This study presents a mathematical description of 2-D object imaging through a thin phase scattering layer by means of CCHM. The results of quantitative phase imaging were numerically simulated and experimentally verified for a weak and strong diffuser characterized by a different ratio of amounts of ballistic and diffuse light. The paper has shown that the phase image can be formed both by ballistic and diffuse light, depending on the diffuser properties. In the case of a weak diffuser, the best signal is always determined by the ballistic light, with resolution comparable or slightly worse than without the diffuser. The quality of the image behind a strong diffuser depends on the mutual shift of the reference and object beam images at the output plane. In some cases, the object can be imaged by both ballistic () and diffuse () light, and in other cases by the diffuse light only with surprisingly good image quality. The signal is, however, more noisy, the resolution worse, and in some cases, the imaging can be rather a phase visualization technique. Even the best choice of can usually lead to a good-quality QPI in a limited area of the image field. However, this area can be extended recombining images for several .