Calculation of protein form birefringence using the finite element method.

An approach based on the finite element method (FEM) is employed to calculate the optical properties of macromolecules, specifically form birefringence. Macromolecules are treated as arbitrarily shaped particles suspended in a solvent of refraction index n1. The form birefringence of the solution is calculated as the difference in its refractive index when all the particles of refractive index n2 are either parallel to or normal to the direction of the polarization of light. Since the particles of interest are small compared to the wavelength of light, a quasi-static approximation for the refractive index is used, i.e., that it is equal to the square root of the dielectric constant of the suspension. The average dielectric constant of the mixture is calculated using the finite element method. This approach has been tested for ellipsoidal particles and a good agreement with theoretical results has been obtained. Also, numerical results for the motor domains of ncd and kinesin, small arbitrarily shaped proteins with known x-ray structures, show reasonable agreement with the experimental data obtained from transient electric birefringence experiments.     

Microtubular origin of mitotic spindle form birefringence. Demonstration of the applicability of Wiener''s equation

Meiosis I metaphase spindles were isolated from oocytes of the sea-star Pisaster ochraceus by a method that produced no detectable net loss in spindle birefringence. Some of the spindles were fixed immediately and embedded and sectioned for electron microscopy. Others were laminated between gelatine pellicles in a perfusion chamber, then fixed and sequentially and reversibly imbibed with a series of media of increasing refractive indices. Electron microscopy showed little else besides microtubules in the isolates, and no other component present could account for the observed form birefringence. An Ambronn plot of the birefringent retardation measured during imbibition was a good least squares fit to a computer generated theoretical curve based on the Bragg-Pippard rederivation of the Wiener curve for form birefringence. The data were best fit by the curve for rodlet index (n1) = 1.512, rodlet volume fraction (f) = 0.0206, and coefficient of intrinsic birefringence = 4.7 X 10(-5). The value obtained for n1 is unequivocal and is virtually as good as the refractometer determinations of imbibing medium index on which it is based. The optically interactive volume of the microtubule subunit, calculated from our electron microscope determination of spindle microtubule distribution (106/mum2), 13 protofilaments per microtubules, an 8 nm repeat distance and our best value for f, is compatible with known subunit dimensions as determined by other means. We also report curves fitted to the results of Ambronn imbibition of Bouin's-fixed Lytechinus spindles and to the Noll and Weber muscle imbibition data.     

Modeling the rod outer segment birefringence change correlated with metarhodopsin II formation.

A rapid birefringence loss associated with metarhodopsin II formation, delta (delta n) MII, is produced when frog rod outer segments are exposed to a bleaching light flash. To analyze the nature of the underlying structure change, measurements of delta (delta n) MII were made in rod outer segments perfused with glycerol solutions to increase the refractive index of the cytoplasmic and intradisk spaces. Comparisons of experimental results with computed changes in the form birefringence component using two- and three-dielectric outer segment models for several putative structure changes were made. It is concluded that delta (delta n) MII can be due to either a change in the intrinsic birefringence component caused by the reorientation of anisotropic molecules, or to a change in the form birefringence component caused by small changes in the cytoplasmic and/or intradisk volumes.     

Light transmission in the human cornea as a function of position across the ocular surface: theoretical and experimental aspects

This article investigates the theoretical basis for differences in visible light transmission through the human cornea as a function of distance from the center. Experimentally, transmission decreases approximately linearly up to 3 mm from the central axis, then quadratically beyond this. It is known that collagen fibril number density and collagen fibril radii change from the central region to the corneal periphery. We modeled, using the direct-summation-of-scattered-fields method, the effects these ultrastructural changes would be expected to have on light transmission, accounting for the increase in corneal thickness from center to edge. Fibril positions for the modeling were obtained from electron micrographs of human cornea. Theoretically, transmission remains fairly constant across the central cornea; then, as the fibril diameter increases, the predicted scattering increases. Interfibrillar spacing changes alter the refractive index ratio between matrix and fibril; this was modeled in our theoretical deductions. Fibril number density had a minimal effect on light propagation. Our theoretical deductions were in broad agreement with our experimental data. It is concluded that the reduced transparency in the peripheral stroma is primarily caused by changes in fibril radius and an increase in refractive index ratio between the fibril and the interfibrillar substance.     

Optically eliminating the visible outlines of pores in intact polycarbonate (Nuclepore) filters

Under the microscope, Nuclepore filters display pore outlines. The polycarbonate material has two refractive indices (n = 1.584 and 1.616), which polarize transmitted light into two sets of rays at right angles to one another. This birefringence was used to eliminate the image of the pore outlines by the use of a specially made mounting medium with n20D = 1.584 in combination with polarized light: in a filter preparation of human leukocytes mounted in a medium with one matching refractive index and focused in polarized light, pore outlines were not visible. The preparation of the matching mounting medium, its use and its properties are described and discussed.     

