Determination of the refractive index of fibres using the modified area method: I. Homogeneous fibres

The mathematical formulae for determining the mean refractive indices and birefringence of homogeneous fibres are modified. This modification depends on calculating the area under the fringe shift and cross-sectional area of homogeneous fibres having nearly circular cross-sectional area taking the refraction of the incident light beam by the fibre into consideration. The mathematical analysis for two-beam and multiple-beam interferometric techniques is dealt with. These formulae are applied to polypropylene fibres with draw ratios of 3.5 and 4 using the two techniques. A comparison between the results when using the new formulae and when neglecting the refraction has been studied. The diffraction of a He–Ne laser beam is used for determining the shape of the cross-sectional area of these fibres. Microinterferograms are given for illustration.