Exploration of the retinal nerve fiber layer thickness by measurement of the linear dichroism

An electro-optic device mounted on a slit lamp to assess the degree of polarization of a light beam that has double passed through the retina about the optic-nerve head in the living human eye is described. The asymmetric structure of the retinal nerve's fiber layer possesses a linear-form dichroism and will partially polarize an unpolarized light beam that is scattered at the fundus of the eye and has double passed the ocular media (cornea, lens, retina). This partial polarization is a function of the retinal nerve's fiber layer thickness, and its measurement may be used for exploring glaucoma and other retinal neuropathies. Experimental conditions allow us to neglect corneal dichroism. The first clinical measurements show a different degree of polarization between normal and glaucomatous eyes and a good correlation with the results obtained by optical coherence tomography.     

Diattenuation and polarization preservation of retinal nerve fiber layer reflectance

The diattenuation spectrum of the retinal nerve fiber layer (RNFL) reflectance has been predicted to depend strongly on the relative refractive index (m) of light-scattering cylinders. To constrain the values of m, diattenuation of the RNFL reflectance of isolated rat retina was measured with a multispectral imaging micropolarimeter. The RNFL reflection has very weak intrinsic diattenuation at all wavelengths (400-830 nm), which rejects all values of m > or = 1.03. Degree of polarization (DOP) for reflection from the RNFL was also measured. DOP was close to unity at all wavelengths, which indicates that the RNFL is a polarization-preserving reflector.     

Theoretical model of the polarization properties of the retinal nerve fiber layer in reflection

In several optical technologies for glaucoma diagnosis, polarized light is used to assess the retinal nerve fiber layer (RNFL) of the eye. For better understanding of the polarization properties of the RNFL, it was modeled as a thick birefringent slab containing parallel light-scattering cylinders, and the Mueller matrix for reflectance was derived. The model predicts that (1) the RNFL reflectance has weak intrinsic diattenuation; (2) the diattenuation spectrum depends strongly on the relative refractive indices of the cylinders; (3) both scattering and birefringence contribute to retardation; and (4) the RNFL reflectance generally preserves polarization, but depolarization may be detectable for thick RNFL at short wavelengths.     

Characteristic properties of Mueller matrices

A complete and minimum set of necessary and sufficient conditions for a real 4 x 4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely, the four conditions obtained from the nonnegativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the transmittance condition. Using the properties of H, a demonstration is also presented of Tr(M(T)M) = 4m(2)00 as being a necessary and sufficient condition for a physical Mueller matrix to be a pure Mueller matrix.     

Use of retinal nerve fiber layer birefringence as an addition to absorption in retinal scanning for biometric purposes

We built a device sensitive to the birefringence of the retinal nerve fiber layer for biometric purposes. A circle of 20 degrees diameter on the retina was scanned around the optic disk with a spot of light from a 785 nm laser diode. The nonbirefringent blood vessels indenting or displacing the retinal nerve fiber layer were seen as "blips" in the measured birefringence-derived signal. For comparison, the reflection-absorption signature of the blood vessel pattern in the scanned circle was also measured. The birefringence-derived signal proved to add useful information to the reflectance-absorption signature for retinal biometric scanning.     

Noise distribution of Mueller matrices retrieved with active rotating polarimeters

Two methods used to retrieve Mueller matrices from intensity measurements are revisited. It is shown that with symmetry or orthogonality considerations, numerical inversions of polarimetric equations can be avoided. With the obtained analytical formulas, noise propagation can be analyzed. If the intensity noise is a Gaussian white noise, the noise of Mueller matrices features remarkable properties. Mueller components are mutually correlated according to a scheme that involves decomposition into four blocks of 2x2 matrices. Variances are unequally distributed: the middle 2x2 block has the highest variance, the element on the bottom right has the lowest. These characteristics have been validated on experimental Mueller images of the free space.     

Linear dichroism of the cornea

The dichroic properties of in vitro sheep corneas were studied with a spectrophotometer in transmission mode for several angles of incidence of light beams. Several models of corneal anisotropy have been presented in the literature. The results presented here allow us to believe that the cornea behaves as a dichroic biaxial crystal. Furthermore, this dichroism is weak when the angle of incidence on the corneal surface stays small. The mathematical model that describes these optical properties of the cornea uses Mueller matrices.     

