A matrix method for tensor transformations in Voigt notation known from the elasticity calculations has been applied to elasto-optical calculations. Using invariant tensor-to-matrix mapping, the second- and fourth-rank Cartesian tensor transformations and basic operations can be performed by means of matrix multiplication. This approach brings what we believe is a new method of correct tensorial operations in Voigt notation, replacing a well-known approach that allocated specific constants to some matrix elements to even up the difference between the tensor transformations and $6 \times 6$ matrix operations. This general approach also simplifies the use of elasto-optical calculations for an arbitrary crystal class in an arbitrary orientation.

中文翻译：

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弹性光学中的张量到矩阵映射

从弹性计算得知的用于Voigt表示法的张量变换的矩阵方法已应用于弹性光学计算。使用不变的张量到矩阵映射，可以通过矩阵乘法来执行第二级和第四级笛卡尔张量变换以及基本运算。这种方法带来了我们认为是Voigt表示法中的正确张量运算的新方法，取代了一种众所周知的方法，该方法将特定常量分配给某些矩阵元素，以使张量变换与$ 6 \乘以6 $矩阵运算之间的差额均匀。这种通用方法还简化了在任意方向上对任意晶体类别使用弹性光学计算的过程。