The principle of the Sagnac imaging spectrometer was introduced,and the Sagnac interferometers' working way in the imaging spectrometer was illustrated. In this thesis,the structure of the solid Sagnac interferometer were analyzed,and discussion were made which based on the angle error directions' formulas which the spectral resolution of imaging spectrometer required the angle direction error of FT lens have to be met. From three vertical directions the rays were studied which passed through the two prisms adhered by glue,the pathway variation of the rays in the entitative Sagnac interferometer,and were aralyzed the relation by formulas between the spectral resolution and the angle deviation of the prisms were shown;the angle error formulas of the entitative Sagnac interferometer prisms were deduced which could meet the requirement of the spectral resolution of the interferometer spectroscopy;using examples to show the applying method of the formulas. If the dispersive induced by deforming of the shape of the prism and error of surfaces shape of the prism were neglected,only when the angle error of the prism were accounted,the angle error of the prisms should be strictly required,generally it should be less than 20″.