Shape reconstruction of physical objects using structured light patterns and multiple layers of movable sheets which each include a transparent region and a pattern region. Shape reconstruction of specular regions on the surface of the object may proceed by a first phase in which a first sheet is moved to the pattern region and all other sheets are moved to the transparent region, and a first sequence of images is captured for patterns projected on the pattern region of the first sheet; and by a second phase in which the first sheet is moved to the transparent region and all other sheets are moved to the pattern region, and a second sequence of images is captured for patterns projected on the pattern region of the second sheet. Based on the captured images, the shape of the surface of an object, particularly objects having a mirror-like or specular surface having at least some specular characteristics, is reconstructed.