Birefringence is an important parameter in polarization sensitive fiber systems.Piezoelectric transducer based single-mode fiber (SMF) stretcher is a common device in optical fiber systems to introduce strain,optical path or phase changes,but people barely pay attention to the birefringence introduced in the fiber stretcher.In this paper,a characterization method of birefringence characteristics of SMF stretcher is proposed to obtain the birefringence distribution along the fiber wound in the stretcher,based on a distributed polarization analyzer achieved by introducing the full Muller matrix analyzing into the optical frequency domain reflectometry.From the experimental results we draw the following important conclusions:the birefringence of SMF wound in the fiber stretcher increases with the increase of driving voltage;when the surface of stretcher for SMF winding is uneven,a higher level background birefringence can be introduced,compared to a smooth surface,and the background birefringence increases more significantly when the driving voltage is applied;designing an appropriate stretching structure and fiber winding method can effectively avoid the change of birefringence during running the fiber stretcher,while a strong background birefringence may be introduced.This work will provide important guide for the evaluation and optimization of the polarization sensitive fiber systems in which the SMF stretchers are used.