We present the spectroscopy of the neutron star low-mass X-ray binary 4U 1636-53 using six simultaneous XMM-Newton and Rossi X-ray Timing Explorer observations. We applied different self-consistent reflection models to explore the features when the disk is illuminated by either the corona or the neutron star surface. We found that the spectra could be well fitted by these two types of models, with the derived emissivity index below a typical value of 3. The relative low emissivity can be explained if the neutron star and the corona, working together as an extended illuminator, simultaneously illuminate and ionize the disk. Additionally, the derived ionization parameter in the lamppost geometry is larger than the theoretical prediction. This inconsistency likely suggests that the corona does not emit isotropically in a realistic context. Furthermore, we also found that there is a possible trend between the height of the corona and the normalization of the disk emission. This could be understood either as a variation in the reflected radiation pressure or in the context of a jet base. Finally, we found that the disk is less ionized if it is illuminated by the neutron star, indicating that the illuminating source has significant influence on the physical properties of the disk. © The Authors 2023.