Birefringence of actin.

The total strain birefringence of F-actin isolated from chicken gizzards was measured as a function of elongation in thin transparent films. Each film held at a certain elongation in a jig was allowed to swell in a penetrating but nondissolving liquid. Seven liquids with different refractive indices were employed. The thickness of the film in each swelling liquid was obtained once equilibrium was established. At each elongation, from 0 to 16%, a Wiener curve was obtained. The minima of the Wiener curves yielded the intrinsic birefringence of F-actin as a function of elongation. The intrinsic birefringence increases with elongation up to 16%, above which the thin films break. The form birefringence at a set refractive index also increases with elongation. The implication of the strain birefringence of F-actin is discussed as it affects the optical properties, mainly light scattering, of tissues such as the fiber cells of lens of the eye.     

A NEW METHOD OF POLARIZATION MICROSCOPIC ANALYSIS : I. Scanning with a Birefringence Detection System

A new method of polarized light analysis is described in which a highly sensitive electronic detector specific for birefringence is used to identify the crystalline axes of an object and then measure its phase retardation due to birefringence. The microscopic system employed in the method consists of an electronic birefringence detection system (BDS), a microscope with strain-free lenses, and a driven stage for passing the specimen at appropriate velocities across the image of an aperture placed at the field stop and imaged in the specimen plane by the condenser. The detector registers retardations directly as voltage at a constant deflection sensitivity of ca. 1.1 v per angstrom unit over a range of 120 angstrom units. The basal rms noise level is 0.002 A for a spot 36 µ in diameter formed by a 95 x, N. A. 1.25 objective pair, and increases in proportion to the reciprocal of the diameter of the scanning spot. The increase in noise with high resolution scanning can be offset by increasing the instrumental time constant, which is adjustable in decades between 0.004 and 0.4 seconds. A number of difficult problems in high extinction polarization microscopy are avoided by the use of modulated light and a rapid electronic detector. For example: (a) The measured distribution of birefringence is unaffected by the usual diffraction anomaly; therefore polarization rectifiers are not required. (b) The detector is selective for birefringence, so that there is no problem in separating contrast due to different optical properties (e.g. dichroism, light scattering). (c) The speed and sensitivity are both increased by between one and two orders of magnitude over that attainable by visual or photographic methods, thereby rendering a vast number of weakly birefringent, light-scattering, and motile objects readily analyzable for the first time with polarized light.     

A long-lasting birefringence change recorded from a tetanically stimulated squid giant axon.

A long-lasting birefringence change (the delayed response) was found to be produced in a tetanically stimulated squid giant axon. The change was independent of the concurrent membrane potential change, summated on repetitive stimulation, and always had a sign representing a decrease in resting birefringence. The axons was placed between a polarizer and an analyzer with their polarizing axes crossed, making an angle of 45 degrees with the longitudinal direction of the axon. The light beam that passed through the axon and the other optical elements was received by a photodiode. The change in light intensity evoked by repetitive stimulation was composed of brief initial responses, which took place in response to individual stimuli, and a delayed response, which developed gradually and lasted for several hundred msec. It was necessary to differentiate the effect of birefringence change from that of turbidity change. Formulas were derived on the assumption that the optical properties of the axon could be represented by a model of a uniaxial crystal that was not only birefringent but also dichroic, its extinction coefficients and the angle of retardation being changed independently on excitation. Calculations with them yielded the resting retardation, which agreed well with those obtained by the Senarmont's method, and the change in birefringence, which agreed well with the other calculated value derived from experiments using a quarter-wave plate. The results of the calculation confirmed the existence of the long-lasting birefringence change in the tetanically stimulated axon.     

Changes in the refractive index of the stroma and its extrafibrillar matrix when the cornea swells

The transparency of the corneal stroma is critically dependent on the hydration of the tissue; if the cornea swells, light scattering increases. Although this scattering has been ascribed to the disruption caused to the arrangement of the collagen fibrils, theory predicts that light scattering could increase if there is an increased mismatch in the refractive indices of the collagen fibrils and the material between them. The purpose of this article is to use Gladstone and Dale's law of mixtures to calculate volume fractions for a number of different constituents in the stroma, and use these to show how the refractive indices of the stroma and its constituent extrafibrillar material would be expected to change as more solvent enters the tissue. Our calculations predict that solvent entering the extrafibrillar space causes a reduction in its refractive index, and hence a reduction in the overall refractive index of the bovine stroma according to the equation n'(s) = 1.335 + 0.04/(0.22 + 0.24 H'), where n'(s) is the refractive index and H' is the hydration of the swollen stroma. This expression is in reasonable agreement with our experimental measurements of refractive index versus hydration in bovine corneas. When the hydration of the stroma increases from H = 3.2 to H = 8.0, we predict that the ratio of the refractive index of the collagen fibrils to that of the material between them increases from 1.041 to 1.052. This change would be expected to make only a small contribution to the large increase in light scattering observed when the cornea swells to H = 8.     

