Fizeau Fringes In Transmission Research Articles

Characterizing The Effect of Thermal Annealing Process on the Physical and Structural Properties of Polybutester Suture Fibers.

In this work the effect of thermal annealing treatment on the different physical, optical and structural of surgical suture fibers were considered. Polybutester monofilaments suture fibers were thermally annealed at temperatures fluctuating from 50-130? for two different periods of 60 and 120 min. The thermal-treatment was supported using taut end settings. Multiple-beam Fizeau fringes in transmission and X-ray diffraction techniques were used to measure the physical and structural properties of the tested sutures. Such as refractive indices, birefringence, dielectric constant, polarizability, dielectric susceptibility and the crystallinity. From the obtained measured data , there was a noticeable increase in the physical properties and crystallinity throughout the annealing process for annealing time 120 min. which indicates that a new reorientation of Novafil suture molecules was performed, which will improve the mechanical properties of the sutures. This is a significant enhancement for these suture fibers to broaden their medical use and improve their clinical results. The new molecular reorientation of the Novafil surgical sutures was performed using the annealing process which demonstrates the polymer-chain relaxation during the thermal annealing process. Micro Interferograms were used to illustrate these findings.

Disintegration of multiple-beam Fizeau fringes in transmission using FFT analysis

An investigation of fast Fourier transformation (FFT) spectrum appears from multiple-beam Fizeau fringes is presented. It is proven theoretically and demonstrated experimentally that the number of the appeared peaks is related to the interfered rays’ number. In addition, a detailed interpretation of (FFT) yields from multiple-beam Fizeau fringes analyses is illustrated. This interpretation proved that every peak of the FFT spectrum represents a set of two-beam interference. Therefore, the higher order FFT peaks are not an error. It is found that the frequencies of the appeared peaks are separated by a constant increment. Therefore, when we apply the inverse fast Fourier transformation (IFFT) on a selected peak we can get a two-beam intensity distribution image with a fringe frequency depending on the peak order number. This study removes confusion and answers some important questions concerning the multiple-beam interference. The presented analysis leads to disintegrate multiple-beam interferogram to its components of two-beam interferograms. This could facilitate recovering the phase map and provides more information from one multiple-beam interferogram.

Intensity distribution of Fizeau fringes in transmission with the real path of the interfered multiple-beams

In this paper, a theory is presented to estimate the intensity distribution of Fizeau fringes in transmission. In this theory the real path of the interfered light beams, through the wedge interferometer, has been considered. Interference of multiple beams has been estimated up to 12 beams considering the phase and amplitude for each beam. The summation of these waves has been done using the vector summation theory. The numerical construction of Fizeau fringes in space has been calculated considering the superposition of different number of beams. The influence of the wedge angle, number of the interfered beams and the wedge gap on the intensity distribution has been investigated. The most interesting observation in this study is the intensity distribution in different planes above the interferometer in both calculated and experimental Fizeau fringes using a He–Ne laser. Some experimental interferograms have been illustrated to confirm the validity of the proposed theory.

On-line opto-viscoelastic analysis of polypropylene fibres using multiple-beam Fizeau fringes in transmission and a modified creep device

A creep device attached to an automated multiple-beam Fizeau system in transmission was modified with a designed digital ruler. This device allows on-line measurements of fibre length during creep experiments in terms of an analogue voltage value. The influence of sustained stress values on creep deformation and optical properties (n||, n⟂ and Δn) for polypropylene (PP) fibres was studied interferometrically. The opto-viscoelastic properties of PP fibres were determined for three different values of constant applied stress of 11.536, 18.717 and 25.905 MPa, at room temperature. Also, the variations of the cross-sectional area and Poisson's ratio were studied during creep extensions. The compliance curves were obtained as a function of both time and applied stresses. Empirical formulae are suggested to describe the creep compliance curves for PP fibres, and the constants of these formulae were determined and described at each applied stress. A Kelvin chain was used to model the mechanical behaviour of the PP fibres under study. The effect of strain on the mean refractive indices, orientation function density and crystallinity was investigated as a result of the recorded data. Microinterferograms are given for illustration. The modified creep device with the designed digital ruler enables one to obtain instantaneous automatic accurate recording of fibre length values during creep experiments. Calculation of refractive indices, orientation function and crystallinity shows a difference in material behaviour at small stresses from that at higher stresses which may be attributed to different strain rates caused by different stresses. Copyright © 2010 Society of Chemical Industry

