Cette thèse propose une nouvelle méthode de détection, intermédiaire entre les deux méthodes existantes en OCT, qui sont: l'OCT dans le domaine temporel et l'OCT dans le domaine fréquentiel (FDOCT). La technique OCT que nous présentons est basée sur un réseau de diffraction. Elle fournit le profil de réflectivité en profondeur de l'échantillon analysé instantanément, sans effectuer de balayage mécanique dans le bras de référence de l'interféromètre ni de traitement numérique du signal réfléchi par l'échantillon. Une partie de cette thèse est dédiée à la description du principe de fonctionnement et à l'architecture du dispositif. En introduisant un balayage transversal dans le système, des images en deux dimensions et en trois dimensions de l'échantillon ont été réalisées. Nous décrivons par la suite comment nous accédons à l'information spectroscopique en profondeur de l'échantillon analysé, de façon optique et sans post-traitement grâce à la même technique. Pour cela, un système de démultiplexage en longueur d'onde est introduit dans le dispositif OCT qui devient ainsi un instrument de spectro-tomographie optique de cohérence. De cette façon, pour chaque point objet analysé, une image en deux dimensions est affichée en temps réel sur un détecteur plan. La direction horizontale correspond à la profondeur tandis que la direction verticale correspond à la décomposition spectrale de la trace de corrélation. Nous présentons le principe du système et montrons quelques résultats expérimentaux.

Glaucoma is the second leading cause of blindness in the world. The disease is characterized by irreversible damage to retinal ganglion cells. Once glaucoma is detected, further vision loss can be prevented by pharmacological or surgical treatment. However, current diagnostic methods lack the necessary sensitivity and up to 40% of vision maybe irreversibly lost before detection occurs. A Swept Source Polarization-Sensitive Optical Coherence Tomography (SS-PSOCT) instrument for high sensitivity cross-sectional imaging of optical anisotropy in turbid media has been designed, constructed, and verified. A multiple-state nonlinear fitting algorithm was used to measure birefringence of the retinal nerve fiber layer with less than 1%± average uncertainty. To perform eye imaging efficiently a slit-lamp based interface for the SS-PSOCT instrument with a Line Scanning Laser Ophthalmoscope (LSLO) was used. This interface allowed for repeatable, stable, and registered measurements of the retina. A fixation target was used to stabilize the volunteer’s eye and image desired areas of the retina. The LSLO allowed for an optimization of the location of OCT scans on the retina and provided a fundus blood vessel signature for registration between different imaging sessions. The SS-PSOCT system was used to measure depth-resolved thickness, birefringence, phase retardation and optic axis orientation of the retinal nerve fiber layer in normal volunteers. The peripapillary area around the optic nerve head (ONH) is most sensitive to glaucoma changes and hence data was acquired as concentric ring scans about the ONH with increasing diameters from 2mm to 5mm. Imaging of normal patients showed that higher values of phase retardation occurred superior and inferior to the optic nerve head especially next to blood vessels and thicker parts of the retinal nerve fiber layer. / text

Today, medical imaging is playing an important role in medicine as it provides the techniques and processes used to create images of the human body or parts thereof for clinical purposes (medical procedures seeking to reveal, diagnose or examine disease) or medical science (including the study of normal anatomy and function). Modalities are developing over time to achieve the highest possible resolution, speed of image acquisition, sensitivity, and specificity. In the past decade, advances in optics, fiber, as well as laser technology have enabled the development of noninvasive optical biomedical imaging technology that can also be applied to endoscopy to reach deeper locations in the human body. The purpose of this dissertation is to investigate a full system design and optimization of an optical coherence tomography (OCT) system to achieve high axial and lateral resolution together with an extended depth of focus for endoscopic in vivo imaging. In this research aimed at advancing endoscopic OCT imaging, two high axial resolution optical coherence tomography systems were developed: (1) a spectrometer-based frequency-domain (FD) OCT achieving an axial resolution of ~2.5 µm using a Ti:Sa femtosecond laser with a 120nm bandwidth centered at 800nm and (2) a swept-source based FD OCT employing a high speed Fourier domain mode locked (FDML) laser that achieves real time in vivo imaging with ~8 µm axial resolution at an acquisition speed of 90,000 A-scans/sec. A critical prior limitation of FD OCT systems is the presence of mirror images in the image reconstruction algorithm that could only be eliminated at the expense of depth and speed of imaging. A key contribution of this research is the development of a novel FD OCT imager that enables full range depth imaging without a loss in acquisition speed. Furthermore, towards the need for better axial resolution, we developed a mathematical model of the OCT signal that includes the effect on phase modulation of phase delay, group delay, and dispersion. From the mathematical model we saw that a Fourier domain optical delay line (FD ODL) incorporated into the reference arm of the OCT system represented a path to higher performance. Here we then present a method to compensate for overall system dispersion with a FDODL that maintains the axial resolution at the limit determined solely by the coherence length of a broadband source. In the development of OCT for endoscopic applications, the need for long depth of focus imaging is critical to accommodate the placement of the catheter anywhere within a vessel. A potential solution to this challenge is Bessel-beam imaging. In a first step, a Bessel-beam based confocal scanning optical microscopy (BCSOM) using an axicon and single mode fiber was investigated with a mathematical model and simulation. The BCSOM approach was then implemented in a FD OCT system that delivered high lateral resolution over a long depth of focus. We reported on the imaging in biological samples for the first time with a double-pass microoptics axicon that demonstrated clearly invariant SNR and 8 um lateral resolution images across a 4 mm depth of focus. Finally, we describe the design and fabrication of a catheter incorporated in the FD OCT. The design, conceived for a 5 mm outer diameter catheter, allows 360 degree scanning with a lateral resolution of about 5 um across a depth of focus of about 1.6 mm. The dissertation concludes with comments for related future work.

