Spatial heterodyne spectroscopy (SHS) is a new spatial interference spectroscopy which can achieve high spectral resolution. The alignment error of the detector array can lead to a significant influence with the spectral resolution of a SHS system. Theoretical models for analyzing the alignment errors which are divided into three kinds are presented in this paper. Based on these models, the tolerance angle of these errors has been given, respectively. The result of simulation experiments shows that when the angle of slope error, tilt error, and rotation error are less than 1.21 degrees, 1.21 degrees, 0.066 degrees respectively, the alignment reaches an acceptable level. (C) 2017 Optical Society of America