Highly accurate surface reconstruction for deflectometry

Deflectometry utilises the deformation of a sample pattern after reflection from a test surface to infer the surface normals. The absolute surface is reconstructed through integration of the slope data, at which small systematic errors can add up to significant shape deviations. In addition, the reconstruction problem is not unique: there are infinitely many solutions that satisfy a given field of surface normals. Therefore, the reconstruction must be constrained by extra information. We have previously presented the use of a confocal distance sensor to obtain a valid starting point for the integration (http://www.dgao-proceedings.de/download/112/112_a2.pdf), whose uncertainty was then taken to be zero. Further improvement is possible when the approximate shape of the measured surface is known. The starting point is then allowed to be altered by using surface reconstruction results. In certain cases, this method even allows finding the distance if it cannot be measured. Once the starting datum has been set, an unconstrained algorithm reconstructs the surface, and for a 200-mm telescope mirror the deflectometric data agree to within 1 µm with a tactile shape measurement.