In order to further realize the miniaturization of the Fourier transform infrared spectrometer, a spatial light modulator and a point detector are introduced in the Fourier transform infrared spectrometer which is based on multistep micro-mirror. The phase of incident optical field is modulated by the multistep micro-mirror, and the distributed measurement is conducted for each interference order using the spatial light modulator. The two multistep micro-mirrors are regarded as two phase diffraction screens, and the spatial light modulator is regarded as an amplitude diffraction screen. The interaction between optical wave and each diffraction screen is analyzed. It is found that the interference optical field is modulated by the spatial light modulator and the diffraction optical field at the multistep micro-mirror margin. The incident optical field is cut off by the multistep micro-mirror margin, which results in the diffraction effect. In order to inhibit the influence of diffraction effect on the system, a method which extends the step order of the multistep micro-mirror is proposed. By means of enlarging the interference area, the influence of the marginal diffraction effect on the internal effective interference order can be avoided. The results indicate that this method can eliminate distortion of the interferogram sequence and achieve signal spectrum recovery effectively.