Measurement of the refractive index of a special sample

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I want to measure the refractive index of a thin cantilever ; however the sample is too small (about tens of microns). on the other hand, the cantilever maybe not flat at all and it is curly. how can I do it?
 
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My sample is too small and curly so that I don't think the normal method to measure the refractive index is useful.