Markus C. Knauer

Shape reconstruction from gradient data

We present a generalized method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object but rather its local slope. These sensors display several advantages, including high information efficiency, sensitivity, and robustness. For many applications, however, it is necessary to acquire the shape, which must be calculated from the slopes by numerical integration. Existing integration techniques show drawbacks that render them unusable in many cases. Our method is based on an approximation employing radial basis functions. It can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.

Deflektometrie macht der Interferometrie KonkurrenzDeflectometry Rivals Interferometry

Zusammenfassung Die Deflektometrie ist eine in den letzten Jahren neu entwickelte Methode zur Vermessung glatter Oberflächen. Sie gestattet es, auch auf Freiformflächen Höhenvariationen im Nanometerbereich zu vermessen. Um die positiven Eigenschaften der Deflektometrie zu verstehen, betrachten wir die physikalischen Grenzen sowie informationstheoretische Aspekte. Abschließend wird die Vielseitigkeit der Deflektometrie anhand von Anwendungsbeispielen demonstriert.

Deflectometry Challenges Interferometry: 3-D-Metrology from Nanometer to Meter

We will discuss deflectometry from the physicist’s and from the information theoretical point of view. The intrinsic features of deflectometry -incoherence, source encoding, high dynamical range, simplicity, and scalability- enable new sensors and unexpected applications. (Digital Holography and Three-Dimensional Imaging, 2009). Download original .PDF file here: