Mueller matrix decomposition for polarized light assessment of biological tissues

The Mueller matrix represents the transfer function of an optical system in its interactions with polarized light and its elements relate to specific biologically or clinically relevant properties. However, when many optical polarization effects occur simultaneously, the resulting matrix elements represent several “lumped” effects, thus hindering their unique interpretation. Currently, no methods exist to extract these individual properties in turbid media. Here, we present a novel application of a Mueller matrix decomposition methodology that achieves this objective. The methodology is validated theoretically via a novel polarized‐light propagation model, and experimentally in tissue simulating phantoms. The potential of the approach is explored for two specific biomedical applications: monitoring of changes in myocardial tissues following regenerative stem cell therapy, through birefringence‐induced retardation of the light's linear and circular polarizations, and non‐invasive blood glucose measurements through chirality‐induced rotation of the light's linear polarization. Results demonstrate potential for both applications. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential polarization imaging. II. Symmetry properties and calculations

Various differential polarization images or Mueller images of model objects are generated using the equations derived in the previous paper (paper I of this series). These calculated images include models of the higher-order organization of metaphase chromosomes, and show the applicability of the differential polarization imaging method to the elucidation of complex molecular organizations. Then, the symmetry behavior of the Mueller matrix elements upon infinitesimal rotations of the optical components about the optical axis of the imaging system is presented. It is shown that the rotational properties of the Mueller images can be used to eliminate the linear polarization contributions to the M14 and M44 images, which appear when these images are generated with imperfect circular polarizations. The relationships between the 16 bright-field Mueller images for four different media, i.e., linearly and circularly isotropic, circularly anisotropic, linearly anisotropic, and linearly and circularly anisotropic, are also derived. For the first three cases simple relationships between the Mueller images are found and phenomenological equations in terms of the optical coefficients are derived. In the last case there are no specific relationships between the Mueller images and instead we briefly present Schellman and Jensen's method for treating this type of medium. The criterion of spatial resolution between adjacent domains of different optical anisotropy is then derived. It is found that in transitions between domains of opposite anisotropy the classical Rayleigh limit must be replaced by a magnitude criterion which depends on the limits of the sensitivity of the detection. Finally, the feasibility of optical sectioning in differential polarization imaging is demonstrated.     

Alignment maps of tissues: I. Microscopic elliptical polarimetry

An automated method for generating a fiber alignment map in tissues, tissue-equivalents, and other fibrillar materials exhibiting linear and circular optical properties and scattering is presented. This method consists of interrogating the sample with elliptically polarized light from a rotated quarter-wave plate and an effective circular analyzer, and implementing nonlinear regression techniques to estimate parameters defining the optical properties of the optic train and the sample. Thus, an account is made for imperfect and misaligned optic elements. The optic train was modeled using the Mueller matrix representation and the combined sample properties by an exponential matrix. Because a sample's Mueller matrix does not uniquely determine the linear, circular, or scattering properties, the circular properties and effective scattering are estimated for a matched isotropic sample to determine and correct for the linear birefringence of an aligned sample. The method's utility is demonstrated by generating an alignment map of an arterial media-equivalent, a relevant test case because of its circumferential alignment and thus showing the method's sample orientation independence.     

偏振光成像技术用于肿瘤病变检测的研究进展

偏振光成像是一种非标记、无损伤检测技术,它与现有非偏振光学方法硬件兼容,但能提供更丰富的样品结构和光学信息,并且对亚波长微观结构变化十分敏感.最近,偏振光成像方法在生物医学,特别是肿瘤癌症检测领域显示出很好的应用前景.本文介绍了常用的偏振光散射成像方法,包括偏振差、偏振度、旋转线偏振成像、偏振显微、穆勒矩阵成像等,并展示这些偏振方法在生物医学领域,特别是癌症检测方面的最新研究进展.目前偏振差、偏振度等成像方法已被初步用于皮肤癌的诊断,而穆勒矩阵包含更为丰富的组织微观结构信息,因而具有更好的诊断应用前景.通过对穆勒矩阵进行分解、变换等处理,可获得具有明确物理意义的成像参数,并发展为针对不同应用的特异性方法.目前,随着新型光源、偏振器件和探测器的出现,特别是数据计算处理能力的急剧提升,偏振成像在数据解释和测量方法方面的研究快速发展,已经在生物医学领域显示出很好的应用前景.     

