Apparatus for mapping an object includes an illumination assembly (30, 50), which includes a single transparency (36) containing a fixed pattern (60, 70, 80) of spots. A light source (34, 52) transilluminates the single transparency with optical radiation so as to project the pattern onto the object (28). An image capture assembly (32) captures an image of the pattern that is projected onto the object using the single transparency. A processor (24) processes the image captured by the image capture assembly so as to reconstruct a three-dimensional (3D) map of the object.