Analytical calculation of the axis angle 2V from extinction measurements on the spindle stage

Florian Dufey

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arXiv · 1703.00070

Analytical calculation of the axis angle 2V from extinction measurements on the spindle stage

Florian Dufey

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Abstract

A concise derivation of the "Joel equations", which allow for the determination of the axis angle 2V from measurements of extinction directions on a spindle stage, is provided starting from the wave-equation. Only analytic methods and no geometric arguments referring to stereographic projections are invoked. For error free data, the resulting equations allow for a closed form solution. If angle data with measurement error are to be used, a maximum likelihood estimation methodology is proposed, which may be solved using e.g. iterative reweighting. The method is tested with and compared to published data.

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Florian Dufey. 2017-02-27. Analytical calculation of the axis angle 2V from extinction measurements on the spindle stage. https://arxiv.org/abs/1703.00070

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