在偏振光学中系统地引入四元数方法。分别给出了在Poincare球和斯托克斯参数基础上建立的偏振光四元数表示，并证明这两种表示是等价的。讨论了偏振光四元数表示的多样性。导出了偏振器件和系统的四元数表示。利用四元数表示证明了偏振系统的等效定理，导出了等价简化系统的组成和四元数表示。提出了偏振系统的四元数矩阵计算方法，得到了四元数表示和Mueller矩阵之间的变换关系。讨论了根据四元数矩阵乘法有条件的交换性优化偏振系统的四元数矩阵算法的途径，并指出了这种算法的应用前景。

The quaternion method is introduced into the polarization optics systematically. Two quaternion representations of polarized light are presented which are based on the Poincare sphere representation and the Stokes parameters, respectively, and their equivalence relation is proved. The diversity of the quaternion representations of the polarized light is discussed. The quaternion representations of polarizing devices and systems are obtained. By using the quaternion representation, the equivalent theorem of polarizing system is proved, and the composition and the quaternion representations of the reduced equivalent system are deduced. The quaternion matrix calculation method for polarizing systems is presented, and the transform relations between the quaternion representations and the Mueller matrixes are obtained. Based on the conditional commutative low of the quaternion matrix multiplication, the optimization way of the quaternion matrix calculation method are discussed, and the application prospects of the algorithm are pointed.