(IUCr) Article Footnotes for Birefringence imaging

Notes

¹The difference between refractive indices is usually much smaller than their values.

²Note that the rotation of the tilt axes of the $[|{\rm sin}\, \delta |]$ contour map through an angle $[\Delta \sigma]$ is equivalent to the rotation of the $[|{\rm sin}\, \delta |]$ contour map through an angle $[-\Delta \sigma]$ .

³In order to measure the goodness of fit, we usually use several different statistics. However, in this paper we present results only for one of them, i.e. the R² statistic. The coefficient is defined as the ratio of the sum of squares due to regression (SSR) and the total sum of squares (SST). The term `sum of squares' means the sum of squared differences between predicted values and the mean (SSR) or between measured values and the mean (SST).

⁴The propagation direction S' does not coincide exactly with the specified axis of the optical indicatrix because muscovite belongs to the monoclinic crystal system. There is also a small shift in the perpendicular direction, possibly because of a very small error in positioning the tilting stage with respect to the axis of the optical system.

⁵Using this technique we determine the orientation of the biaxial sample with respect to one of the axes of the optical indicatrix, which, in general, does not have to coincide with any of the crystallographic axes of the biaxial sample, as in monoclinic and triclinic crystal systems (see, for example, Born & Wolf, 1999; Wahlstrom, 1960).

⁶Note that although the representation of the $[|{\rm sin}\, \delta |]$ function in the Cartesian coordinate system requires equal spacing between angle units in the $[\psi _{1}]$ - $[\psi _{2}]$ plane, it does not have any effect on the relations between variables and, moreover, makes the interpretation of the plot easier.

⁷Comprehensive information on the preferred orientation techniques is given by Wenk & Van Houtte (2004) and Kocks et al. (1998).