Experimental studies have shown that a "bump" occurs in the atmospheric spectrum just prior to turbulence cell dissipation.1,3,4 In weak optical turbulence, this bump affects calculated scintillation. The purpose of this thesis was to determine if a "non-bump" atmospheric power spectrum can be used to model scintillation for plane waves and spherical waves in moderate to strong optical turbulence regimes. Scintillation expressions were developed from an "effective" von Karman spectrum using an approach similar to that used by Andrews et al.8,14,15 in developing expressions from an "effective" modified (bump) spectrum. The effective spectrum extends the Rytov approximation into all optical turbulence regimes using filter functions to eliminate mid-range turbulent cell size effects to the scintillation index. Filter cutoffs were established by matching to known weak and saturated scintillation results. The resulting new expressions track those derived from the effective bump spectrum fairly closely. In extremely strong turbulence, differences are minimal.

Optical Coherence Tomography (OCT) is a coherence-gated, micrometer-resolution imaging technique that focuses a broadband near-infrared laser beam to penetrate into optical scattering media, e.g. biological tissues. The OCT resolution is split into two parts, with the axial resolution defined by half the coherence length, and the depth-dependent lateral resolution determined by the beam geometry, which is well described by a Gaussian beam model. The depth dependence of lateral resolution directly results in the defocusing effect outside the confocal region and restricts current OCT probes to small numerical aperture (NA) at the expense of lateral resolution near the focus. Another limitation on OCT development is the presence of a mixture of speckles due to multiple scatterers within the coherence length, and other random noise. Motivated by the above two challenges, a multiple scattering model based on Rytov approximation and Gaussian beam optics is proposed for the OCT setup. Some previous papers have adopted the first Born approximation with the assumption of small perturbation of the incident field in inhomogeneous media. The Rytov method of the same order with smooth phase perturbation assumption benefits from a wider spatial range of validity. A deconvolution method for solving the inverse problem associated with the first Rytov approximation is developed, significantly reducing the defocusing effect through depth and therefore extending the feasible range of NA.

Optical diffraction tomography (ODT) is a tomographic technique that can be used to measure the threedimensional (3D) refractive index distribution within living cells without the requirement of any marker. In principle, ODT can be regarded as a generalization of optical projection tomography which is equivalent to computerized tomography (CT). Both optical tomographic techniques require projection-phase images of cells measured at multiple angles. However, the reconstruction of the 3D refractive index distribution post-measurement differs for the two techniques. It is known that ODT yields better results than projection tomography, because it takes into account diffraction of the imaging light due to the refractive index structure of the sample. Here, we apply ODT to biological cells in a micro uidic chip which combines optical trapping and microfluidic flow to achieve an optofluidic single-cell rotation. In particular, we address the problem that arises when the trapped cell is not rotating about an axis perpendicular to the imaging plane, but instead about an arbitrarily tilted axis. In this paper we show that the 3D reconstruction can be improved by taking into account such a tilted rotational axis in the reconstruction process.

This thesis deals with the problem of practical application of FDTD technique for simulation of image formation in coherence controlled holographic microscope. Various ways for obtaining scattering matrices are explored in detail and the optimal technique based on a rigorous calculation of the far field is proposed. The scattering matrix, containing information about the observed sample, is subsequently used in analytic calculation of holographic signal; two levels of approximation of pupil function are also evaluated. The results are compared with a traditional approach based on Rytov approximation resulting in specification of the parameter domain where the approximation is applicable. Based on the simulations of the microscope, the dependence of axial resolution on apertures of the objective and the condenser and sensitivity of the signal to changes of refractive index of the sample is also studied.

SuperDARN est un réseau de radars HF cohérents dédié à l'étude de la convection du plasma ionosphérique à haute latitude qui trouve ses principales applications dans l'étude des relations Soleil/Terre. On s'intéresse ici aux effets des interactions entre l'onde radar émise et les gradients d'ionisation de différentes échelles et à leur impact sur la mesure. Des études sont menées pour détecter la signature du mouvement cyclotron des ions, superposé aux mouvements turbulents, dans les spectres mesurés. Ensuite, l'effet des moyennes échelles (100 m à 10 km) est mis en évidence sur la mesure des largeurs spectrales. Des études statistiques montrent que la détermination des paramètres est affectée par le rapport entre la fréquence émise et la fréquence plasma et par la distance de l'écho. Nous proposons une interprétation en terme de décorrélation du front d'onde au cours de la propagation, validée par la mise en place de simulations s'appuyant sur des paramètres réalistes de l'ionosphère.

