Excalibr II

The computer program EXCALIBR (Bloss and Riess, 1973; Bloss, 1981, p. 202) has been rewritten and markedly improved. Like EXCALIBR, EXCALIBR II solves optical extinction data, as determined with a spindle stage, and determines the optic axial angle 2V and the orientation of the crystal’s optical indicatrix. EXCALIBR II uses a modification to Joel’s equation as a means of obtaining the optic axes of a crystal. The new algorithm eliminates the need to solve the extinction data, quartet by quartet, as the first step towards finding a solution, as required by EXCALIBR. Furthermore, EXCALIBR II successfully solves extinction data where one optic axis of a biaxial crystal is 90° to the spindle axis, an orientation that had thwarted its predecessor. EXCALIBR II also accurately determines the optical indicatrix orientation for uniaxial crystals. The new program runs 10 times faster than EXCALIBR. In addition, creating data files is simplified by free-formatted input. After solving extinction data for several different wavelengths and/or temperatures, EXCALIBR II calculates the angular change of each optic direction with wavelength and/or temperature along with the error on the angle. Using a simple t-test, it then computes a p-value to aid in the decision as to whether the optical direction truly exhibits dispersion. This is a more valid and sensitive procedure than the χ2 test used by EXCALIBR, particularly because the covariance in each optic vector’s coefficients are taken into consideration and the results are invariant to the vector’s orientation.