The Shannon sampling framework is widely used for discrete representation of analog bandlimited signals, starting from samples taken at the Nyquist rate. In many practical applications, signals are not bandlimited. In order to accommodate such signals within the Shannon-Nyquist framework, one typically passes the signal through an anti-aliasing filter, which essentially performs bandlimiting. In applications such as RADAR, SONAR, ultrasound imaging, optical coherence to-mography, multiband signal communication, wideband spectrum sensing, etc., the signals to be sampled have a certain structure, which could manifest in one of the following forms: (i) sparsity or parsimony in a certain bases; (ii) shift-invariant representation; (iii) multi-band spectrum; (iv) finite rate of innovation property, etc.. By using such structure as a prior, one could devise efficient sampling strategies that operate at sub-Nyquist rates. In this Ph.D. thesis, we consider the problem of sampling and reconstruction of finite-rate-of-innovation (FRI) signals, which fall in one of the two classes: (i) Sum-of-weighted and time-shifted (SWTS) pulses; and (ii) Sum-of-weighted exponential (SWE). Finite-rate-of-innovation signals are not necessarily bandlimited, but they are specified by a finite number of free parameters per unit time interval. Hence, the FRI reconstruction problem could be solved by estimating the parameters starting from measurements on the signal. Typically, parameter estimation is done using high-resolution spectral estimation (HRSE) techniques such as the annihilating filter, matrix pencil method, estimation of signal parameter via rotational invariance technique (ESPRIT), etc.. The sampling issues include design of the sampling kernel and choice of the sampling grid structure. Following a frequency-domain reconstruction approach, we propose a novel technique to design compactly supported sampling kernels. The key idea is to cancel aliasing at certain set of uniformly spaced frequencies and make sure that the rest of the frequency response is specified such that the kernel follows the Paley-Wiener criterion for compactly supported functions. To assess the robustness in the presence of noise, we consider a particular class of the proposed kernel whose impulse response has the form of sum of modulated splines (SMS). In the presence of continuous-time and digital noise cases, we show that the reconstruction accuracy is improved by 5 to 25 dB by using the SMS kernel compared with the state-of-the-art compactly supported kernels. Apart from noise robustness, the SMS kernel also has polynomial-exponential reproducing property where the exponents are harmonically related. An interesting feature of the SMS kernel, in contrast with E-splines, is that its support is independent of the number of exponentials. In a typical SWTS signal reconstruction mechanism, first, the SWTS signal is trans formed to a SWE signal followed by uniform sampling, and then discrete-domain annihilation is applied for parameter estimation. In this thesis, we develop a continuous-time annihilation approach using the shift operator for estimating the parameters of SWE signals. Instead of using uniform sampling-based HRSE techniques, operator-based annihilation allows us to estimate parameters from structured non-uniform samples (SNS), and gives more accurate parameters estimates. On the application front, we first consider the problem of curve fitting and curve completion, specifically, ellipse fitting to uniform or non-uniform samples. In general, the ellipse fitting problem is solved by minimizing distance metrics such as the algebraic distance, geometric distance, etc.. It is known that when the samples are measured from an incomplete ellipse, such fitting techniques tend to estimate biased ellipse parameters and the estimated ellipses are relatively smaller than the ground truth. By taking into account the FRI property of an ellipse, we show how accurate ellipse fitting can be performed even to data measured from a partial ellipse. Our fitting technique first estimates the underlying sampling rate using annihilating filter and then carries out least-squares regression to estimate the ellipse parameters. The estimated ellipses have lesser bias compared with the state-of-the-art methods and the mean-squared error is lesser by about 2 to 10 dB. We show applications of ellipse fitting in iris images starting from partial edge contours. We found that the proposed method is able to localize iris/pupil more accurately compared with conventional methods. In a related application, we demonstrate curve completion to partial ellipses drawn on a touch-screen tablet. We also applied the FRI principle to imaging applications such as frequency-domain optical-coherence tomography (FDOCT) and nuclear magnetic resonance (NMR) spectroscopy. In these applications, the resolution is limited by the uncertainty principle, which, in turn, is limited by the number of measurements. By establishing the FRI property of the measurements, we show that one could attain super-resolved tomograms and NMR spectra by using the same or lesser number of samples compared with the classical Fourier-based techniques. In the case of FDOCT, by assuming a piecewise-constant refractive index of the specimen, we show that the measurements have SWE form. We show how super-resolved tomograms could be achieved using SNS-based reconstruction technique. To demonstrate clinical relevance, we consider FDOCT measurements obtained from the retinal pigment epithelium (RPE) and photoreceptor inner/outer segments (IS/OS) of the retina. We show that the proposed method is able to resolve the RPE and IS/OS layers by using only 40% of the available samples. In the context of NMR spectroscopy, the measured signal or free induction decay (FID) can be modelled as a SWE signal. Due to the exponential decay, the FIDs are non-stationary. Hence, one cannot directly apply autocorrelation-based methods such as ESPRIT. We develop DEESPRIT, a counterpart of ESPRIT for decaying exponentials. We consider FID measurements taken from amino acid mixture and show that the proposed method is able to resolve two closely spaced frequencies by using only 40% of the measurements. In summary, this thesis focuses on various aspects of sub-Nyquist sampling and demonstrates concrete applications to super-resolution imaging.