Absolute optical surface measurement with deflectometry

Deflectometry utilises the deformation and displacement of a sample pattern after reflection from a test surface to infer the surface slopes. Differentiation of the measurement data leads to a curvature map, which is very useful for surface quality checks with sensitivity down to the nanometre range. Integration of the data allows reconstruction of the absolute surface shape, but the procedure is very error-prone because systematic errors may add up to large shape deviations. In addition, there are infinitely many combinations for slope and object distance that satisfy a given observation. One solution for this ambiguity is to include information on the object’s distance. It must be known very accurately. Two laser pointers can be used for positioning the object, and we also show how a confocal chromatic distance sensor can be used to define a reference point on a smooth surface from which the integration can be started. The used integration algorithm works without symmetry constraints and is therefore suitable for free-form surfaces as well. Unlike null testing, deflectometry also determines radius of curvature (ROC) or focal lengths as a direct result of the 3D surface reconstruction. This is shown by the example of a 200 mm diameter telescope mirror, whose ROC measurements by coordinate measurement machine and deflectometry coincide to within 0.27 mm (or a sag error of 1.3μm). By the example of a diamond-turned off-axis parabolic mirror, we demonstrate that the figure measurement uncertainty comes close to a well-calibrated Fizeau interferometer.