Light scattering and form birefringence of parallel cylindrical arrays that represent cellular organelles of the retinal nerve fiber layer

The retinal nerve fiber layer (RNFL) comprises bundles of unmyelinated axons that run across the surface of the retina. The cylindrical organelles of the RNFL (axonal membranes, microtubules, neurofilaments, and mitochondria) as seen by electron microscopy were modeled as parallel cylindrical arrays in order to gain insight into their optical properties. Arrays of thin fibrils were used to represent organelles that are thin relative to wavelength, and the model took into account interference effects that may arise from spatial order. Angular and spectral light-scattering functions were calculated for the backscattering hemisphere. Scattering was much larger from axonal membranes than from microtubules or neurofilaments. Spectra from 400 to 700 nm show that scattering increases at shorter wavelengths for both axonal membranes and microtubules. At 560 nm, scattering from mitochondria modeled as thick cylinders was approximately the same as that from microtubules but showed little wavelength dependence. The model reveals differences in backscattered polarization ratios that may permit experimental discrimination between microtubule and membrane mechanisms for the RNFL reflectance. Calculated backscattering exceeds measured values by at least 1 order of magnitude, but calculated form birefringence for microtubule arrays is approximately the same as measured birefringence.     

Definition of a parametric form of nonsingular Mueller matrices

The goal of this paper is to propose a mathematical framework to define and analyze a general parametric form of an arbitrary nonsingular Mueller matrix. Starting from previous results about nondepolarizing matrices, we generalize the method to any nonsingular Mueller matrix. We address this problem in a six-dimensional space in order to introduce a transformation group with the same number of degrees of freedom and explain why subsets of O(5,1), the orthogonal group associated with six-dimensional Minkowski space, is a physically admissible solution to this question. Generators of this group are used to define possible expressions of an arbitrary nonsingular Mueller matrix. Ultimately, the problem of decomposition of these matrices is addressed, and we point out that the "reverse" and "forward" decomposition concepts recently introduced may be inferred from the formalism we propose.     

Interpretation of nondepolarizing Mueller matrices based on singular-value decomposition

A product decomposition of a nondepolarizing Mueller matrix consisting of the sequence of three factors--a first linear retarder, a horizontal or vertical "retarding diattenuator," and a second linear retarder--is proposed. Each matrix factor can be readily identified with one or two basic polarization devices such as partial polarizers and retardation waveplates. The decomposition allows for a straightforward interpretation and parameterization of an experimentally determined Mueller matrix in terms of an arrangement of polarization devices and their characteristic parameters: diattenuations, retardances, and axis azimuths. Its application is illustrated on an experimentally determined Mueller matrix.     

On the algebraic characterization of a Mueller matrix in polarization optics. II. Necessary and sufficient conditions for Jones-derived Mueller matrices

Abstract

We show that every Mueller matrix, that is a real 4 × 4 matrix M which transforms Stokes vectors into Stokes vectors, may be factored as M = L ₂ KL ₁ where L ₁ and L ₂ are orthochronous proper Lorentz matrices and K is a canonical Mueller matrix having only two different forms, namely a diagonal form for type-I Mueller matrices and a non-diagonal form (with only one non-zero off-diagonal element) for type-II Mueller matrices. Using the general forms of Mueller matrices so derived, we then obtain the necessary and sufficient conditions for a Mueller matrix M to be Jones derived. These conditions for Jones derivability, unlike the Cloude conditions which are expressed in terms of the eigenvalues of the Hermitian coherency matrix T associated with M, characterize a Jones-derived matrix M through the G eigenvalues and G eigenvectors of the real symmetric N matrix N = [Mtilde]GM associated with M. Appending the passivity conditions for a Mueller matrix onto these Jones-derivability conditions, we then arrive at an algebraic identification of the physically important class of passive Jones-derived Mueller matrices.     

Imaging of the optic disc and retinal nerve fiber layer: the effects of age, optic disc area, refractive error, and gender.

We cross-sectionally examined the relationship between age, optic disc area, refraction, and gender and optic disc topography and retinal nerve fiber layer (RNFL) measurements, using optical imaging techniques. One eye from each of 155 Caucasian subjects (age range 23.0-80.8 y) without ocular pathology was included. Measurements were obtained by using the Heidelberg Retina Tomography (HRT), the GDx Nerve Fiber Analyzer, and the Optical Coherence Tomograph (OCT). The effects of age were small (R2 < 17%) and were limited to specific HRT, GDx, and OCT parameters. Disc area was significantly associated with most HRT parameters and isolated GDx and OCT parameters. Refraction and gender were not significantly associated with any optic disc or RNFL parameters. Although effects of age on the optic disc and RNFL are small, they should be considered in monitoring ocular disease. Optic disc area should be considered when cross-sectionally evaluating disc topography and, to a lesser extent, RNFL thickness.     

