Classical X-ray Computed Tomography (CT) and radiography are based on X-ray absorption and cannot show soft tissue structures as well as Magnetic Resonance Imaging (MRI). Detecting the phase delay/advance of X-rays that travel through the body could enhance soft tissue contrast 10 - 100 times. Submicron-period X-ray transmission gratings for medical x-ray energies can substantially enhance the phase detection sensitivity, but fabrication is a great challenge. This invention includes a method to fabricate multilayer transmission gratings of large areas. The design uses multilayer deposition of alternating materials on a staircase substrate to form micro grating arrays of extremely small periods and high aspect ratio in large areas. This invention should substantially improve the visibility of soft tissue structures and reduce radiation dose to patients.