Phasor approach of Mueller matrix optical scanning microscopy for biological tissue imaging

Mueller matrix microscopy is an advanced imaging technique providing a full characterization of the optical polarization fingerprint of a sample. The Lu-Chipman (LC) decomposition, a method based on the modeling of elementary polarimetric arrangements and matrix inversions, is the gold standard to extract each polarimetric component separately. However, this models the optical system as a small number of discrete optical elements and requires a priori knowledge of the order in which these elements occur. In stratified media or when the ordering is not known, the interpretation of the LC decomposition becomes difficult. In this work, we propose a new, to our knowledge, representation dedicated to the study of biological tissues that combines Mueller matrix microscopy with a phasor approach. We demonstrate that this method provides an easier and direct interpretation of the retardance images in any birefringent material without the use of mathematical assumptions regarding the structure of the sample and yields comparable contrast to the LC decomposition. By validating this approach through numerical simulations, we demonstrate that it is able to give access to localized structural information, resulting in a simple determination of the birefringent parameters at the microscopic level. We apply our novel, to our knowledge, method to typical biological tissues that are of interest in the field of biomedical diagnosis.     

Nonlinear optical spectroscopy of chiral molecules

We review nonlinear optical processes that are specific to chiral molecules in solution and on surfaces. In contrast to conventional natural optical activity phenomena, which depend linearly on the electric field strength of the optical field, we discuss how optical processes that are nonlinear (quadratic, cubic, and quartic) functions of the electromagnetic field strength may probe optically active centers and chiral vibrations. We show that nonlinear techniques open entirely new ways of exploring chirality in chemical and biological systems: The cubic processes give rise to nonlinear circular dichroism and nonlinear optical rotation and make it possible to observe dynamic chiral processes at ultrafast time scales. The quadratic second-harmonic and sum-frequency-generation phenomena and the quartic processes may arise entirely in the electric-dipole approximation and do not require the use of circularly polarized light to detect chirality. They provide surface selectivity and their observables can be relatively much larger than in linear optical activity. These processes also give rise to the generation of light at a new color, and in liquids this frequency conversion only occurs if the solution is optically active. We survey recent chiral nonlinear optical experiments and give examples of their application to problems of biophysical interest.     

Mueller矩阵在生物医学检测方面应用的实验研究

Mueller矩阵是公认的能很好地表述介质偏振特性的一种方法,由于散射光偏振在生物组织无创伤诊断技术等诸多领域中的重要应用价值,对组织散射特性的Mueller矩阵的研究成为国际上组织光学的热点之一。研究设计了一种新的测量Mueller矩阵的实验装置:斜入射正接收装置,并推导出一组后续数据处理的算法。由此所获得的Mueller矩阵空间分布图的清晰度不亚于其它所报道的,并且测量方法具有结构简单、方便、准确等优点。实验结果表明:入射角影响Mueller矩阵空间分布图;随着介质浓度的增大,随机介质后向散射Mueller矩阵各元素的空间分布图样减小;同时列举了真实生物组织样品(肌肉组织)的后向散射Mueller矩阵的实测结果,由此证明各向异性生物组织的后向散射Mueller矩阵各元素的空间分布图样与纤维的走向有关。     

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

Light interacts with an organism''s integument on a variety of spatial scales. For example in an iridescent bird: nano-scale structures produce color; the milli-scale structure of barbs and barbules largely determines the directional pattern of reflected light; and through the macro-scale spatial structure of overlapping, curved feathers, these directional effects create the visual texture. Milli-scale and macro-scale effects determine where on the organism''s body, and from what viewpoints and under what illumination, the iridescent colors are seen. Thus, the highly directional flash of brilliant color from the iridescent throat of a hummingbird is inadequately explained by its nano-scale structure alone and questions remain. From a given observation point, which milli-scale elements of the feather are oriented to reflect strongly? Do some species produce broader "windows" for observation of iridescence than others? These and similar questions may be asked about any organisms that have evolved a particular surface appearance for signaling, camouflage, or other reasons.In order to study the directional patterns of light scattering from feathers, and their relationship to the bird''s milli-scale morphology, we developed a protocol for measuring light scattered from biological materials using many high-resolution photographs taken with varying illumination and viewing directions. Since we measure scattered light as a function of direction, we can observe the characteristic features in the directional distribution of light scattered from that particular feather, and because barbs and barbules are resolved in our images, we can clearly attribute the directional features to these different milli-scale structures. Keeping the specimen intact preserves the gross-scale scattering behavior seen in nature. The method described here presents a generalized protocol for analyzing spatially- and directionally-varying light scattering from complex biological materials at multiple structural scales.     

