Fizeau Fringes Research Articles

Opto-thermal properties of fibers XVIII?Skin-core structures variations in nylon 6 fibers due to different annealing conditions

Nylon 6 fibers (Amilan) were annealed at constant temperature 140 ± 1°C for different time durations (1–10 h). Refractive indices have been previously measured interferometerically. Two independent techniques were used to study the optical anisotropy and density in these fibers. The first was the application of a multiple-beam to determine the skin and core “mean” refractive indices and birefringence of the samples. The technique used multiple-beam Fizeau fringes in transmission. The second technique was an acoustic method for measuring the density of the investigated fibers. The optical results were used to calculate the optical orientation factors for skin and core. The values of (Δα/3α0), which depend upon the molecular structure of the polymer, remain constant and in agreement with the previous published data. The density results were used to calculate the degree of crystallinity of nylon 6 fibers. In addition, the results were used to calculate the mean square density fluctuation, the harmonic mean polarizability of the dielectric, specific refractivity of the isotropic dielectric and the virtual refractive index. Also, the number of monomer units per unit volume, and n1 and n2, which are the refractive indices of fully oriented fiber, were calculated and found to be (1.606 and 1.534). Hermans optical orientation functions have been compared with the generalized Lorentz-Lorenz equation given by de Vries. Microinterferograms and curves are given for illustration. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 3349–3360, 2001

Interferometric determination of (skin-core) optical andorientation structural parameters of drawn polypropylene fibres

Multiple-beam Fizeau fringes in transmission were used to study the changesof the principal optical properties of six samples of drawn polypropylenefibres. The resulting data of the mean, skin and core refractive indicesand birefringence of these fibres were used to calculate some structuralparameters such as the optical orientation function, orientation angle, theisotropic refractive index, the virtual refractive index, the number ofmolecules per unit volume and the random links per chain. Poisson's ratio and thestrain optical coefficient are also determined. The distribution ofsegments at an angle with respect to the draw ratio and the electricpolarizability constant (Δα/3α0) and other parametersand constants are determined. The generalized Lorentz-Lorenz equationgiven by de Vries has been used to compare the results obtained by Herman'soptical orientation function. Microinterferograms, tables and graphs aregiven for illustration.

Multiple-beam interferometric determination of Poisson’s ratio and strain distribution profiles along the cross section of bent single-mode optical fibers

Multiple-beam Fizeau fringes crossing bent single-mode optical fibers immersed in matching liquid reveal the existence of induced birefringence. Changes in the fiber cladding refractive index delta n were measured from the fringe shift to an accuracy of +/- 1 x 10(-4). Mathematical expressions were deduced to evaluate Poisson's ratio and to describe the radial strain distribution profiles of bent optical fibers from the experimental values of the fringe shifts. Experimental results were obtained from microinterferograms. Studying bent fibers by application of Fizeau fringes interferometry provides a nondestructive, accurate, sensitive, and reliable method to measure their parameters and characteristics.

Theoretical model for the transverse interference pattern of GRIN optical fiber using a laser sheet of light

A new technique (El-Ghandoor et al., Opt. Laser Technol. 31(7) (1999) 481–488) has been applied to study the shape of transverse interference fringes, instead of multiple beam Fizeau fringes (Marhic, Stein, Appl. Phys. Lett. 35 (1975) 1678–1682), from a GRIN optical fiber. In this technique, a laser light sheet is used to illuminate and pass directly through the optical fiber. Theoretical expressions are derived for the optical path differences of three groups of interference beams. The first one passes through the cladding, the core, and then the cladding once again; the second passes through the cladding only, and the third passes through the surrounding air. Theoretical expressions for the shape of transverse interference fringes formed across isotropic non-absorbing optical fibers are also calculated.

Interferometric characterization of single-mode bent optical fibers

Multiple beam Fizeau fringes in transmission have been used to demonstrate and to measure the change of principal stresses in the cladding of single-mode optical fibers due to bending. The study represents a nonlinear relation between the difference of maximum radial values of cladding’s refractive indices with the radii of curvature in the cladding of the bent optical fibers. The limiting acceptable bending radius has been investigated.

