Fizeau Fringes In Transmission Research Articles

Applying multiple-beam Fizeau fringes for measuring the refractive indices of liquids

Multiple-beam Fizeau fringes in transmission have been used to measure the refractive indices of water, glycerol, dimethyl formamide and three mixtures of liquids at a wavelength of 546.1 nm and temperature . A small drop of the liquid under study is introduced between the two silvered surfaces of a wedge interferometer illuminated by a parallel beam of light. The refractive index of this liquid is the quotient of the separation between two successive fringes in the air region to that in the liquid region. The relative error in measuring the liquid refractive index using this method ranges from 0.02 to 0.0006 depending on the type of reading instrument and interferometer wedge angle used.

Optothermal properties of fibers. III. Optical anisotropy in nylon 66 fibers as a function of annealing process

Nylon 66(ICI Polyamide 66, Carded & Combed Top) fibers were annealed in the temperature range 80–180°C for 1–10 h. Refractive indices and birefringence were measured interfer-ometrically. Two independent techniques were used to study the optical anisotropy in these fibers. The first technique was to study the effect of annealing on the swelling properties of fibers from its diffraction pattern using a He—Ne laser beam. The second was the application of multiple-beam Fizeau fringes in transmission to determine the skin and core refractive indices and double refraction of annealing samples. The application was carried out using multiple-beam Fizeau fringes in transmission to determine Cauchy's constants and the dispersive coefficient for the fiber layers. The resulting data were used to calculate the mean polarizability per unit volume and the isotropic refractive indices. Behavior of optical properties at different annealing conditions is discussed. The results obtained clarify the new reorientation, and each layer change occurred due to annealing at different conditions. Microinterferograms and curves are given for illustration. © 1996 John Wiley & Sons, Inc.

Optothermal properties of fibers. IV. Optical properties of nylon 66 fibers as a function of quenching process

In this work, optical properties of samples of nylon 66 fibers were quenched in coarse-grained ice after annealing in the temperature range 80-180°C for 1-10 h. Two independent techniques were used to study optical parameters in these fibers. The first technique is the application of the diffraction technique to study the effect of quenching on the swelling factors of these fibers for some different liquids at room temperature of 25 ± 1°C. The second method dealt with the application of multiple-beam Fizeau fringes in transmission to estimate the refractive indices and birefringence of the skin and core of these fibers. The obtained results were utilized to calculate the polarizability per unit volume, isotropic refractive indices, and the Cauchy's dispersion constants. The relationship between n s ∥ , ⊥, n c ∥ , ⊥, n a ∥ , ⊥, Δn s , Δn c , Δn a , n (iso)s , n (iso)c , and n (iso)a and different annealing times and temperatures is given for these fibers. Microinterferograms and curves are also given.

Optothermal properties of fibers. VI. Effect of annealing on some of the optical and dynamic mechanical parameters of polyester fibers

Changes in the structure of annealed polyester fibers (Egyptian manufacture) at a constant time of 5 h and different temperatures (80-190°C) were studied interferometrically. The Pulta polarizing interference microscope was used for determining the mean refractive indices and mean birefringence of these fibers. The multiple-beam Fizeau fringes in transmission was also used for determining the refractive indices of the skin and core of these fibers. Also, the acoustic method was used for measuring the density and mechanical loss factor of these fibers. Relations between the mean refractive indices, birefringences polarizabilities per unit volume, and mechanical parameters of annealed polyester fibers with different temperatures are discussed to clarify the thermal effects. Illustrations are given using graphs and microinterferograms.

Effect of Annealing on the Optical and Mechanical Properties of Cold Drawn Polypropylene Fibres

Refractive indices and birefringence changes with strain produced by different stresses in annealed and unannealed polypropylene fibres (4 : 1 draw ratio, 515 tex polypropylene from Bolton, UK) were measured interferometrically. Calculations were carried out using multiple-beam Fizeau fringes in transmission to determine the Cauchy's constants, dispersive coefficient and the dielectric constant at infinity. The orientation factor and orientation angle of the fibre material were calculated for different strain values. Poisson's ratio and the strain optical coefficient were also determined. An empirical formula is suggested to correlate the orientation factor, orientation angle, area of cross-section and birefringence with the draw ratio, and the constants of this formula were determined. The effect of the draw ratio on the refractive index profile was studied. Microinterferograms and curves are given as illustrations.

Opto-thermal properties of fibres: 3-effect of anisotropic optical parameters in polypropylene fibres as a function of annealing process

This study deals with the changes in the optical properties of polypropylene fibres (4:1 draw ratio 515 tex polypropylene, Bolton, UK) due to the effect of thermal annealing on its structural characteristics. Changes in the structure of annealed polypropylene fibres at a constant time of 2 h and different temperatures (60–140 °C) were studied interferometrically. The diffraction of a He-Ne laser beam was used to measure the dimensional parameters transverse sectional shape and the area of the polypropylene fibres sections. An optical microscope was used to confirm the geometrical parameters of the cross-sections. The diffraction technique was utilized to study the effect of annealing on swelling factors of these fibres for some different liquids at room temperature 19 ± 1 °C. Two methods were applied for the measurement of the refractive indices and birefringence of the polypropylene annealed and unannealed fibres. The first was concerned with the application of the Becke-line method for determining the refractive indices and the birefringence of the skin layer. The second method used multiple-beam Fizeau fringes in transmission to observe the changes in the values of the refractive indices due to the annealing process in the skin and core layers. Also, the mean refractive indices and their profiles were determined, taking the refraction and different temperatures into consideration. The resulting data were used to calculate the polarizabilities per unit volume and the isotropic refractive index.