An interferometric method for determining the mean refractive indices of highly birefringent fibres

An interferometric method with its mathematical derivation is suggested to determine the mean refractive indices and birefringence of highly birefringent fibres using multiple-beam Fizeau fringes in transmission. The application of this method depends on measuring the cross-sectional area of the fibre and the area enclosed under the fringe shift. It is very difficult to measure the area enclosed under the fringe shift in case of highly birefringent fibres, as these fibres have a relatively large optical path difference and a bad connection with the surrounding medium fringe. This difficulty is solved using the suggested method. Poly(aryel ether ether ketone) (PEEK) and poly(ethylene 2,6-naphthalene-dicarboxylate) (PEN) were used as applied examples of highly birefringent fibres for the suggested method. The refractive indices and birefringence of polypropylene fibre with draw ratio 4 are determined using the suggested and conventional methods. The results of the two methods are compared and it is found to be in agreement with the previously published data. The diffraction of He–Ne laser beam was used to determine the mean value of cross-sectional areas of fibres. Microinterferograms and tables are given for illustrations.

Effect of creep strain on the optomechanical properties and some structural properties of terylene fibers

AbstractThis article sheds light on the effect of creep strain [ϵ(t); %] on the optomechanical properties and some structure properties of terylene fibers at several constant applied loads. Automated multiple‐beam Fizeau fringes in transmission were used with a mechanical creep device attached to a wedge interferometer where the fiber was subjected to a constant load. This technique was used to determine the mean refractive indices and the mean birefringence values of terylene fibers under different conditions of ϵ(t). The obtained optical results were used to evaluate the optical orientation function, optical stress coefficient, density, crystallinity, and mean‐square density fluctuation with ϵ(t). The obtained results show that, under a constant load, the terylene fibers extended with time, the rate of which decreased with time. An empirical formula is suggested to represent the variation of ϵ(t) of terylene fibers with time, and the constants of this formula were determined. A mechanical model is proposed to represent ϵ(t) of terylene fibers, which consists of two Kelvin elements combined in series, which were used to provide an accurate fit to the experimental creep curve. The stress–strain curve via creep was studied to determine some mechanical parameters of the investigated fibers: Young's modulus, yield stress, and yield strain. Illustrations with microinterferograms, graphs, and tables are given. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

The Activation Energy and Some Structural Parameters of Thermally Treated Polypropylene Suture Fibers

Multiple-beam Fizeau fringes in transmission were used to study the changes in optical parameters of thermally treated polypropylene PP suture fibers. Changes in the refractive indices and birefringence have been measured interferometrically on thermally treated PP suture fibers at temperatures of 19 to 40 ± 0.5°C. From the optical parameters; the mean polarizability of monomer units, the density, stress optical coefficient, the thermal stress and the activation energy of PP sutures were calculated. The results of density and optical measurements were used to calculate the crystallinity and the specific refractivity of the isotropic dielectric. Additionally, we calculated the mean square density fluctuation, the segment anisotropy, the molar refractivity and form birefringence. Relations between evaluated and measured parameters are given for illustration. The present study throws light on the changes due to slight thermal treatments as an example of thermal human end uses. Curves are given for illustration.

Determination of the Spectral Dispersion Curves of Highly Oriented Fibers Using Multiple-Beam Microinterferometry

ABSTRACT A method is suggested with its mathematical analysis to determine the spectral dispersion curves of highly oriented fibers using multiple-beam Fizeau fringes in transmission. This method depends on the use of the well-known Caushy's dispersion formula for determining the initial interference order of the deviated fringes inside the fibers. The suggested method overcomes the difficulties of measuring large optical path length differences that are produced by highly oriented fibers. The spectral dispersion curves obtained using this method are in good agreement with those obtained using conventional variable wavelength interferometry (VAWI) technique. Microinterferograms are given for illustration.