A long-lasting birefringence change recorded from a tetanically stimulated squid giant axon

A long-lasting birefringence change (the delayed response) was found to be produced in a tetanically stimulated squid giant axon. The change was independent of the concurrent membrane potential change, summated on repetitive stimulation, and always had a sign representing a decrease in resting birefringence. The axon was placed between a polarizer and an analyzer with their polarizing axes crossed, making an angle of 45° with the longitudinal direction of the axon. The light beam that passed through the axon and the other optical elements was received by a photodiode. The change in light intensity evoked by repetitive stimulation was composed of brief initial responses, which took place in response to individual stimuli, and a delayed response, which developed gradually and lasted for several hundred msec. It was necessary to differentiate the effect of birefringence change from that of turbidity change. Formulas were derived on the assumption that the optical properties of the axon could be represented by a model of a uniaxial crystal that was not only birefringent but also dichroic, its extinction coefficients and the angle of retardation being changed independently on excitation. Calculations with them yielded the resting retardation, which agreed well with those obtained by the Sénarmont's method, and the change in birefringence, which agreed well with the other calculated value derived from experiments using a quarter-wave plate. The results of the calculation confirmed the existence of the long-lasting birefringence change in the tetanically stimulated axon.     

Biofilm thickness measurements by light microscopy

Light microscopy has been used to measure biofilm thickness. The vertical displacement of the sample required to focus from the biofilm-liquid interface to the biofilm-substratum interface is measured by the stage micrometer. Biofilm thickness is proportional, but not equal, to the measured vertical displacement. An expression for the proportionality constant, k_f, in terms of refractive indices is determined from a geometric analysis of the light path. k_f can be estimated as the ratio of the refractive index of the film to the refractive index of the media interfacing the film between the objective lens and the sample. The thickness of any transparent film may be determined by light microscopy when the refractive index of the film is known.     

Negative refraction angular characterization in one-dimensional photonic crystals

Background

Photonic crystals are artificial structures that have periodic dielectric components with different refractive indices. Under certain conditions, they abnormally refract the light, a phenomenon called negative refraction. Here we experimentally characterize negative refraction in a one dimensional photonic crystal structure; near the low frequency edge of the fourth photonic bandgap. We compare the experimental results with current theory and a theory based on the group velocity developed here. We also analytically derived the negative refraction correctness condition that gives the angular region where negative refraction occurs.

Methodology/Principal Findings

By using standard photonic techniques we experimentally determined the relationship between incidence and negative refraction angles and found the negative refraction range by applying the correctness condition. In order to compare both theories with experimental results an output refraction correction was utilized. The correction uses Snell''s law and an effective refractive index based on two effective dielectric constants. We found good agreement between experiment and both theories in the negative refraction zone.

Conclusions/Significance

Since both theories and the experimental observations agreed well in the negative refraction region, we can use both negative refraction theories plus the output correction to predict negative refraction angles. This can be very useful from a practical point of view for space filtering applications such as a photonic demultiplexer or for sensing applications.     

位相分辨偏振灵敏光学相干层析术:组织双折射特性的成像与定量分析

我们研制了一种基于光纤的位相分辨偏振灵敏光学相干层析成像系统。该系统中的偏振状态控制设量在参考臂而非光源臂上,因而使得光抵达样品的传输效率大大提高。鉴于光源的部分偏振性,入射于样品上的光含有任意偏振状态的分量,通过对参考光偏振状态的调制,就可相干地提取对应于入射光四种正交偏振状态并经样品后向散射的光信号。基于斯托克斯矢量夹角在无损光纤系统传输的变换不变性,我们能利用测量臂中光信号的斯托克斯参数来确定双折射样品深度分辨的位相延迟信息。利用所研制的偏振灵敏光学相干层析成像系统,不仅确认了韧带和软骨的双折射性质,而且定量分析了不同条件下韧带的双折射变化．研究结果表明：韧带松弛可使其双折射特性明显减弱,而韧带经拉伸后,其双折射特性的变化却不明显。     

Optical Fiber Micro-Taper with Circular Symmetric Gold Coating for Sensor Applications Based on Surface Plasmon Resonance

We describe a novel, fully symmetrical deposition method, based on a sputtering technique and use of a gold ring target for deposition of a gold layer uniform around the taper waist. With such a circular symmetric coating, the plasmon resonance effect in the fiber taper becomes completely independent of the polarization of the illuminating light. We have measured the complex refractive index of such sputtered gold layers. On this basis, model calculations have been performed to describe the plasmon resonance as a function of taper waist diameter, gold layer thickness, analyte interaction length, and analyte refractive index. Optimized parameters especially for measurement in aqueous solutions are derived from these theoretical calculations. Experimental results are shown to be in good agreement with the theoretical analysis.     

