Non-contact measurement of circular surfaces via photometric stereo in polar coordinates

The measurement of the warpage of injection molded parts in polymer processing is a central task in the quality control of production processes. Complex high-end products are very challenging in terms of quality inspection. Therefore, a lot of effort is made in order to measure the shape using contact measuring systems, despite the reduced flexibility and increased duration of the measurement process. This paper presents a new approach of non-contact measurement using Photometric Stereo. Photometric Stereo brings all the benefits of an optical, contact-free measurement system along with fast analysis of the data. The principle of operation consists of two parts: the optical measurement of the gradient field by an industrial gigE-camera and the surface reconstruction by a global least squares approach. The minimum of three light-sources was extended to a set-up with four LEDs to gain more precision by additional data. A new surface reconstruction method, based on surface reconstruction from polar gradient fields was developed and tested. This is the first approach of using gradient fields in polar coordinates to direct surface reconstruction from gradients for industrial Photometric Stereo. For the evaluation of the proposed method a fully functional test set-up was built. The resulting measurement set-up is robust enough to be used directly on the shop floor for quality control.