Estimation of Jones matrix, birefringence and entropy using Cloude-Pottier decomposition in polarization-sensitive optical coherence tomography.

Polarization sensitive optical coherence tomography (PS-OCT) is a functional extension of OCT. In addition to imaging based on tissue reflectivity, PS-OCT also enables depth-resolved mapping of sample polarization properties such as phase-retardation, birefringent axis orientation, Stokes vectors, and degree of polarization uniformity (DOPU). In this study, PS-OCT was used to investigate the polarization properties of melanin. In-vitro measurements in samples with varying melanin concentrations revealed polarization scrambling, i.e. depolarization of backscattered light. Polarization scrambling in the PS-OCT images was more pronounced for higher melanin concentrations and correlated with the concentration of the melanin granules in the phantoms. Moreover, in-vivo PS-OCT was performed in the retinas of normal subjects and individuals with albinism. Unlike in the normal eye, polarization scrambling in the retinal pigment epithelium (RPE) was less pronounced or even not observable in PS-OCT images of albinos. These results indicate that the depolarizing appearance of pigmented structures like, for instance, the RPE is likely to be caused by the melanin granules contained in these cells.

A polarization sensitive optical coherence tomography (PS-OCT) instrument was used to investigate the retinal pigment epithelium (RPE). The instrument uses the polarization properties of light to record backscattered intensity, retardation and fast axis orientation simultaneously and needs only one measurement per sample location to retrieve these parameters. The polarization state of light backscattered from within the RPE was found to be random. This can be observed in PS-OCT images by random retardation and axis orientation values within the RPE layer. In diseased eyes where the normal retinal structure is corrupted (e.g. RPE atrophy, RPE detachment) the localization of the RPE within OCT images which do not provide polarization information (standard OCT) is rather difficult. Since the RPE is the only structure within the retina to cause this polarization scrambling, PS-OCT can be used for contrast enhancement and enables the exact localization of the RPE in these pathologies. Therefore it is possible to determine if the RPE is still preserved in regions of interest. Furthermore, in patients with RPE atrophy an enhanced penetration depth into the choroid and even into the sclera was observed. Because of birefringence introduced by the sclera the border between choroid and sclera could easily be determined.

Assessing tissue birefringence with imaging modality polarization-sensitive optical coherence tomography (PS-OCT) could improve the characterization of in vivo tissue pathology. Among the birefringent components, collagen may provide invaluable clinical information because of its alteration in disorders ranging from myocardial infarction to arthritis. But the features required of clinical imaging modality in these areas usually include the ability to assess the parameter of interest rapidly and without extensive data analysis, the characteristics that single-detector PS-OCT demonstrates. But beyond detecting organized collagen, which has been previously demonstrated and confirmed with the appropriate histological techniques, additional information can potentially be gained with PS-OCT, including collagen type, form versus intrinsic birefringence, the collagen angle, and the presence of multiple birefringence materials. In part I, we apply the simple but powerful fast-Fourier transform (FFT) to both PS-OCT mathematical modeling and in vitro bovine meniscus for improved PS-OCT data analysis. The FFT analysis yields, in a rapid, straightforward, and easily interpreted manner, information on the presence of multiple birefringent materials, distinguishing the true anatomical structure from patterns in image resulting from alterations in the polarization state and identifying the tissue/phantom optical axes. Therefore the use of the FFT analysis of PS-OCT data provides information on tissue composition beyond identifying the presence of organized collagen in real time and directly from the image without extensive mathematical manipulation or data analysis. In part II, Helistat phantoms (collagen type I) are analyzed with the ultimate goal of improved tissue characterization. This study, along with the data in part I, advance the insights gained from PS-OCT images beyond simply determining the presence or absence of birefringence.

In this paper we compare two radar target direction-of-arrival (DOA) estimation algorithms, the classical moving window (MW) and the asymptotic maximum likelihood (AML) estimators. The first technique for azimuth DOA estimation exploits multiple detections in the same time-on-target and the second one exploits the fact that the radar antenna mechanical scanning impresses an amplitude modulation on the signals backscattered by the target. Performances of the estimators are numerically investigated through Monte Carlo simulation in terms of root-mean-square-error (RMSE), probability of detection for a fixed probability of false alarm, and probability of "splitting". The obtained results show that the asymptotic maximum likelihood estimator generally outperforms the classical moving window estimator.

Morphological changes in the outer retina such as drusen are established biomarkers to diagnose age-related macular degeneration. However, earlier diagnosis might be possible by taking advantage of more subtle changes that accompany tissues that bear polarization-altering properties. To test this hypothesis, we developed a method based on polarization-sensitive optical coherence tomography with which volumetric data sets of the macula were obtained from 10 young (<25 years) and 10 older (>54 years) subjects. All young subjects and 5 of the older subjects had retardance values induced by the retinal pigment epithelium and Bruch's membrane (RPE-BM) complex that were just above the noise floor measurement (5°-13° at 840 nm). In contrast, elevated retardance, up to 180°, was observed in the other 5 older subjects. Analysis of the degree of polarization uniformity (DOPU) demonstrates that reduced DOPU (<0.4) in the RPE is associated with elevated double pass phase retardation (DPPR) below the RPE-BM complex, suggesting that the observed elevated DPPR in older subjects is the result of increased scattering or polarization scrambling. Collectively, our measurements show that the outer retina can undergo dramatic change in its polarization properties with age, and in some cases still retain its clinically normal appearance.

Estimating the failure rate of the log-logistic distribution by smooth adaptive and bias-correction methods

We developed a tissue discrimination algorithm of polarization sensitive optical coherence tomography (PS-OCT) based on the optical properties of tissues. We calculated the three-dimensional (3D) feature vector from the parameters intensity, extinction coefficient, birefringence, which were obtained by PS-OCT. The tissue type of each pixel was determined according to the position of the feature vector in the 3D feature space. The algorithm was applied for discriminating tissues of the human anterior eye segment. The conjunctiva, sclera, trabecular meshwork (TM), cornea, and uvea were well separated in the 3D feature space, and we observed them with good contrast. The TM line can be observed in the 3D discriminated volume, as observed by gonioscopy.We validated our method by applying our algorithm and histological data to porcine eyes. A marker was injected into sub-Tenon's space and the tissues that were anterior to the marker and posterior to the marker were successfully segmented by our algorithm.

Polarization-sensitive optical coherence tomography (PS-OCT) extends OCT by analyzing the polarization states of backscattered light to quantify tissue birefringence. However, conventional implementations require polarization-diverse detection and are therefore incompatible with most commercial OCT systems. As a result, PS-OCT has largely remained restricted to specialized research groups, limiting its broader scientific and clinical use. Here, we present a modular PS-OCT framework that integrates with a standard spectral-domain OCT platform through a detachable rotating achromatic half-wave plate in the sample arm. This waveplate modulates both incident and reflected polarization states. Three or more repeated measurements at distinct waveplate orientations enable reconstruction of the sample's round-trip Jones matrix and the corresponding polarization properties. To mitigate random phase variations between repeated measurements, we introduce a retarder-constrained phase optimization strategy. We validate the framework with imaging of birefringent phantoms and the human retina in vivo, demonstrating reliable reconstruction of retardance and optic axis orientation. This approach requires only minimal hardware modification and is readily deployable on mainstream OCT systems. Lowering technical barriers paves the way for rapid and widespread deployment of PS-OCT across diverse biomedical applications in both research and clinical environments.

Polarization sensitive optical coherence tomography (PS-OCT) is an imaging technique based on light scattering. PS-OCT performs rapid two- and three-dimensional imaging of transparent and translucent samples with micrometer scale resolution. PS-OCT provides image contrast based on the polarization state of backscattered light and has been applied in many biomedical fields as well as in non-medical fields. Thereby, the polarimetric approach enabled imaging with enhanced contrast compared to standard OCT and the quantitative assessment of sample polarization properties. In this article, the basic methodological principles, the state of the art of PS-OCT technologies, and important applications of the technique are reviewed in a concise yet comprehensive way.

Parametrized families of distributions for the circular unitary ensemble in random matrix theory are considered; they are connected to Toeplitz determinants and have many applications in mathematics (for example, to the longest increasing subsequences of random permutations) and physics (for example, to nuclear physics and quantum gravity). We develop a theory for the unknown parameter estimated by an asymptotic maximum likelihood estimator, which, in the limit, behavesas the maximum likelihood estimator if the latter is well defined and the family is sufficiently smooth. They are asymptotically unbiased and normally distributed, where the norming constants are unconventional because of long range dependence.

Leveraging the polarization property of light to evaluate the birefringence of tissues as well as changes due to pathological conditions has been gaining interest over the past two decades with the introduction of different variants of optical coherence tomography (OCT) including polarization-sensitive OCT (PS-OCT) and cross-polarization OCT (CP-OCT). Because OCT sources are partially polarized, PS-OCT and CP-OCT generally require a linear polarizer and polarization-maintaining fibers to enable a linearly polarized input beam into the interferometer. While recent studies have suggested using an unpolarized input beam to reduce the system's complexity, the effect of unpolarized light on the point spread function (PSF) of OCT has not been fully studied. This work proposed a mathematical framework to evaluate the contribution of unpolarized light to the PSF of OCT. Simulation and experiments were performed for three OCT sources to assess the validity of the proposed model. Overall, simulations were in good agreement with experiments and revealed that unpolarized light introduced two additional reflectors into the reflectivity profile of the source, which were more pronounced in the cross-polarization configuration. This additional information can lead to misinterpretation of the birefringence of tissues in PS-OCT and CP-OCT. Their effect on image quality was evaluated in ex vivo corneal imaging of porcine eyeballs.

Polarization sensitive optical coherence tomography (PS-OCT) was used to measure and image retardation and birefringent axis orientation of in vitro human cornea. We used a two-channel PS-OCT system employing a phse sensitive recording of the interferometric signals in two orthogonal polarization channels. Using an algorithm based on a Hilbert transform, it is possible to calculate the retardation and the slow axis orientation of the sample with only one A-scan per transversal measurement location. While the retardation information is encoded in the amplitude ratio of the two interferometric signals, the axis orientation is encoded entirely in their phase difference. We present maps of retardation and slow axis distribution of normal and pathologic human cornea in longitudinal cross sections and en face images, obtained at the back sruface of the cornea. The results can be explained by a birefringence model based on stacked collagen fibril lamellae of different orientations.

The differential Mueller matrix offers useful insight into the polarization properties of biological tissue imaged with polarization sensitive optical coherence tomography. We present the theory and experimentally demonstrate local depolarization in addition to local retardation.

Optimal asymptotic least squares estimation in a singular set-up

A new method based on polarization-sensitive optical coherence tomography (PS-OCT) is introduced to determine the polarization properties of human retinal vessel walls, in vivo. Measurements were obtained near the optic nerve head of three healthy human subjects. The double pass phase retardation per unit depth (DPPR/UD), which is proportional to the birefringence, is higher in artery walls, presumably because of the presence of muscle tissue. Measurements in surrounding retinal nerve fiber layer tissue yielded lower DPPR/UD values, suggesting that the retinal vessel wall tissue near the optic nerve is not covered by retinal nerve fiber layer tissue (0.43°/µm vs. 0.77°/µm, respectively). Measurements were obtained from multiple artery-vein pairs, to quantify the different polarization properties. Measurements were taken along a section of the vessel wall, with changes in DPPR/UD up to 15%, while the vessel wall thickness remained relatively constant. A stationary scan pattern was applied to determine the influence of involuntary eye motion on the measurement, which was significant. Measurements were also analyzed by two examiners, with high inter-observer agreement. The measurement repeatability was determined with measurements that were acquired during multiple visits. An improvement in accuracy can be achieved with an ultra-broad-bandwidth PS-OCT system since it will provide more data points in-depth, which reduces the influence of discretization and helps to facilitate better fitting of the birefringence data.