In order to realize the microminiaturization of the Fourier transform spectrometer (FTS) further, the micro lens array is introduced to FTS based on stepped micro-mirrors, which is used to collect each interference optical field unit modulated by stepped micro-mirrors synchronously. Because of the spatial modulation mode, the system wavefront aberration causes the wavefront distortion of each interference optical field unit. The scalar diffraction model of the interaction between the optical field with wavefront aberration and the stepped micro-mirrors, and the micro lens array is built. By means of calculation, the wavefront aberration is found impairing the intensity of each point in interference image at different levels, and introducing the low-frequency spectrum noise to the recovered spectrum. The analyses show that the intensity attenuation of interference image points results from the intensity modulation by wavefront aberration Strehl ratio of each interference optical field unit, and the low-frequency spectrum noise is mainly from the Fourier spectrum of Strehl ratio. According to the modulation characteristic of the wavefront aberration on interferogram, a method that using the wavefront aberration Strehl ratio to correct the interferogram intensity is proposed. The results indicate that this method improves the distortion of the recovered spectrum effectively.