Temperature dependence of optical properties of aqueous dispersions of phosphatidylcholine

Aqueous dispersions of dipalmitoyl phosphatidyl choline exhibit a sharp decrease in turbidity at the crystal-liquid phase transition temperature of 41°C. The intensity of light scattered at 45°, 90°, and 135° also undergoes a sharp drop at the same temperature. Similarly, the refractive index of such dispersions decreases abruptly with the phase transition. Employing the relationship between light scattering intensity and specific refractive increment, it can be shown that about one half of the change in absorbancy and scattering are accounted for by the change in refractive index. The change in refractive index can be entirely accounted for by the known expansion and corresponding decrease in density of the bilayer. That part of the observed change in scattering and turbidity which is not accounted for by the observed change in average refractive index is apparently due to a decrease in the anisotropy of the bilayer during the melting process. Calculations based on a model which, although oversimplified, is consistent with the known thinning of the bilayer during the melting process, give quantitative agreement with experimental results. Below the phase transition temperature other changes in optical properties are observed; near 32°C, the light scattering envelope changes and the turbidity of dispersions drops markedly. The average refractive index remains constant in this region. For this and other reasons, it is postulated that these pre-transition changes indicate an aggregation-disaggregation phenomenon.     

Morphological characterization of tendon development during chick embryogenesis: measurement of birefringence retardation

Morphological observations and physical measurement of (I) birefringence retardation, (2) mean fibre profile width, and (3) cell volume fraction were used to characterize chick hind limb extensor tendon development. Observations were made at days 7, 10, 14 and 17 embryologic and 1-1.5 post-hatching. Microanatomical observations illustrated a sequential development of tendon microanatomy consisting of (1) a uniaxial cellular framework with discontinuous collagen fibril bundles present in day 7 embryos; (2) a continuous network of birefringent collagen fibres, and early evidence of tendon fasciculation and crimp development by embryonic day 10; and (3) completion of the basic cytoarchitecture of tendon observed at day 14 of embryogenesis. These observations suggest that collagen deposition in tendon involves first a longitudinal and then a lateral organization of tendon fibroblasts. Associated with the progressive anatomical development of tendon was an increase in birefringence retardation, mean collagen fibre profile width, and a decrease in the cell volume fraction. Birefringence retardation per unit thickness, however, did not change. This suggested that the fibril packing density of the fibres remained constant, although the fibres were observed to increase in size. These results indicate that collagen fibrillogenesis in vivo can be quantitatively studied by measurement of the birefringence retardation using polarized light.     

Birefringence of tropomyosin crystals.

The birefringence of tropomyosin crystals was measured in the temperature range 5 degrees-35 degrees C. The experimental results are compared with a simple model calculation based on the theory developed by Wiener for the optical properties of colloidal systems. The difference between experimental and theoretical values is less than 15%, which denotes a good agreement given the simplicity of the model. A value of 0.011 was obtained for the intrinsic birefringence of the tropomyosin molecule. The temperature dependence of the crystal birefringence could be accounted for in part by a change of the unit cell parameters; this change was experimentally observed by others in x-ray diffraction experiments.     

Specimen preparation and quantification of collagen birefringence in unstained sections of articular cartilage using image analysis and polarizing light microscopy

To establish an optimal method for analysis of the collagen structures from unstained tissue sections, a computerized image analysis system using a charge coupled device camera coupled to a polarizing light microscope was used. Retardation values of birefringence, which are proportional to the content and fibril orientation of collagen in the extracellular matrix of articular cartilage, were determined from sections prepared in different ways. In the superficial zone of articular cartilage, the highest retardation values were recorded from sections cut parallel to the so-called split lines indicating the anisotropic arrangement of collagen. Complete digestion of glycosaminoglycans reduced the retardation value by approximately 6.0%, suggesting a minor, but not insignificant, contribution of glycosaminoglycans to the birefringence of the matrix. The use of a mounting medium with a refractive index close to that of the collagen (e.g. DPX) increased the specificity of the method, since the optical anisotropy of collagen derives predominantly from the intrinsic (structural) birefringence. In conclusion, analysis of unstained sections after careful removal of paraffin and glycosaminoglycans from the tissues provides a sensitive and rapid quantitative assessment of oriented collagen structures in articular cartilage