Dynamic optomechanical behaviour investigations on undrawn polypropylene fibres

A stress-strain device is constructed and connected to a wedge interferometer. It is used to investigate interferometrically the dynamic optomechanical properties of a polymer fibre. Multiple-beam Fizeau fringes in transmission using this equipment are used for carrying out the investigation on undrawn polypropylene fibres. The mean refractive indices and birefringence are calculated at different stresses and draw ratios. An empirical formula is deduced for the relation between the stress and the mean birefringence for undrawn polypropylene fibres and the constants of this formula are determined. The stress-strain diagram of this fibre is studied also. Poisson's ratio, Young's modulus, elastic shear modulus, yield stress and yield strain are calculated. Also an expression is proposed which is valid for either Young's modulus or elastic shear modulus related to the birefringence and the constants in this expression are determined for each case. The effect of stress on the refractive index profile is investigated. Microinterferograms are given for illustration.

Analysis of Fizeau fringes crossing fibres with trilobal shaped cross‐section having skin–core structure

AbstractA mathematical formula is derived for the shape of multiple‐beam Fizeau fringes crossing a trilobal fibre having a core surrounded by multiple skins. Fizeau fringes in transmission crossing the fibre were obtained experimentally to calculate their optical parameters. Microinterferograms are given for illustration.

Effect of the oxidative power of iodination on the optical properties of Alpaca fibres

This study deals with the changes in the optical properties of Alpaca fibres due to the effect of the oxidative power of iodine on the structural characteristics of Alpaca fibres. The diffraction of a He-Ne laser beam was used to measure the dimensional parameters, transverse sectional shape and area of the Alpaca fibre sections. Optical and scanning electron microscopes were used to confirm the geometrical parameters of the cross-sections. Two methods were applied for the measurement of the refractive indices and birefringence of the Alpaca wool fibres. The first was concerned with the application of multiple-beam Fizeau fringes in transmission before treating the fibre with iodine. The second method made use of a double refracting interference microscope (the Pluta polarizing interference microscope). The double beam technique was considered the most suitable in determining the mean refractive indices and the double refraction of the samples after the iodine treatment. Large changes were observed in the values of the refractive indices due to the iodination process, while the birefringence exhibited no appreciable change. Examination of the Alpaca fibres by X-ray diffractometry showed that the crystalline parts had been completely decomposed and degraded due to the effect of I 2, which causes oxidative scission of the intermolecular disulphide bonds of the keratins.

Interferometric studies on fibres with irregular transverse sections

Multiple-beam Fizeau fringes in transmission and at reflection were applied to the study of the optical properties of fibres with irregular cross-section ( Orlon 42 and nylon fibres). The mathematical expressions used for the application of multiple-beam Fizeau fringes to determine the refractive indices and birefringence of fibres are given. The experimental techniques used for producing multiple-beam Fizeau fringes in transmission and at reflection are also given. Interferometric methods were applied to study the variation of refractive indices with wavelength of light and along the fibre axis. Values of refractive indices were used to calculate Cauchy's dispersion constants. The value of thermal coefficient of refractive index has been calculated. Illustrations are given using multiple-beam interferograms.

Opto-mechanical properties of fibres—5: Refractive index profile of stretched ‘terylene’ polyester fibres

The changes of cross-sectional area and refractive-index profile of ‘Terylene’ polyester fibres after stretching have been studied. The cross-sectional shape is determined from the diffraction pattern of a HeNe laser beam. Multiple-beam Fizeau fringes in transmission are used to determine the refractive index profile of these fibres at different draw ratios. A microstrain device connected to a wedge interferometer is utilized for this purpose. Microinterferograms are given for illustration.

Opto-mechanical properties of fibres. 3: Optical properties of Nylon 66 fibres as a function of the draw ratio

Refractive indices and birefringence of six samples of nylon 66 fibres having different draw ratios are determined using two-beam and multiple-beam microinterferometry. Four independent techniques have been used for this purpose. The first one used a HeNe laser beam to determine the geometrical parameter of the fibre from its diffraction pattern. The second is the application of the Becke-line method to determine refractive indices and birefringence of the fibre's skin. The third is the application of multiple-beam Fizeau fringes in transmission to determine the mean refractive indices and mean birefringence of these fibres with different draw ratios. Finally, the Pluta polarising interference microscope have been used for determining the mean refractive indices and mean birefringence of these fibres. Relationships between the mean refractive indices, birefringence and polarisabilities per unit volume with draw ratio are given for these fibres. Illustrations are given using microinterferograms.

Stress birefringence in compressible polymer fibres with irregular transverse sections

From an interferometric point of view a mathematical formula is developed for computing the exact optical path variations associated with a deformed cross-section of a fibre due to the drawing process. Fizeau fringes in transmission crossing Perlon fibres are obtained to illustrate the experimental applicability of the new corrected formula. The correction term is expressed as a function of the material compressibility, applied stress and the draw ratio. The birefringence of Perlon fibres is changed mechanically according to two different mechanisms in successive ranges of draw ratio. The mechanical response of Perlon fibres is found to be dependent on the direction with respect to the fibre axis. Another term is suggested to describe the mechanical anisotropy of a polymer. Microinterferograms are given for illustration.

Opto-mechanical properties of fibres—1: Optical Anisotropy in stretched nylon 6 fibres

Multiple-beam Fizeau fringes in transmission have been used to study the changes of refractive indices and birefringence of nylon 6 fibres extended dynamically. A micro-strain device connected to a wedge interferometer is utilized for this purpose. An empirical formula is selected to represent the variation of birefringence of nylon 6 fibres with draw ratio. This formula is used for fitting the experimental data and for evaluation of non-tabulated values. Microinterferograms are given for illustration.

Interferometric investigation of optical dispersion of blue Cashmeline fibres

Multiple-beam Fizeau fringes in transmission have been applied to investigate the optical dispersion properties of blue Cashmeline fibres. The refractive indices were determined at different wavelengths for light vibrating parallel and perpendicular to the fibre axis. It was observed that both n/sub /// and nperpendicular to follow Cauchy's dispersion relation over the visible range of the spectrum. The constants A and B of Cauchy's formula were estimated. The observed results were interpreted in terms of the axial symmetry of the fibre.

Structural characteristics and optical properties of vestan (polyester) fibres

Refractive indices and birefringence for skin and core changes with strain, produced by different stresses in undrawn vestan fibres, were measured interferometrically. Applications were carried out using multiple-beam Fizeau fringes in transmission to determine the Cauchy's constants and dispersive coefficient for the fibre layers. The resulting data were used to calculate the polarizability per unit volume for each layer. The scanning electron microscope (SEM), optical microscope and He-Ne laser beam were applied to estimate the geometrical parameters of the fibre cross-section. A comparative study between the three methods used for measuring the fibre diameter was made. The effect of temperature on the refractive index and birefringence for each fibre layer has been also investigated. The relationship between temperature and birefringence of the fibres was studied and the thermal coefficient of the refractive index was determined. An empirical formula is suggested to relate temperature and birefringence. Illustrations are given using microinterferograms.

Optical Anisotropy in Mohair Fibers

The diffraction from a He-Ne laser beam was used to measure the dimensional parameters, transverse sectional shape, and area of mohair fibers. Multiple-beam Fizeau fringes in transmission, and double refracting interference microscopy (Pluta polarizing interference microscope) were used to measure the refractive indices and birefringence of the mohair. The double-beam technique was applied to determine the mean re fractive indices for plane polarized light vibrating parallel and perpendicular to the fiber axis and thus the mean birefringence. Two other recent analytical methods were employed to study the optical properties of fibers from the interference patterns pro duced by the formation of multiple-beam Fizeau fringes crossing mohair fibers. These methods were used to determine Cauchy's constants and the thermal coefficient of refractive indices of the skin and core of the mohair. A comparative study of these methods is discussed and illustrated using photomicrographs.

Effect of gamma irradiation on the refractive indices, birefringence and optical absorption of blue Cashmeline fibre

Multiple-beam Fizeau fringes in transmission have been applied to gamma -irradiated blue Cashmeline fibres, to determine their refractive indices for plane-polarised monochromatic light at gamma =5461 AA, vibrating parallel and perpendicular to the fibre axis, and the birefringence over the range from 5 Mrad up to 200 Mrad.

Optical anisotropy in gamma-irradiated fibres under vacuum

The change of optical anisotropy in polymeric fibres by γ-irradiation is suggested to develop a simple method for γ-ray dosimetry. Multiple-beam Fizeau fringes in transmission and in reflection are used in this study for the determination of the refractive indices and birefringence of γ-irradiated Dralon fibres. Variation of the refractive indices of these fibres with the temperature and wavelength of light are also studied. Empirical formulae are suggested to correlate the optical properties of the irradiated fibres with the applied dose. Lorenz-Lorentz equation is applied to calculate the polarizability of the irradiated fibres per unit volume. Illustrations are given by multiple-beam microinterferograms in transmission and in reflection.

The optical behaviour of polyethylene fibres with different draw ratios

Seven samples of polyethylene fibres with different draw ratios were studied by means of the measurement of their refractive indices and birefringence. In this study three independent techniques were used. These techniques were the Becke line, two-beam and multiple-beam Fizeau fringes. Variation of refractive index of the fibre with temperature was determined for two different draw ratios. Applications were carried out in which multiple-beam Fizeau fringes in transmission were used to determine the constants of Cauchy's dispersion formula. The resulting data were utilized to calculate the polarizability per unit volume of the fibre material. Relationships between the optical parameters and the draw ratios are given. The results obtained clarify the effect of the draw ratio on the optical behaviour of polyethylene fibres. Microinterferograms are given for illustration.