Coherence property of x-rays is critical in the grating-based differential phase contrast (DPC) imaging because it is the physical foundation that makes any form of phase contrast imaging possible. Loss of coherence is an important experimental issue, which results in increased image noise and reduced object contrast in DPC images and DPC cone beam CT (DPC-CBCT) reconstructions. In this study, experimental results are investigated to characterize the visibility loss (a measurement of coherence loss) in several different applications, including different-sized phantom imaging, specimen imaging and small animal imaging. Key measurements include coherence loss (relative intensity changes in the area of interest in phase-stepping images), contrast and noise level in retrieved DPC images, and contrast and noise level in reconstructed DPC-CBCT images. The influence of size and composition of imaged object (uniform object, bones, skin hairs, tissues, and etc) will be quantified. The same investigation is also applied for moiré pattern-based DPC-CBCT imaging with the same exposure dose. A theoretical model is established to relate coherence loss, noise level in phase stepping images (or moiré images), and the contrast and noise in the retrieved DPC images. Experiment results show that uniform objects lead to a small coherence loss even when the attenuation is higher, while objects with large amount of small structures result in huge coherence loss even when the attenuation is small. The theoretical model predicts the noise level in retrieved DPC images, and it also suggests a minimum dose required for DPC imaging to compensate for coherence loss.