and 1.180 diagonal field of view in the SWIR band. The lens surfaces are rotational symmetric and calculated to have good control of non-paraxial rays. We have achieved designs with excellent performance, and with total system length of less than 60 mm.

Ultra-compact SWIR telephoto lens design with SMS method

In this work, we propose two new optical structures, using the Simultaneous Multiple Surfaces (SMS) method, comprised of 2 reflecting surfaces and 2 refracting surfaces, 800mm focal length, f/8 (aperture diameter 100 mm) and 1.18 0 diagonal field of view in the SWIR band. The lens surfaces are rotational symmetric and calculated to have good control of non-paraxial rays. We have achieved designs with excellent performance, and with total system length of less than 60 mm.

Method for the characterization of Fresnel lens flux transfer performance

Fresnel lenses and other faceted or micro-optic devices are increasingly used in multiple applications like solar light concentrators and illumination devices, just to name some representative. However, it seems to be a certain lack of adequate techniques for the assessment of the performance of final fabricated devices. As applications are more exigent this characterization is a must. We provide a technique to characterize the performance of Fresnel lenses, as light collection devices. The basis for the method is a configuration where a camera images the Fresnel lens aperture. The entrance pupil of the camera is situated at the focal spot or the conjugate of a simulated solar source. In this manner, detailed maps of the performance of different Fresnel lenses are obtained for different acceptance angles.

A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

Modelling the human accommodation system using finite element analysis

The human accommodation system has been extensively examined for over a century, with a particular focus on trying to understand the mechanisms that lead to the loss of accommodative ability with age (Presbyopia). The accommodative process, along with the potential causes of presbyopia, are disputed; hindering efforts to develop methods of restoring accommodation in the presbyopic eye. One method that can be used to provide insight into this complex area is Finite Element Analysis (FEA). The effectiveness of FEA in modelling the accommodative process has been illustrated by a number of accommodative FEA models developed to date. However, there have been limitations to these previous models; principally due to the variation in data on the geometry of the accommodative components, combined with sparse measurements of their material properties. Despite advances in available data, continued oversimplification has occurred in the modelling of the crystalline lens structure and the zonular fibres that surround the lens. A new accommodation model was proposed by the author that aims to eliminate these limitations. A novel representation of the zonular structure was developed, combined with updated lens and capsule modelling methods. The model has been designed to be adaptable so that a range of different age accommodation systems can be modelled, allowing the age related changes that occur to be simulated. The new modelling methods were validated by comparing the changes induced within the model to available in vivo data, leading to the definition of three different age models. These were used in an extended sensitivity study on age related changes, where individual parameters were altered to investigate their effect on the accommodative process. The material properties were found to have the largest impact on the decline in accommodative ability, in particular compared to changes in ciliary body movement or zonular structure. Novel data on the importance of the capsule stiffness and thickness was also established. The new model detailed within this thesis provides further insight into the accommodation mechanism, as well as a foundation for future, more detailed investigations into accommodation, presbyopia and accommodative restoration techniques.

Visual and quality outcomes following bilateral implantation of a trifocal intraocular lens

Purpose: To examine visual outcomes following bilateral implantation of the FineVision trifocal intraocular lens (IOL; PhysIOL, Liège, Belgium). Methods: 26 patients undergoing routine cataract surgery were implanted bilaterally with the FineVision Trifocal IOL and followed up post-operatively for 3 months. The FineVision optic features a combination of 2 diffractive structures, resulting in distance, intermediate (+1.75 D add) and near vision (+3.50 D add) zones. Apodization of the optic surface increases far vision dominance with pupil aperture. Data collected at the 3 month visit included uncorrected and corrected distance (CDVA) and near vision; subjective refraction; defocus curve testing (photopic and mesopic); contrast sensitivity (CSV-1000); halometry glare testing and a questionnaire (NAVQ) to gauge near vision function and patient satisfaction. Results: The cohort comprised 15 males and 11 females, aged 52.5–82.4 years (mean 70.6 ± 8.2 years). Mean post-operative UDVA was 0.22 ± 0.14 logMAR, with a mean spherical equivalent refraction of +0.02 ± 0.35 D. Mean CDVA was 0.13 ± 0.10 logMAR monocularly, and 0.09 ± 0.07 logMAR binocularly. Defocus curve testing showed an extensive range of clear vision in both photopic and mesopic conditions. Patients showed high levels of satisfaction with their near vision (mean ± 0.9 ± 0.6, where 0 = completely satisfied, and 4 = completely unsatisfied) and demonstrated good spectacle independence. Conclusion: The FineVision IOL can be considered in patients seeking spectacle dependence following cataract surgery, and provide good patient satisfaction with uncorrected vision.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.