Advances in characterisation, calibration and data processing speed of optical coherence tomography systems

This thesis describes advances in the characterisation, calibration and data processing of optical coherence tomography (OCT) systems. Femtosecond (fs) laser inscription was used for producing OCT-phantoms. Transparent materials are generally inert to infra-red radiations, but with fs lasers material modification occurs via non-linear processes when the highly focused light source interacts with the materials. This modification is confined to the focal volume and is highly reproducible. In order to select the best inscription parameters, combination of different inscription parameters were tested, using three fs laser systems, with different operating properties, on a variety of materials. This facilitated the understanding of the key characteristics of the produced structures with the aim of producing viable OCT-phantoms. Finally, OCT-phantoms were successfully designed and fabricated in fused silica. The use of these phantoms to characterise many properties (resolution, distortion, sensitivity decay, scan linearity) of an OCT system was demonstrated. Quantitative methods were developed to support the characterisation of an OCT system collecting images from phantoms and also to improve the quality of the OCT images. Characterisation methods include the measurement of the spatially variant resolution (point spread function (PSF) and modulation transfer function (MTF)), sensitivity and distortion. Processing of OCT data is a computer intensive process. Standard central processing unit (CPU) based processing might take several minutes to a few hours to process acquired data, thus data processing is a significant bottleneck. An alternative choice is to use expensive hardware-based processing such as field programmable gate arrays (FPGAs). However, recently graphics processing unit (GPU) based data processing methods have been developed to minimize this data processing and rendering time. These processing techniques include standard-processing methods which includes a set of algorithms to process the raw data (interference) obtained by the detector and generate A-scans. The work presented here describes accelerated data processing and post processing techniques for OCT systems. The GPU based processing developed, during the PhD, was later implemented into a custom built Fourier domain optical coherence tomography (FD-OCT) system. This system currently processes and renders data in real time. Processing throughput of this system is currently limited by the camera capture rate. OCTphantoms have been heavily used for the qualitative characterization and adjustment/ fine tuning of the operating conditions of OCT system. Currently, investigations are under way to characterize OCT systems using our phantoms. The work presented in this thesis demonstrate several novel techniques of fabricating OCT-phantoms and accelerating OCT data processing using GPUs. In the process of developing phantoms and quantitative methods, a thorough understanding and practical knowledge of OCT and fs laser processing systems was developed. This understanding leads to several novel pieces of research that are not only relevant to OCT but have broader importance. For example, extensive understanding of the properties of fs inscribed structures will be useful in other photonic application such as making of phase mask, wave guides and microfluidic channels. Acceleration of data processing with GPUs is also useful in other fields.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Millimeter-wave measurements of the complex dielectric constant of an advanced thick film UV photoresist

The first measurement of the relative permittivity (εr) and loss tangent (tan δ) of EPON™ SU-8 advanced thick film ultraviolet photoresist is reported at frequencies between 75–110 GHz (W-band). The problems associated with such a measurement are discussed, an error analysis given, and values of εr=1.725±0.08 and tanδ =0.02±0.001 are determined.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics II. Application to reflection and refraction at a dielectric interface

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.

Complex natural resonances of conducting planar objects buried in a dielectric half-space

A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's formulation C with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT), The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. We investigate the pole trajectories as we vary the distance between strips and the depth and orientation of single, buried strips, The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations.

(1−x)MgAl2O4-xTiO2 dielectrics for microwave and millimeter wave applications

The MgAl2O4 ceramics were prepared by the conventional solid-state ceramic route and the dielectric properties studied in the microwave frequency region (3–13 GHz). The phase purity and crystal structure were identified using the X-ray diffraction technique. The MgAl2O4 spinel ceramics show interesting microwave dielectric properties (εr = 8.75, Qux f = 68 900 GHz (loss tangent = 0.00017 at 12.3 GHz), τf =−75 ppm/◦C). The MgAl2O4 has high negative τf, which precludes its immediate use in practical applications. Hence the microwave dielectric properties of MgAl2O4 spinels were tailored by adding different mole fractions of TiO2. The εr and Q factor of the mixed phases were increased with the molar addition of TiO2 into the spinel to form mixtures based on (1−x)MgAl2O4-xTiO2 (x = 0.0−1.0). For x = 0.25 in (1−x)MgAl2O4-xTiO2, the microwave quality factor reaches a maximum value of Qux f = 105 400 GHz (loss tangent = 0.00007 at 7.5 GHz) where εr and τf are 11.035 and −12 ppm/◦C, respectively. The microwave dielectric properties of the newly developed 0.75MgAl2O4-0.25TiO2 dielectric is superior to several commercially available low loss dielectric substrates.

