High precision shape reconstruction of optical wavefronts for the assessment of optical systems

Wavefront sensors are of fundamental importance for the development and assessment of optical systems. The Shack Hartmann sensor (SHS) in particular is widely used because it is compact, vibration-insensitive, and has a large dynamic range. Large or strongly curved wavefronts are a challenge for the wavefront sensor, as they exceed its aperture size or dynamic range. This makes especially the development of next-generation optical systems, such as freeform optics, difficult. Scanning such a wavefront with an SHS mounted on a positioning system enables the direct measurement of the wavefront at multiple locations. To obtain the wavefront the measurements have to be registered resulting in the need for registration algorithms. This thesis investigates registration algorithms that enable a precise reconstruction of the wavefront. Rigid body transformation as well as propagation of the wavefronts is considered for the registration. Parallel registration of the wavefronts is analysed and compared to sequential registration based on the well-established iterative closest point (ICP) algorithm. Results obtained with parallel registration are of high precision at the scale of tens of nanometers and are at least a factor of 10 better than those obtained with sequential registration. Moreover, an investigation of the algorithms is carried out with the goal of fast registration needed for their application within production lines. The resulting algorithms have short computation times down to 100 ms on a personal computer (2.6GHz) making them suitable for inline metrology. The algorithms are evaluated with respect to the shape of the wavefront and high precision results are obtained considering plane, highly divergent, and freeform wavefronts. Moreover, the influence of measurement errors and sensor misalignment on the performance of the algorithms is analysed. Finally, the incorporation of a priori information for the improvement of the registration results is evaluated. Besides the registration-based approach where all parts of the wavefront are measured with the SHS, approaches for determining the wavefront from sparse measurements are investigated. The wavefront is measured at a few locations with the SHS which leads to a significant decrease in the measurement time compared to the registration-based approach. The modal reconstruction of the wavefront from the measurement data is proposed. In particular, the reconstruction of plane and highly divergent wavefronts is evaluated with respect to measurement errors, and its functionality is proven via simulations and experiments.