A spectral-discrimination method for tear-film lipid-layer thickness estimation from fringe pattern images.

Examination of the tear-film lipid layer is often helpful in the prognosis of prospective contact lens patients and contact lens related problems, and in the analysis of symptomatic noncontact lens-wearing patients. In particular, the thickness of the lipid layer is considered to be an informative cue in studying the tear-film stability and uncovering of certain disorders. We propose a method for the accurate estimation of the lipid-layer thickness, exploiting the intensity and color information in Fizeau fringe images. The technique is based on a quantitative measure for discriminating among the spectra associated with different thicknesses. We propose an optical system for imaging the interference patterns, develop a mathematical model based on the physics of the fringe formation and sensing, and describe the calibration of the optical system using this model. The thickness extraction is readily carried out utilizing a lookup table. The proposed method would enable objective evaluation of the lipid layer characteristics, and provide a means for examining the dynamic changes in its thickness and spatial distribution during inter-blink periods.

Conduction studies on copper indium diselenide thin films

Thin films of CuInSe 2 were prepared by thermal evaporation onto well cleaned glass substrates kept at 303 K. The thicknesses of the films were measured by Tolansky (Fizeau fringes) technique. XRD results reveal that the films are polycrystalline in nature. Thin film capacitors of the type (Al–CuInSe 2–Al) have been fabricated. Dielectric and ac conduction studies were performed on a stabilised sample of thickness 175 nm at various frequencies (10 kHz to 5 MHz) and temperatures (303–353 K). DC conduction studies were also carried out on a sample of thickness 230 nm. The value of dielectric constant has been evaluated as 10.8 at 5 MHz and at room temperature. From the ac conduction studies, it was confirmed that the mechanism responsible for the conduction process is electronic hopping. From the dc conduction mechanism, it has been observed that the Schottky type of conduction is predominant in the high field region and the Schottky barrier height has been determined as 0.1 eV. The ac and dc activation energies have also been calculated as 0.12 and 0.27 eV, respectively.

Comparative study on interferometric techniques for measurement of the optical properties of a fibre

The spectral dispersion curve and the refractive index profiles of polypropylene fibre are determined. Multiple-beam Fizeau fringes, a two-beam interference Pluta microscope, a manual variable wavelength system and the automatic variable wavelength interference technique (VAWI) are used to compare the results. A comparison of the optical properties measured using these four techniques is outlined. Also, the advantages, accuracy and limitations of these techniques are dealt with. Microinterferograms are illustrated.

Influence of temperature on the optical and structural properties along the diameter of: I. Polymer fibres

A modified heating device connected to a wedge interferometer is designed to study the influence of temperature on the optical and structural properties along the diameter of undrawn polypropylene fibres. To determine the optical orientation function profile, a model that divides the circular cross section into very small circular zones is suggested. The refractive indices and optical orientation function of each zone are considered assuming there is a constant fully oriented birefringence throughout the fibre. This investigation provides useful information about the structural properties of polypropylene fibres and throws light on its opto-thermal behaviour. The investigation is carried out using multiple-beam interference Fizeau fringes in transmission. Microinterferograms are given for illustration.

Interferometric determination of induced birefringence due to bending in single-mode optical fibres

Multiple beam Fizeau fringes in transmission have been used to demonstrate and to measure the radial change of the refractive index and the related induced birefringence in the cladding of bent single-mode fibres to an accuracy of .

Optothermal properties of fibers. IX. Study changes of optical parameters by multiple-beam technique due to thermal annealing for natural silk fibers

Multiple-beam Fizeau fringes were used for studying the effect of the annealing process on the refractive indices and birefringence of natural silk fibers (best yellow Italian silk, Ford & Co. Ltd). Silk fibers were annealed at a constant time of 2 h with different annealing temperatures ranging from 60 to 160 ± 1°C. A scanning electron microscope was used for measuring the cross-sectional shape and a longitudinal view of the natural silk fibers. The Becke-line method was used for measuring the skin refractive indices and the birefringence of the natural silk fibers. The thermal coefficient of the refractive index, Cauchy dispersion constants, dispersive power, dielectric constant at infinity, polarizability per unit volume, isotropic polarizability, and isotropic refractive index were determined interferometrically. Microinterferograms and curves are given for illustration.