Detection of necking deformation along polypropylene fibres axis at low draw ratios using multiple-beam microinterferometry

A modified drawing device attached with an automated system for producing multiple-beam Fizeau fringes in transmission is used to study the mechanical deformation along polypropylene (PP) fibres at low draw ratios. Two drawing processes are used for drawing PP fibres. In the first process (fast drawing), the necking deformations are formed at draw ratios from 1.2 to 1.9 along the fibre axis. While in the other process (slow/step drawing), these deformations disappeared. The refractive indices calculated at different positions along the fibre axis during the fast- and slow-drawing processes. To overcome the formation of necking deformation along the PP fibres during fast-drawing process, the slow-drawing technique is recommended. Microinterferograms are given for illustration.

Detecting and avoiding the necking deformation along polypropylene fibre axis using the fringe pattern analysis of multiple-beam microinterferometry

A fibre-drawing device attached with the system for producing multiple-beam Fizeau fringes in transmission is used to optimize the optical properties during the cold drawing of polypropylene (PP) fibres. This system is automated for interference pattern analysis. Two drawing processes for the PP fibres are applied and investigated. The first one is fast drawing in which the necking deformation is predicted and the other is the slow (step) drawing in which the necking can be avoided. The refractive index profiles ( n ∥ and n ⊥ ) of PP fibres are determined at different positions along the fibre axis during the fast and slow drawing processes. The fibre interference patterns are automatically digitized and stored in a computer storage media. The slow drawing technique for PP fibres is recommended to overcome the deformation difficulties along the fibre axis due to necking during the drawing processes. Microinterferograms in case of light vibrating parallel and perpendicular to the fibre axis are given for illustration.

Interferometric Determination of Orientation and Some Optical Parameters of annealed Polyester Fibres

Multiple-beam Fizeau fringes in transmission have been applied to annealed PET fibres, to determine the refractive indices of their skin and core layers for plane polarized monochromatic light at λ =546.1 nm, vibrating parallel and perpendicular to the fibre axis. We obtained the optical orientation parameters by applying the equations used by Hermans and Ward. Some structural parameters such as electric polarizability were determined. The density of the samples studied was measured by a system based on the theory of vibrating strings. The density and optical results were used to calculate the degree of crystallinity, the mean square density fluctuation, the form birefringence, the number of monomeric units per unit volume, the harmonic mean polarizability of the dielectric, and the harmonic mean specific refractive index. The generalized Lorentz-Lorenz equation given by de Vries was used to determine the structural parameters of annealed PET fibres. Comparisons between the experimental results and those obtained by using the Lorentz-Lorenz and Hermans equations are given. Refractive index profiles are also given. The results show the new reorientation and layer changes accompanying annealing under different conditions. Illustrations are given of multiple-beam microinterferograms in transmission.

Determining the optical properties of highly oriented fibres using a multiple-beam technique

Mathematical formulae are modified for the shape of multiple-beam Fizeau fringes in transmission to determine the mean refractive indices and birefringence of highly oriented fibres. These modified mathematical formulae are applied with the multiple-beam interference method to determine the optical anisotropy of polypropylene fibre with a draw ratio of 3.5. The refractive indices and birefringence results are compared with those obtained using the conventional method and are found to be in good agreement. The new method is also applied for (poly(ethylene 2,6-naphthalene-dicarboxylate), 1000 denier/248 filaments, PEN-Q50M4 (PEN) and poly(ethylene terephthalate) 1000 denier/250 filaments, PET-BHT, highly oriented yarn, Teijin, Japan (PET)) highly oriented fibres. Illustrations are given through microinterferograms.

Theory and measurement of Young's modulus radial profiles of bent single-mode optical fibers with the multiple-beam interference technique.

Multiple-beam Fizeau fringes in transmission have been applied to the study of the nonlinear stress-strain relationship due to bending in the cladding of single-mode optical fibers. The present study yields a relation between the variation of refractive indices of bent single-mode fibers, represented by the fringe shift, and the nonlinear radial change of Young's modulus along the fiber cross section. Experimentally, the study confirms the nonlinear asymmetric stress-strain relation across the fiber cross section. This relation is due to the asymmetric distribution of the compression and tensile stresses over the fiber cross section rather than to the shift in the centroid (neutral axis).

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.

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.

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 .

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