Air cross grids, for absorbing scattered secondary radiation and improving X-ray imaging in general radiography and in mammography, are provided with a large plurality of open air passages extending through each grid panel. These passages are defined by two large pluralities of substantially parallel partition walls, respectively extending transverse to each other. Each grid panel is made by laminating a plurality of thin metal foil sheets photo-etched to create through openings defined by partition segments. The etched sheets are aligned and bonded to form the laminated grid panel, which is moved edgewise during the X-ray exposure to pass primary radiation through the air passages while absorbing scattered secondary radiation arriving along slanted paths.