Automatic fringe analysis of two-beam interference patterns for measurement of refractive index and birefringence profiles of fibres

Automatic fringe pattern analysis is a powerful and inexpensive digital image-processing technique. Two-beam polarizing interference Pluta microscope [Pluta M. Opt Acta 1971;18:661, Pluta M. J Microsc 1972;96:309] is automated by the computer-aid via CCD camera and digital frame grabber. Software program is prepared to deal with the duplicated (separated and overlapped) Microinterferograms produced by two-beam polarizing microscope. It also gives an accurate and fast automatic measurement of refractive index and birefringence profiles for fibres. In this paper, the refractive index and birefringence profiles of two different types of fibres, basalt and polypropylene (PP) fibres are presented. A new method to determine the birefringence profile of fibres from non-duplicated microinterferogram is suggested. The cold drawing process for PP fibres is studied.     

Effect of UV radiation on the optical and some structural properties of irregular rayon acetate fibers

This recent study shed demonstration on how the structural parameters changes due exposure to UV radiation and different wavelengths. So this article throws light on the changes of the optical properties and some structural properties due exposure to UV radiation and different wavelengths on irregular rayon acetate fibers. Pluta polarizing interference microscope is used to study the changes for refractive indices and birefringence with different exposure times at three different intensities on irregular rayon acetate fibers. As the principal optical parameters determined, these give an indication of the isotropic refractive index, stress optical coefficient, stress due to UV radiation, optical configuration parameter, segment anisotropy, the number of molecules per unit volume and polarizability of a monomer unit can be obtained. Also by using different wavelengths are given the spectral dispersions, Cauchy's dispersion constants, the resonant wavelength, the oscillation energy, the dispersion energy, the dielectric constant and the dielectric susceptibility for rayon acetate fibers with different wavelengths at room temperatures. Illustrations are given using graphs and microinterferograms.     

The effect of mechanical drawing on optical and structural properties of nylon 6 fibres

The Pluta polarizing double-refracting interference microscope was attached to a mechanical drawing device to study the effect of cold drawing on the optical and structural properties of nylon 6 fibres. The microscope was used in its two positions for determining the refractive indices and birefringence of fibres. Different applied stresses and strain rates were obtained using the mechanical-drawing device. The effect of the applied stresses on the optical and physical parameters was investigated. The resulting optical parameters were utilized to investigate the polarizability per unit volume, the optical orientation factor, the orientation angle and the average work per chain. The refractive index and birefringence profiles were measured. Relationships between the average work per chain and optical parameters at different strains rates were determined. An empirical formula was deduced for these fibres. Micro-interferograms are given for illustration.     

Determination of the optical and geometrical properties of fibres having skin–core structure

A method is suggested to determine both the refractive index and the transverse sectional shape and area of fibres, having skin–core structure, at the same time for the same region of the fibre. The method depends on using a fibre rotator device attached with Pluta polarizing interference microscope, to record the variation of the fibre thickness at each angle of rotation. Nylon 6 fibres having skin–core structure were used in this study. Beck-line method was used to determine the refractive index of the skin for light vibrating parallel and perpendicular to the fibre axis. To confirm the results of the suggested method, the optical microscope was used to determine the transverse sectional shapes of bundles of nylon 6 fibres. The mean refractive indices of the skin and core of nylon 6 fibres were determined. Microinterferograms are given for illustration.     

Study of optical parameters of two fluorinated isothiocyanato nematic liquid crystals exhibiting high birefringence

Optical studies have been carried out on two fluorinated isothiocyanato nematic liquid crystal (LC) compounds 4′-butylcyclohexyl-3, 5-difluoro-4-isothiocyanatobiphenyl and 4′-pentylcyclohexyl-3, 5-difluoro-4-isothiocynatobiphenyl. Transition temperatures of the two samples were confirmed using a polarizing microscope. The two LC compounds were found to exhibit fairly high clearing temperatures. Measurements of refractive indices of the two compounds were done by using thin prism method with He-Ne laser beam of wavelength 630 nm. Birefringence of the two LC compounds was calculated from the measured refractive indices. Both the compounds are found to display fairly high values of birefringence. Validation of a modified four-parameter model, based on Vuks equation describing the temperature dependence of refractive indices of the two liquid crystals, is also presented in this paper. The model is validated by fitting the experimentally measured values of refractive indices, birefringence and average refractive indices of the two nematic LCs with the theoretical values. In this paper, the calculation of order parameters of the LCs is presented by using two methods: direct extrapolation method based solely on the birefringence data and by using modified Vuks method based on Haller’s extrapolation. As observed from the obtained results, this procedure of calculating order parameter gives very reasonable results.     

