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.