Coherent diffraction imaging (CDI) has become a powerful imaging modality in synchrotron x-ray imaging and electron microscopy communities. In the far-field geometry, image quality of CDI depends strongly on the performance of detector; specifically, the dynamic range, pixel size, and the absence of missing data. Coherent modulation imaging (CMI), an innovative variant of CDI, improves the algorithmic convergence by inserting a modulator upstream of the detector. Here, we explore the potential of CMI in eliminating nonideal effects of detector by modifying the modulus constraint to extrapolate the missing part of diffraction pattern. Nine folds of extrapolation in area of diffraction pattern have been shown feasible in experiment; while sixteen folds in simulation. For image quality measured by Structural Similarity (SSIM), our method shows a maximum of 32% improvement over the traditional method. Our method provides a way to alleviate the effects of beamstop, gaps between modules, limited dynamic range, and limited detector size for CMI.