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In a static wind imaging Michelson interferometer (SWIMI) developed by us, two-arm glasses are used to achieve the achromatic thermally compensation. The arm glass is cemented with the beam splitter. The tilt of the arm glass would cause a change to the optical path difference (OPD), thereby reducing the visibility of the interferogram and introducing phase error to the SWIMI system, which eventually responsible for errors in the inversion of temperature and wind velocity. In this paper, we present the principle of static wind imaging interferometer and derivate the variation of OPD caused by the two-dimensional tilt of arm glass in detail. By considering a rectangle incident beam, we analyze the effect of arm glass tilt on wind speed and temperature inversion. The results show that in order to realize the wind velocity error less than 3 m/s, the temperature error less than 3 K, and the instrument visibility greater than 0.8, the two-dimensional tilted angle of arm glass should be less than 1". The tolerance of tilted angle can expand by adjusting the refractive index of the medium on both two sides of the arm glass or by adjusting the reflector mirror of the interferometer precisely. The results would be helpful for the cement of arm glass, beam splitter of SWIMI, and provide a reference for the design of a field-widened wind imaging interferometer. [ABSTRACT FROM AUTHOR]