Determination of GR-IN optical fibre parameters from transverse interferograms considering the refraction of the incident ray by the fibre

The core–cladding refractive index difference Δn and the index gradient profile parameter of the graded index (GR-IN) optical fibre has been determined. The curve representing the real path, in the core region, due to refraction of the beam and the change in the exit wavefront are considered. Multiple-beam Fizeau fringes and two-beam interference Pluta polarizing microscope, are used for this investigation. A new method, based on a derived mathematical expression, is used with a prepared computer program to estimate the fringe shift inside GR-IN of the fibre core. The estimated and experimental values of the fringe shift, along the core radius, are used to obtain the refractive index profile of the optical fibre. A comparison between the new method and a previous model considering the refraction has been shown. Microinterferograms are given for illustrations.     

Determining the opto-mechanical and geometrical properties of high-density polyethylene fibres

A method is described to determine the opto-mechanical and geometrical properties of high-density polyethylene, HDPE, fibres at the same time for the same region from the fibre. Variations of the transverse sectional shapes, areas, optical and mechanical properties of fibres during the cold drawing process were investigated. A rotator-mechanical drawing device was used for rotating the fibre around its longitudinal axis during the cold drawing process. The Pluta polarizing two-beam interference microscope was attached with the rotator-mechanical drawing device for detecting these variations under the interferometer. The rotator-mechanical drawing device permits determining the tensile stress–strain curve, Poisson's ratio and strain optical coefficient for HDPE fibres. Also, it permits determining the refractive index profile of the drawn fibres taking into considering the transverse sectional area and the enclosed area under the fringe shift. The optical orientation factor and orientation angle was calculated for HDPE fibre to clarify the orientation of molecules during the cold drawing process. Microinterferograms are utilized for illustrations.     

有机材料在各种波长的折射率计算

使用Vogel方法和介质的色散关系,计算有机化合物在各波长的折射率n(λ).用Vogel方法把化合物分子分解成碎片,加和得到化合物在某几个波长的折射率.假设化合物在所计算的波长范围内为正常色散关系,使用Voyel方法得到的两个折射率,通过Cauchy公式得到色散曲线,从而得到各波长的折射率n(λ).通过对有机化合物芪盐和高分子材料聚苯乙烯的各波长折射率进行计算,并与材料在某一特定波长的实际折射率对比,证明了计算结果比较准确.并对双折射液晶材料的折射率计算进行了探索.     

Application of multiple-beam white-light fringes for measuring the refraction and dispersion of mica

Multiple-beam white-light interference fringes are applied to measure the two refractive indices of a mica sample and their dispersion across the visible spectrum. In addition, the mica birefringence and its dispersion are measured. A mica sample of dimensions 2 × 5 mm² and an immersion liquid of nearly the same refractive index are used. Only a single shot interferogram is needed to measure all the aforementioned parameters. Cauchy's and a modified single-term Sellmeier dispersion formula are used for fitting the experimental data and extracting the parameters required.     

Refractive index, birefringence, third-order non-linearity and piezoelectric resonance studies of L-lysine monohydrochloride dihydrate single crystals

The principal refractive indices of L-lysine monohydrochloride dihydrate (L-LMHCl) single crystal for different wavelengths were measured by minimum deviation method at room temperature. The experimental values of refractive indices fit well with the theoretical Cauchy's equations. The birefringence and the crossing angle between the optical axes were calculated. The parameters of Sellmeier's single term dispersion equation were determined by least square method. A simple interferometric technique was used to observe the interference patterns along the optic plane and to qualitatively analyze the optical homogeneity of the grown crystal. The nonlinear refractive index (n₂) and nonlinear absorption coefficient (β) were also determined using Z-scan technique. The piezoelectric resonance in dielectric dispersions was observed at room temperature.     

石英晶体双折射率紫外至近红外波段色散特性实验的研究

介绍了偏光干涉测量石英晶体双折射率色散特性及其相关数据处理方法。利用偏光干涉光谱极值点的精确判断,完成极值点波长对应的材料的双折射率的测量,获得了紫外至近红外光波段石英晶体的最大双折射率与波长关系离散的数据曲线,经多项式拟合数据处理,进而得到任意波长的双折射率函数关系式。此方法对其它各向异性晶体材料的双折射率色散特性的研究同样适应。     

Polarizability tensor of the O2−-molecule in hyperoxide crystals

Refractive indices and birefringence of NaO₂, KO₂, RbO₂ and CsO₂ were measured with a double beam interference method in the visible and at room temperature. K-, Rb- and Cs-hyperoxides are positive uniaxial showing large birefringence. The dispersion of the refractive indices in the visible range can be described in terms of a one oscillator model. With a point dipole approximation it is possible to calculate the tensor of the electronic polarizability of the O₂^?-molecule-ion, based on the computed Lorentz correction factors of the dipole sum for the tetragonal lattice.     

Birefringence dispersion in a quartz crystal retrieved from a channeled spectrum resolved by a fiber-optic spectrometer

We present a simple method for measuring the wavelength dependence of both the phase and group birefringences in a quartz crystal of known thickness. The method utilizes interference of polarized waves resolved by a fiber-optic spectrometer as a channeled spectrum (spectral fringes). The fringe order versus the precise position of the interference maximum in the spectrum is fitted to the approximate function, from which the phase birefringence as a function of wavelength is retrieved. We also determine the group birefringence dispersion. The functions measured in a range from 500 to 900 nm are compared with those resulting from the available dispersion relation, and very good agreement is confirmed.     

Geometrical cross-sectional imaging by a heterodyne wavelength-scanning interference confocal microscope

We developed a heterodyne interference confocal microscope, using wavelength modulation of a laser diode to realize quick separate measurement of the refractive indices and geometrical thicknesses of multiple layers. This microscope requires only a single axial movement of the specimen. We can display the geometrical cross sections of the interfaces and the refractive indices of a three-layered object.     

Multi-mode opto-thermo-mechanical stretching system for determination of 3D refractive index along the axis of stretched and/or heated fibres

A multi-mode opto-thermo-mechanical stretching system was modified to study the changes in the 3D of optical and structural properties of stretched fibre along its axis. The structural deformation of isotactic Polypropylene, (iPP), fibres was studied at different draw ratios. The modified system coupled with Pluta polarising interference microscope was used to determine the variation of the birefringence in three dimensions during stretching process. Using this modified system, the multi-necking was detected. Subfringe analysis technique was used to determine the phase distribution of the obtained microinterferograms, which were given for illustration.     

椭偏法测量云母波片相位延迟量及双折射率(英文)

为了得到云母波片的相位延迟量和双折射率随波长的变化关系,利用椭偏光谱仪连续测量了云母波片在400～770nm光谱范围内的延迟量.在对云母波片进行校准后,测量的数据被光电探测器收集并输送到计算机,根据输出的数据可以得到云母波片的相位延迟量随波长的变化.利用测得的延迟量计算出了云母波片在一定光谱范围内的双折射率,得到了云母波片的双折射率色散曲线,并通过拟合得到了双折射率色散公式.该方法能测量任意波片的相位延迟量,并且具有测量方便、周期短、精度高等特点.     

偏光棱镜长度孔径比与材料特性的关系

为了掌握激光偏光棱镜的长度孔径比情况,根据激光的特点和不同晶体材料特性,利用光在各向异性晶体中的传播规律,分析了长度孔径比受材料双折射率、胶合剂折射率等因素的影响。研究显示,同一材料中两个主折射率的较大者决定了长度孔径比的最小值,而较小者决定了长度孔径比的最大值;有较大主折射率的材料,相应器件长度孔径比也小;选用低折射率的胶合剂,有利于缩小器件长度孔径比。此结果也可以作为多波长使用情况下的偏光器件的设计参考。     

Interferometric determination of refraction and dispersion of human blood-serum, saliva, sweat and urine

Multiple-beam interference fringes of equal chromatic order are produced in air and liquid sample interferometric gaps. The two gaps are of the same thickness and simultaneously enclosed in a wedge interferometer. A single shot interferogram containing fringes in the two gaps is sufficient to deduce the needed experimental data. Locations of the fringe maxima, in the two gaps, are introduced in a non-numerical procedure for determining the gap thickness and the liquid-phase refractive indices across the visible spectrum. The method has been used for measuring the phase refractive indices of human blood-serum, saliva, sweat, urine and water liquids. A third-order polynomial dispersion relation is applied for fitting the measured phase indices. Group refractive indices have been derived and fitted to the same dispersion formula.     

Optical properties of a liquid crystal with small ordinary and extraordinary refractive indices and small optical anisotropy

Optical properties of a nematic liquid crystal with small refractive index and small birefringence were studied. The ordinary and extraordinary refractive indices and birefringence were measured as functions of temperature by using an Abbe refractometer and wedge nematic cells. From values of these indices the nematic orientational order parameter was calculated by using several methods and corresponding mathematical models. Kuczyński et al. method was found to be suitable for determining the order parameter also for materials featuring small ordinary refractive index, with unknown density.     

Measurement of the spectral dispersion curves of low birefringence polymer fibres

A method is suggested to overcome the difficulties of measuring the spectral dispersion of low birefringence fibres, that produce small optical path difference, δ<3λ, where δ is the optical path difference and λ is the wavelength of light used. This method depends on variable wavelength interferometry (VAWI). The suggested method is used to measure the spectral dispersion of birefringence of polypropylene fibre with a draw ratio 4 (low birefringence fibre). This method is also used to measure the spectral dispersion of birefringence of a polyester staple from ICI (high birefringence fibre). Also, the conventional VAWI method is used to measure the spectral dispersion of this fibre to confirm the results obtained by the suggested method. Microinterferograms are given for illustration.