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The fringe shape across a graded index (GRIN) fibre immersed in a silvered liquid wedge, when analysed to its elements, is found to be the result of two half ellipses and a saddle. For a step index fibre, the elements contributing to its fringe shape are merely two half ellipses. Using a matching liquid cancels the outer half ellipse in both cases. The central dip contributes an extra half ellipse and a saddle over the dip but in the reverse direction away from the wedge apex. Such analyses furnishes the basis of a method to deduce the characteristics of GRIN fibres, namely alpha and Delta n, which is tested on liquids of different refractive indices.
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Barakat et al. (1993) studied this question.
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