A.A. Hamza

On the determination of the refractive index of a fibre. II. Graded index fibre

Two- and multiple-beam interference fringes are used to measure the refractive index of graded index fibres. A general expression considering the refraction of the beam by the graded index fibre has been derived, from which expressions for homogeneous and skin-core fibres can be obtained. Comparison between the results with the method used when neglecting refraction is dealt with using Philips, LDF (TM) optical fibres and drawn polypropylene. Considering the derived expressions in the refractive index determination gives a correction even when a matching liquid is used, this suggests that the refraction method should be used especially for graded index fibre.

The interferometric methods applied to the studies of fibrous materials

This paper describes the use of interferometric methods in fibre science. Different techniques of double-beam and multiple-beam microinterferometry are given, together with their application in the investigation of fibre properties. The use of the polarizing microscope in this respect is also given. Double-beam and multiple-beam interferometric methods were applied to determine the mean refractive indices and birefringence of polyester fibres. The results are illustrated by microinterferograms. Accurate results are obtained when considering the area under the interference fringe shift representing the path difference integrated across the fibre. The double-beam interference microscope is a quick method for the determination of the optical properties of fibres. The interference fringes produced from the multiple-beam interferometric methods are extremely sharp and the amount of information in this case is considerable. The fringe displacement in this case is proportional to twice the phase difference introduced by the fibre. Therefore, multiple-beam interferometric methods are much more sensitive than the double-beam methods.

Multiple-beam interferometric studies on fibres with irregular transverse sections

An analysis of multiple-beam Fizeau fringes crossing fibres with irregular transverse sections is given. The area enclosed under the fringe shift is considered to represent the path difference integrated across the fibre. The method is applied to the determination of refractive indicies and birefringence of dralon fibres. Microinterferograms are given for illustration.

Refractive index profile of polyethylene fiber using interactive multiple-beam fizeau fringe analysis

A multiple-beam interference Fizeau fringes technique is used to measure the refractive index profile of drawn polyethylene fiber. The interference fringe shift in the fiber region has been analyzed automatically using an interactive algorithm. The method takes into consideration the refraction of the light beam when crossing the fiber. Plane polarized light vibrating parallel and perpendicular to the fiber axis are used to obtain the refractive index profiles of both cases. These profiles are used to determine some optical parameters such as the birefringence, the optical orientation function, the polarizability per unit volume, and the value Δα/3αo, which related to the material structure. The reliability of the method is tested considering the results of drawn polyethylene fiber samples using the manual technique.

Stress birefringence in polypropylene fibres

Abstract Refractive indices and birefringence changes with strain produced by different stresses in undrawn polypropylene fibres have been measured dynamically by interferometry. A micro-strain device connected to a wedge interferometer has been constructed. Using this wedge interferometer, multiple-beam Fizeau fringes in transmission are made to cross the fibre perpendicular to its axis. As these fringes cross the fibre they suffer a shift, the area enclosed under which is considered to represent the optical path difference integrated across the fibre. It has been found that the relation between strain and birefringence is linear up to strains of 86%. For greater strain the rate of change of birefringence with strain is decreased. Poissons ratio is calculated over three strain ranges. An empirical formula is suggested to represent the variation of cross-sectional area of polypropylene fibres with draw ratio, and the constants of this formula are determined. Micro-interferograms are given for illustration.

Optical Anisotropy of Poly (P-Phenylene Terephthalamide) Fibres

The principal polarizabilities of poly(p‐phenylene terephthalamide)—PPT—fibres were calculated using the molecular model of Northolt, together with the values of bond polarizabilities given by Denbigh and also by Bunn & Daubeny. Following generally accepted practice, the Lorentz‐Lorenz expression was utilized to derive the principal refractive indices (and the birefringence) of the PPT fibres.

Interferometric determination of optical properties of fibres with irregular transverse sections and having a skin-core structure

Multiple-beam Fizeau fringes in transmission and at reflection were used to investigate the optical properties of layers of fibres with irregular transverse sections having a skin-core structure. Mathematical expressions have been derived for the values of refractive indices and birefringence of these fibres. These expressions were applied to determine the optical properties of two samples of nylon-6 fibres.

Determination of spectral dispersion curves of polypropylene fibres

A new mathematical formula is derived to determine the spectral dispersion curve of a fibre having a circular cross sectional shape. This formula depends on the principle of a variable wavelength interferometric technique taking into consideration the area under the fringe shift instead of the fringe shift itself. This method overcomes the difficulty of the presence of any irregularity of the transverse circular cross sectional shape of the fibre. Analysis of the new mathematical formula is given and applied experimentally for polypropylene fibres with draw ratio 3.5 and 4.0. Optical microscopy and optical diffraction methods are used to determine the cross sectional area of the fibres. Also, conventional VAWI and two-beam methods are applied for these fibres to confirm the results of the new analysis. Microinterferograms are given for illustration.

Multiple-beam Fizeau fringes crossing a cylindrical multi-layer fibre

Mathematical expressions are derived for the shape of multiple-beam Fizeau fringes crossing a cylindrical multi-layer fibre. The area enclosed by the deviation of the interference fringe as it crosses the fibre is considered to represent the path difference integrated across the fibre. This interferometric method is applied to determine the refractive indices and birefringence of each layer of polypropylene fibres.

Optical Properties and Birefringence Phenomena in Fibers

The Becke-line method, the multiple-beam Fizeau fringes method in transmission to fibers, and the Pluta microscope measurements of optical properties of fibers are discussed. This study uses cellulose triacetate, cuperammonium, nylon, and polyvinyl alcohol fibers.