A miniature snapshot Fourier-transform imaging spectrometer is proposed to realize the real-time detection of images and spectra of moving scenes and fast-changing targets. Interferometric imaging spectra are acquired in real time using two multi-stage micro-mirrors to modulate the distributed phase of multiple image fields formed by a micro-lens array. Based on phase modulation by the micro-lens array and multi-stage micro-mirrors on the optical field, a theoretical model is established for multiple interferometric imaging. Numerical results show that the interferometric image points with different field of view (FOV) are located at different areas on the detector plane. However, in the case of a large FOV, the interferometric image units between adjacent channels have crosstalk and the recovered spectrum is distorted. To suppress the crosstalk between adjacent channels, the FOV angle can be controlled within the limited FOV determined by the diffraction and defocusing effects of the micro-lens array and multi-stage micro-mirrors. Simultaneously, the FOV introduces phase errors, which causes monotonously increasing normalized spectral errors according to the FOV angle. Based on the normalized spectral error analysis results, the FOV can be rationally designed to achieve effective detection of a specific area in target scenes.