Confocal scanning optical microscopy and three-dimensional imaging

Summary— Confocal scanning optical microscopy has significant advantages over conventional fluorescence microscopy: it rejects the out-of-locus light and provides a greater resolution than the wide-field microscope. In laser scanning optical microscopy, the specimen is scanned by a diffraction-limited spot of laser light and the fluorescence emission (or the reflected light) is focused onto a photodetector. The imaged point is then digitized, stored into the memory of a computer and displayed at the appropriate spatial position on a graphic device as a part of a two-dimensional image. Thus, confocal scanning optical microscopy allows accurate non-invasive optical sectioning and further three-dimensional reconstruction of biological specimens. Here we review the recent technological aspects of the principles and uses of the confocal microscope, and we introduce the different methods of three-dimensional imaging.     

Raman optical activity of proteins, carbohydrates and glycoproteins

On account of its sensitivity to chirality, Raman optical activity (ROA), which may be measured as a small difference in the intensity of vibrational Raman scattering from chiral molecules in right- and left-circularly polarized incident light, or as the intensity of a small circularly polarized component in the scattered light, is a powerful probe of the structure of biomolecules. Protein ROA spectra provide information on secondary and tertiary structures of polypeptide backbones, backbone hydration and side-chain conformations, and on structural elements present in unfolded states. Carbohydrate ROA spectra provide information on the central features of carbohydrate stereochemistry, especially that of the glycosidic link. Glycoprotein ROA spectra provide information on both the polypeptide and carbohydrate components. This article describes the ROA technique and presents and discusses the ROA spectra of a selection of proteins, carbohydrates, and a glycoprotein. The many structure-sensitive bands in protein ROA spectra are favorable for applying pattern recognition techniques, illustrated here using nonlinear mapping, to determine structural relationships between different proteins.     

A device for the rapid measurement of molecular model co-ordinates for X-ray crystallography

A device for the rapid and accurate measurement of model molecular co-ordinates, to be used in conjunction with a Richards optical comparator, is described. The device may be operated in either a manual or automatic mode. The manual mode allows an operator to find the co-ordinates of a desired atom by optical superposition of the transmitted image of a small marker light upon the reflected image of the atom to be measured. The automatic mode allows the operator to position the marker light automatically by entering preselected co-ordinates from an electronic console. This mode of operation facilitates the rapid construction and comparison of structures the atomic co-ordinates of which are already known. The device utilizes pulsed stepping motors to position the marker light and incorporates modularized solid-state circuitry throughout. Several applications of the device are described.     

Polarimetric optical scanning microscopy of zebrafish embryonic development using the coherency matrix

Many of the most important resolution improvements in optical microscopy techniques are based on the reduction of scattering effects. The main benefit of polarimetry-based imaging to this end is the discrimination between scattering phenomena originating from complex systems and the experimental noise. The determination of the coherency matrix elements from the experimental Mueller matrix can take advantage of scattering measurements to obtain additional information on the structural organization of a sample. We analyze the contrast mechanisms extracted from (a) the coherency matrix elements, (b) its eigenvalues and (c) the indices of polarimetric purity at different stages of zebrafish embryos, based on previous work using Mueller matrix optical scanning microscopy. We show that the use of the coherency matrix and related decompositions leads to an improvement in the imaging contrast, without requiring any complicated algebraic operations or any a priori knowledge of the sample, in contrast to standard polarimetric methods.     

Differential polarization imaging. I. Theory

A theory of differential polarization imaging is derived using Mueller calculus. It is shown that, for any arbitrary object, 16 images (in general different) can be obtained by combining different incident polarizations of light and measuring the specific polarization components transmitted or scattered by the object. These are called the Mueller images of the object. Mathematical expressions of these images for an object of arbitrary geometry are derived using classical vector diffraction theory and the paraxial and thin lens approximations. The object is described as a collection of point polarizable groups. The electromagnetic fields are calculated using the first Born-Approximation, but extension of the theory to higher-order approximations is shown to be straightforward. These expressions are obtained for the transmission, or bright-field, geometry, and the scattering, or dark-field, configuration. In both cases, the contributions of scattering, absorption, and background illumination to the Mueller images are characterized. The contributions of linear dichroism, circular dichroism, and linear and circular intensity differential scattering to certain Mueller images are established. It is shown that the Mueller images represent a complete two-dimensional mapping of the molecular anisotropy of the object.     

Development of vacuum-ultraviolet circular dichroism measurement system using a polarizing undulator

We have developed an improved circular dichroism (CD) and linear dichroism (LD) simultaneous measurement system for the vacuum ultraviolet (VUV) region by polarization modulation techniques using a four-period Onuki-type crossed undulator as a polarized light source. The system has been constructed at the VUV beamline BL-5 in the electron storage ring TERAS, at AIST. Our improvements, in particular the adoption of an optical chopper as the detection method of incident light, have resulted in a flat baseline and a consequent simplification of the Mueller matrix calculation for our optical system. Based on the Mueller matrix calculation, we have successfully measured real VUV-CD and LD spectra of leucine films for wavelengths down to 160 nm with absolute optical constants. The obtained spectra show good consistency with spectra measured by conventional methods.     