Power characteristics of dielectric optical piet hein waveguides

A fairly rigorous analytical treatment of the power characteristics of dielectric optical waveguides with Piet Hein core-cross sectional geometry is presented in this paper. This kind of wareguide structure would be advantageous owing to the absence of corners, which are found in rectangular guides, resulting in undesirable loss (hit to the scattering of light. In order to simplify this theoretical approach. em approximation of vanishing refractive index difference between the guiding and the non-guiding sections is implemented. The variation eJ logarithmic power is shown for different dimensions of the core, corresponding to different azimuthal modal indices. It is found that the nutlet with higher index values carry less logaritlunic power in the lower tail of the propagation 's constant range, and this feature affects the higher tail. A better kind of uniformity of the power distribution is observed near the higher tail of the range of propagation Constants

Scattering Behaviour of fractal based metallo-dielectric structures

The scattering behaviour of fractal based metallodielectric structures loaded over metallic targets of different shapes such as flat plate, cylinder and dihedral corner reflector are investigated for both TE and TM polarizations of the incident wave. Out of the various fractal structures studied,square Sierpinski carpet structure is found to give backscattering reduction for an appreciable range of frequencies. The frequency of minimum backscattering depends on the geometry of the structure as well as on the thickness of the substrate. This structure when loaded over a dihedral corner reflector is showing an enhancement in RCS for corner angles other than 90◦.

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Multivariate analysis of the dielectric response of materials modeled using networks of resistors and capacitors

We discuss the modeling of dielectric responses of electromagnetically excited networks which are composed of a mixture of capacitors and resistors. Such networks can be employed as lumped-parameter circuits to model the response of composite materials containing conductive and insulating grains. The dynamics of the excited network systems are studied using a state space model derived from a randomized incidence matrix. Time and frequency domain responses from synthetic data sets generated from state space models are analyzed for the purpose of estimating the fraction of capacitors in the network. Good results were obtained by using either the time-domain response to a pulse excitation or impedance data at selected frequencies. A chemometric framework based on a Successive Projections Algorithm (SPA) enables the construction of multiple linear regression (MLR) models which can efficiently determine the ratio of conductive to insulating components in composite material samples. The proposed method avoids restrictions commonly associated with Archie’s law, the application of percolation theory or Kohlrausch-Williams-Watts models and is applicable to experimental results generated by either time domain transient spectrometers or continuous-wave instruments. Furthermore, it is quite generic and applicable to tomography, acoustics as well as other spectroscopies such as nuclear magnetic resonance, electron paramagnetic resonance and, therefore, should be of general interest across the dielectrics community.

Dielectric properties and physical features of phosphate glasses containing iron oxide

Microwave techniques were applied to the study of dielectric properties of phosphate glasses on the basis of contributions from permanent and induced dipolar polarization of local structural units interacting with the electrical component of the electromagnetic radiation. The dielectric constant of the selected glass system (100-x)(50P(2)O(5)center dot 25Li(2)O center dot 25Na(2)O)center dot xFe(2)O(3), where 0 <= x <= 21 is in mol%, was measured using a microwave setup assembled to measure the phase shift of the standing wave pattern produced by the insertion of the sample. It is shown that the Fe2+ ions contribute effectively to the dielectric constant, as expected from the interactions of the dipoles of the local charge compensation pairs with the microwave radiation. However, there is the possibility of occurrence of some ions Fe3+, in general, at low iron content, which reinforces the glass structure and, therefore, decreases the dielectric constant. There is a gradual conversion from Fe3+ to Fe2+ as the iron ions increases. This is possibly the reason of the anomaly in the dielectric constant values observed in the results. These assumptions can be checked by results of electronic paramagnetic resonance (EPR) and optical absorption (OA). The dielectric constant of the glasses studied in this work was found to increase with the temperature in the range of 25-330 degrees C. (C) 2007 Elsevier B.V. All rights reserved.

Huge values of room-temperature dielectric constants in pellets of poly(3-methylthiophene)

Room temperature data of impedance and phase angle in pellets of electrochemically synthesized ClO4- doped poly(3-methylthiophene) (P3MT) were analyzed assuming the sample being represented by a parallel resistor-capacitor (RC) circuit or by a series RC circuit. The last assumption proved to be the correct one, and to confirm it we use the sample as the RC component of a resistor-capacitor-inductor series resonator. We discuss the possibility of this RC series behavior to be due to a charge-density wave characteristic also evidenced from the huge values of the low-frequency dielectric constant of the system.

Surface impedance for scattered field on a dielectric-coated circular cylinder

In the scattering analysis of a circular cylindrical structure, the impedance boundary condition (IBC) can approximate and simplify the perfect electric conductor (PEC) boundary condition. The circular cylinder problem can be solved with modal methods but they require a large number of terms when the cylinder radius is large in terms of the wave length. The uniform theory of diffraction (UTD) [1] is commonly used to overcome this issue. The two-dimensional problem of scattering on a circular cylinder covered by a dielectric layer has been analyzed by [2]–[5], but their solutions either do not consider oblique incidence, fail on the transition region or use a constant surface impedance.

Surface impedance for electromagnetic fields over a dielectric-coated circular cylinder

For small or medium size conformal array antennas in terms of the wave length, modal solutions in spectral domain for mutual coupling analysis are convenient for canonical shapes such as circular cylinder [1] or sphere [2], but as the antenna dimensions increase a large number of terms are necessary. For large structures the uniform theory of diffraction (UTD) is commonly used to solve this problem for canonical and arbitrarily convex shaped perfect electric conductor (PEC) surfaces [3]. A UTD solution for mutual coupling on an impedance cylinder has been introduced in [4], [5] but using a constant surface impedance.