L'imagerie des paramètres physiques du sous-sol à partir d'enregistrements sismiques de surface constitue un problème inverse non linéaire. L'inversion des formes d'onde élastique est une méthode d'imagerie quantitative multiparamètres de diffractants, nécessitant au préalable la connaissance précise d'un macromodèle de vitesse. <br /><br />Le problème direct associé, la propagation des ondes élastiques, est résolu dans le domaine fréquentiel, permettant la prise en compte efficace d'acquisitions multisources et multirécepteurs, par une méthode numérique de différences finies modélisant la propagation de tous les types d'onde (ondes de volume, de surface, diffractées, réfractées ...). Le stencil de différences finies choisi permet simule précisément la surface libre et la propagation des ondes de surface. <br /><br />Cette inversion linéarisée s'appuie sur une méthode de gradient, qui minimise une fonction coût contenant les différences entre données observées et calculées. Deux paramètres sismiques sont reconstruits à partir de sismogrammes verticaux et horizontaux. L'inversion est effectuée des basses fréquences vers les hautes fréquences, introduisant des longueurs d'onde de plus en plus courtes dans les images des paramètres. Ces dernières sont sensibles au choix des approximations physiques effectuées pour calculer le gradient de la fonction coût (approximation de Born ou de Rytov), au dispositif d'acquisition, au préconditionnement des données et au choix des paramètres inversés. <br /><br />Cette méthode est ensuite appliquée à des milieux contenant une surface libre. La surface libre est une interface très contrastée qui donne lieu à des ondes de surface très énergétiques dans les sismogrammes. Les milieux de subsurface sont complexes, les ondes qui s'y propagent subissent des réflexions ou diffractions multiples. Lorsque le milieu contient deux anomalies dont le contraste en vitesse vaut $20 \%$, l'inversion les localise correctement dans un macromodèle connu. Les images sont améliorées et l'amplitude des anomalies est très bien reconstruite lorsque le nombre de fréquences inversées augmente et les données sont sélectionnées des faibles déports vers les grands déports. Avec une anomalie fortement contrastée comme une cavité vide, l'inversion retrouve correctement la position, la forme et la taille de l'objet mais son amplitude est sous-estimée.<br /><br />L'application à des données réelles verticales de subsurface acquises dans un milieu complexe contenant une cavité maçonnée montre que le milieu hétérogène issu de l'inversion ajuste mieux les données et permet de bien reproduire les ondes inversées. Néanmoins, la cavité n'est pas imagée.

Diplomová práca sa zaoberá rozptylom elektromagnetického žiarenia na biologickej bunke použitím metódy konečných diferencií v časovej oblasti (FDTD), Bornovej aproximácie a Rytovovej aproximácie. Metóda FDTD dáva presné výsledky v širokej škále problémov. Je spravené porovnanie Bornovej aproximácie a Rytovovej aproximácie prostredníctvom FDTD metódy. Ďaľšia časť práce zahrnuje krátky popis koherenciou riadeného holografického mikroskopu CCHM. Záverečná časť sa venuje zobrazeniu rozptýleného poľa získaného z jednotlivých simulácií pomocou simulácie objektového ramena mikroskopu CCHM.

Microwave imaging finds numerous applications involving optically obscured targets. One particular area is breast cancer detection, since microwave technology promises fast low-cost image reconstruction without the use of harmful radiation typical of X-ray mammography. However, the success of microwave imaging is hindered by a critical issue, the complex nature of near-field electromagnetic scattering in tissue. To overcome this, specialized image reconstruction algorithms alongside sensitive measurement hardware are required. In this work, real-time near-field microwave imaging algorithms known as quantitative microwave holography and scattered power mapping are explored. They are experimentally demonstrated to identify potential tumor regions in tissue phantoms. Alongside this development, quality control techniques for evaluating microwave hardware are also described. Two new methods for improving the image reconstruction quality are also presented. First, a novel technique, which combines two commonly used mathematical approximations of scattering (the Born and Rytov approximations), is demonstrated yielding improved image reconstructions due to the complimentary nature of the approximations. Second, a range migration algorithm is introduced which enables near-field refocusing of a point-spread function (PSF), which is critical for algorithms that rely on measured PSFs to perform image reconstruction. / Thesis / Doctor of Philosophy (PhD) / Breast cancer remains as one of the highest causes of cancer-related deaths in women in Canada. Though X-ray mammography remains the gold standard for regular breast cancer screening, its use of harmful radiation, painful breast compression, and radiologist dependent evaluation remain as detracting factors for its use. Over the past 40 years, researchers have been exploring the use of microwave technology in place of X-ray mammography. Microwave radiation, used at power levels similar to that of a cellphone, has been demonstrated successfully in simulations of breast scans. However, in experimental evaluations with breast phantoms, the complex scattering path of the radiation through tissue complicates image reconstruction. In this thesis, methods of improving the accuracy of microwave algorithms are explored, alongside new breast phantom structures that replicate well the electrical properties of tissue. The results of this work demonstrate the flexibility of microwave imaging, and the adversities that still need to be overcome for it to begin seeing clinical use.

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

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