Relating retinal nerve fiber thickness to behavioral sensitivity in patients with glaucoma: application of a linear model

Glaucoma causes damage to the retinal ganglion cells and their axons, and this damage can be detected with both structural and functional tests. The purpose of this study was to better understand the relationship between a structural measure of retinal nerve fiber layer (RNFL) and the most common functional test, behavioral sensitivity with static automated perimetry (SAP). First, a linear model, previously shown to describe the relationship between local visual evoked potentials and SAP sensitivity, was modified to predict the change in RNFL as measured by optical coherence tomography. Second, previous work by others was shown to be consistent with this model.     

Size determination by use of two-dimensional Mueller matrices backscattered by optically thick random media

Here we are concerned with the systematic study of polarized light transport in thick, isotropic, homogeneous random media and of the associated inverse problem. An original spatial and intensity rescaling of the polarization transport allows one to account implicitly for the volume fraction. This parameter elimination permits a complete exploration, by means of Monte Carlo simulations of the dependence of polarized light transport on microscopic parameters. Analysis of the Mueller matrices obtained from the simulations show that additional correlations (with respect to scalar transport) are obtained between the microscopic parameters and the spatial distribution of specific elements of the Mueller matrix. As a consequence, using carefully chosen polarization states, one can determine an average particle size independently of the volume fraction of particles, with only the knowledge of the refractive-index ratio being required. This analysis is validated with experimental Mueller matrices obtained for emulsions of various size, concentration, and polydispersity.     

Investigation of Mueller matrices of anisotropic nonhomogeneous layers in application to an optical model of the cornea

We consider a system of anisotropic layers as an optical model of the eye cornea. Effective refraction indices for normally incident light are calculated with the assumption that each layer consists of closely packed uniform cylinders (fibrils). Jones matrix formalism is used to describe light propagation through the cornea. We calculate the Jones matrices from the experimentally measured Mueller matrices. Two algorithms are used for this purpose. The experiments have shown that ~20% of cornea area studied had the structure well described by the helical model proposed.     

Analysis of textured films and periodic grating structures with Mueller matrices: A new challenge in instrumentation with the generation of angle-resolved SE polarimeters

Current Mueller polarimeters, with either spectral or angular resolution, feature high enough precision and speed to be suitable for many demanding applications, with specific advantages over conventional spectroscopic ellipsometry (SE). Due to the simultaneous determination of depolarization, birefringence and diattenuation Mueller polarimetry (MP) can open new fields in surface and thin film characterization techniques with new and very powerful intrinsic analyses of roughness and/or anisotropy. For more conventional applications, such as scatterometry (i.e. the determination of the shape of periodic structures from optical measurements, mostly used in microelectronics), MP may overpass SE in terms of systematic errors and/or measurement spot size, as discussed from two examples. However, numerical simulations remain a key point to take full advantage of MP capabilities for the new challenges emerging in nanometrology.     

不同聚合物基压电纤维复合材料应变性能的温度稳定性

压电纤维复合材料驱动器应用于航天器件中时要经历严酷的环境载荷,其中温度对压电纤维复合材料驱动性能的影响至关重要.本研究制备了三种不同聚合物基压电纤维复合材料,并在-15～60℃的环境温度下测试了压电纤维复合材料的自由应变性能.结果表明,不同聚合物基压电纤维复合材料的自由应变性能均强烈依赖于环境温度,其自由应变性能均呈现...     

Comparison of polarimetric techniques for the identification of biological and chemical materials using Mueller matrices, lateral waves, and surface waves

Optical polarimetric techniques to identify and characterize biological and chemical materials have received much attention recently for their broad applications in biophotonics, biochemistry, biomedicine, and pharmacology. We present here several options for the measurement of optical rotation, diattenuation, and the index of depolarization. These include polar decomposition, identification of specific pairs of Mueller matrix elements that are proportional to optical activity, and the cross-polarized components of lateral waves and surface waves at the interface between free space and the optically active material.     

树脂基搭接碳纤维智能层的力阻特性

提出一种具有局部搭接结构的树脂基碳纤维智能层, 将其敷设于结构表面以检测结构受载时的变形, 实现对结构大范围监测。基于该智能层, 采用单轴拉伸和三点弯曲的加载方式, 对构件进行应变和位移检测。实验发现, 碳纤维局部搭接结构是引起力阻效应的主要因素, 其单位应变的电阻率变化的灵敏度达到104, 相当于非搭接连续碳纤维复合材料力阻效应灵敏度的34倍。实验结果还进一步表明, 树脂基搭接碳纤维智能层力阻曲线光滑稳定, 其传感极限约为8500 με。建立了树脂基搭接碳纤维复合材料的电学模型, 揭示了这种力阻效应主要来源于搭接界面处层间电阻的变化, 并从纤维轴向力、搭接面积和层间剪应变三个方面解释了这种层间电阻变化的机制。