Improving the precision of parallel registration by incorporating a priori information

This paper presents an algorithm for the precise registration of optical wavefronts. A wavefront exceeding the spatial or dynamic measurement range of a wavefront sensor, e.g. a Shack-Hartmann sensor, can be measured in multiple sub-measurements, each providing a segment of the wavefront. Sensor misalignment during the measurements results in the demand for registration algorithms to precisely reconstruct the entire wavefront from the segments. The proposed algorithm registers the segments in parallel and incorporates a priori information about the uncertainty of the sensor misalignment obtaining high-quality registration. A simulative analysis of the algorithm with respect to sensor misalignment and measurement errors is presented together with an application of the algorithm to a measured divergent wavefront. In the scope of the analysis, the algorithm is compared to state-of-the-art registration algorithms, such as the iterative closest point (ICP) algorithm, where an improvement of the registration performance by a factor of 3 is obtained. Results show that the algorithm is able to reconstruct a divergent and a freeform wavefront with an RMS registration error of a few tens of nanometers with a standard deviation of 80 µm and 2.4 mrad.