The iteration progress of coherent modulation imaging (CMI) is equivalent to gradient search algorithm, and a CMI convergence model is established. From the perspective of solving equations, the basic conditions to ensure the uniqueness of reconstruction results are put forward, i.e., the number of non-zero points of the diffraction pattern with a modulation plate is twice as much as that without the modulation plate, or the ratio of the spectrum cut-off width after enlarging λL (λ is the wavelength and L is the diffraction distance) times with the modulation plate to the spectrum cut-off width without the modulation plate is at least 0.414. It is verified by simulation. This study provides a theoretical basis for further optimization of CMI.