Influence of creep on optical properties of polypropylene fibers

The change in some optical properties with the creep extension is measured for polypropylene fibers at several constant applied loads. Multiple-beam Fizeau fringes in transmission are used to determine the mean refractive indices and the mean birefringence of these fibers at different values of creep extensions. Also, the effect of creep extension on the birefringence profile of the fiber is studied. The creep-extension dependence of these optical properties for polypropylene fibers is demonstrated using a stress-strain device connected to a wedge interferometer where the fiber is subjected to a constant load. The results show that under constant load the fiber will extend with time at a rate which decreases as time increases. An empirical formula is suggested to represent the variation of creep extension (%) of polypropylene fibers with time in the time interval of 0-55 min and the constants of this formula are determined. Microinterferograms are given for illustration.

Optothermal properties of fibers. X. Temperature dependence of the skin?core structure of nylon-6 fibers

Refractive indices and birefringence for skin and core changes with annealing, produced by different annealing conditions in nylon-6 fibers, were measured interferometrically. Applications were carried out using multiple-beam Fizeau fringes in transmission to determine Cauchy's constants and dispersive coefficients for the fibers. The resulting data were used to calculate the polarizability per unit volume for each layer. By optical microscopy, the geometrical parameters of the fiber cross section were found. The effect of temperature and time of annealing on the refractive index and birefringence for each layer were also investigated. The relationships between temperature and time of annealing with the optical parameters were drawn. Illustrations are given using microinterferograms and curves. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 695–709, 1997

White-light Fizeau interferometer

A white-light Fizeau interferometer is described. Commonly, white-light fringes can be produced only by using a virtual wedge instrument such as a Michelson interferometer. By use of a series arrangement of a Fabry-Perot interferometer in front of a two-beam Fizeau interferometer, white-light fringes can be produced. For white-light fringes to be obtained, the thickness of the air gap between the Fizeau plates has to be adjusted to the same thickness as the air gap between the Fabry-Perot plates (or in more general terms to a rational multiple of this value). The contrast of the two-beam type of Fizeau fringes depends on the reflectivity of the Fabry-Perot plates.

Refractive index profile of GRIN optical fibre considering the area under the interference fringe shift: I. The matching case

An expression has been derived to determine the refractive index profile of a graded index (GRIN) optical fibre using and . This expression considers the area enclosed under the interference fringe shift when using a liquid of refractive index exactly matching the cladding one. Multiple-beam Fizeau fringes are used to obtain the profile shape constant and the refractive index difference between the fibre centre and its cladding. Another two methods are applied to compare the results. The suggested method has the advantage that it gives the exact solution and it provides a simple relation between the measured quantities.

An analysis of Fizeau fringes crossing fibres with different skin-core transverse sections

Mathematical expressions for Fizeau fringes crossing fibres with an unusual, irregular skin-core cross-section are derived. Firstly, for a fibre of a circular cross-section with a shifted elliptical core apart from its center and secondly, for a fibre of elliptical cross-section with a shifted circular core apart from its center. These expressions lead to the determination of refractive indices and birefringence for fibres having these special structures.

Interferometric measurement of some structural parameters of drawn polyethylene fibres

Multiple-beam interference Fizeau fringes are used to determine the optical orientation function and molecular structure of drawn polyethylene fibres. The optical orientation function across the fibre radius is obtained at a certain draw ratio, and the measurements of at different draw ratios can be used to give useful information about the fibre structure. Empirical formulae are suggested to correlate the birefringence with the refractive indices and with the draw ratio. Some parameters dependent on the fibre structures are also determined. Illustrations are made using microinterferograms.

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. 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. 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.