Capturing the surface texture and shape of pollen: a comparison of microscopy techniques

Research on the comparative morphology of pollen grains depends crucially on the application of appropriate microscopy techniques. Information on the performance of microscopy techniques can be used to inform that choice. We compared the ability of several microscopy techniques to provide information on the shape and surface texture of three pollen types with differing morphologies. These techniques are: widefield, apotome, confocal and two-photon microscopy (reflected light techniques), and brightfield and differential interference contrast microscopy (DIC) (transmitted light techniques). We also provide a first view of pollen using super-resolution microscopy. The three pollen types used to contrast the performance of each technique are: Croton hirtus (Euphorbiaceae), Mabea occidentalis (Euphorbiaceae) and Agropyron repens (Poaceae). No single microscopy technique provided an adequate picture of both the shape and surface texture of any of the three pollen types investigated here. The wavelength of incident light, photon-collection ability of the optical technique, signal-to-noise ratio, and the thickness and light absorption characteristics of the exine profoundly affect the recovery of morphological information by a given optical microscopy technique. Reflected light techniques, particularly confocal and two-photon microscopy, best capture pollen shape but provide limited information on very fine surface texture. In contrast, transmitted light techniques, particularly differential interference contrast microscopy, can resolve very fine surface texture but provide limited information on shape. Texture comprising sculptural elements that are spaced near the diffraction limit of light (~250 nm; NDL) presents an acute challenge to optical microscopy. Super-resolution structured illumination microscopy provides data on the NDL texture of A. repens that is more comparable to textural data from scanning electron microscopy than any other optical microscopy technique investigated here. Maximizing the recovery of morphological information from pollen grains should lead to more robust classifications, and an increase in the taxonomic precision with which ancient vegetation can be reconstructed.     

混浊介质后向散射特性的Mueller矩阵实验测量

Mueller矩阵是一种公认的能很好地表述介质偏振特性的方法.由于散射光偏振在生物组织无创伤诊断技术等诸多领域中的重要应用价值,对组织散射特性的Mueller矩阵的研究成为国际上组织光学的热点之一.与现有测量Mueller矩阵的实验方法相比,斜入射正接收装置用来测量Mueuer矩阵是一个更加行之有效的方法,再结合一种新的算法来处理后续数据,由此所获得的Mueller矩阵空间分布图的清晰度不亚于其它文献的报道.这种测量方法结构更简单,具有测量更方便、准确等优点.结果表明:入射角影响Mueller矩阵的空间分布图.随着介质浓度的增大,随机介质后向散射Mueller矩阵各元素的空间分布图样减小.     

A comprehensive study on the electronic structure,dielectric and optical properties of alkali-earth metals and transition metal hydroxides M(OH)2

In the present work, the physical properties of alkali-earth metal and transition metal hydroxides are comprehensively investigated using the density functional theory. Here, the alkali-earth metals Ca, Mg, and transition metals Cd, Zn are considered from the II-A and II-B groups in the periodic table of elements. The first principle electronic structure calculations show that these bulk hydroxide materials are direct band gap material. Ca(OH)₂ and Mg(OH)₂ exhibit an insulating behavior with a very large band gap. However, Cd(OH)₂ and Zn(OH)₂ are found to be wide band gap semiconductors. The dielectric and optical studies reveal that these materials have a high degree of anisotropy. Hence, the light propagation in these materials behaves differently in the direction perpendicular and parallel to the optical axis, and exhibits birefringence. Therefore, these materials may be useful for optical communication. The calculated electron energy loss suggests that these materials can also be used for unwanted signal noise suppression. The wide band gap makes them useful for high-power applications. Moreover, Ca(OH)₂ and Mg(OH)₂ are found to be suitable for dielectric medium.     

Using Optics to Measure Biological Forces and Mechanics

Spanning all size levels, regulating biological forces and transport are fundamental life processes. Used by various investigators over the last dozen years, optical techniques offer unique advantages for studying biological forces. The most mature of these techniques, optical tweezers, or the single-beam optical trap, is commercially available and is used by numerous investigators. Although technical innovations have improved the versatility of optical tweezers, simple optical tweezers continue to provide insights into cell biology. Two new, promising optical technologies, laser-tracking microrheology and the optical stretcher, allow mechanical measurements that are not possible with optical tweezers. Here, I review these various optical technologies and their roles in understanding mechanical forces in cell biology.