Measurement of the 3-D shape of specular polyhedrons using an M-array coded light source

In this paper we describe a method for measuring three-dimensional shape of specular polyhedron by using an M-array coded light source. Determination of a shape of specular surface is important especially for industrial applications. However, owing to specular reflection, it is difficult to measure the shape of specular surfaces by applying the methods for diffusing surfaces. We reconstruct the shape of specular objects from the image of M-array coded light source observed after being reflected by the object. Using the “window property” of M-array, the correspondence is found between a point on the image of reflected light source and a point on light source. By assuming that the surface is locally a plane, normal vectors of the surface are determined from the correspondence, and three-dimensional shape of the surface is reconstructed. This method enables us to measure the shape of specular polyhedron by using a simple equipment. The method was tested for a polyhedron of 10 cm of each side, 50 cm apart from the camera. The shape of the polyhedron was reconstructed correctly. The precision of the measurement was about 1 mm