The accurate method to calculate secondary fringes of field-widened, achromatic, temperature-compensated wind imaging interferometer (FATWindII) is presented, and the distribution of secondary fringes on instrument detector is simulated. The effects of secondary fringes on inversion errors of temperature and wind velocity are calculated. The formulas of modulation functions and phase shifts are derived when the wedge compensating glasses with arbitrary tilt angles, and the optimal tilt angles of wedge compensating glasses are obtained in FATWindII. By adopting antireflection film and wedge compensating glasses, the relative intensity of secondary fringes is reduced to below 2.5%, and the inversion errors of temperature and wind velocity introduced by the effects of secondary fringes can be minimized to about 0.05 K and 0.045 m·s-1 respectively. The research has important theoretical significance and practical guidance for the FATWind instrument design, fabrication and calibration.