Robust wavefront segment registration based on a parallel approach

Reconstructing highly divergent wavefronts from sparse measurements

The paper presents a concept for the sparse measurement and reconstruction of highly divergent wavefronts enabling measurements at high throughputs and beyond the dynamic range of the wavefront sensor. In the proposed concept, a direct measurement of the wavefront is carried out, where a few segments of the wavefront are measured with Shack-Hartmann sensors (SHSs). In total about 1% of the wavefront is measured and used for the reconstruction of the entire wavefront, which makes the concept suitable for applications where low measurement times are needed. A simulation analysis and an experimental validation of the concept are carried out, and results show that a wavefront with a divergence of 62° can be reconstructed with a root-mean-square error of about 200 nm.

Fast modal reconstruction of large plane wavefronts from sparse measurements using Shack-Hartmann sensors

A concept for the fast measurement and reconstruction of optical wavefronts using Shack-Hartmann sensors (SHSs) is presented. For wavefronts with a diameter at the scale of several tens of millimeters, hundreds of measurements with an SHS may be necessary to cover the wavefront. In the proposed concept, a few SHSs are used to measure about 2% of the entire wavefront, providing sufficient measurement data for its successful reconstruction. The small number of SHSs mounted in parallel makes the concept suitable for time-critical applications. A simulation analysis is performed, and an experimental validation of the concept is presented, demonstrating that the wavefront can be reconstructed with an RMS error of about 100 nm.

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.

Iterative parallel registration of strongly misaligned wavefront segments

The paper presents an algorithm for the precise registration of multiple wavefront segments containing large misalignment and phase differences. The measurement of a wavefront with huge dynamics or a large aperture size can be carried out in multiple Shack-Hartmann sensor measurements of segments of the wavefront. The registration algorithm is flexible with respect to the shape of the wavefront and can reconstruct a plane as well as divergent wavefronts, making it suitable for freeform wavefronts. The algorithm enables parallel registration of the wavefront segments which is carried out in an iterative manner to compensate for large misalignment errors. A simulative analysis of the proposed algorithm compares its performance to a fast parallel registration (FPR) algorithm and the established iterative closest point (ICP) algorithm. For a sensor misalignment of up to 100 μm and 3 mrad the algorithm registers a plane and a divergent wavefront with a precision that is a factor 4 and 12 better than the registration precision of the FPR and ICP algorithm.

Fast, precise, and shape-flexible registration of wavefronts

A fast and precise algorithm for wavefront reconstruction by the registration of wavefront segments is presented. If the wavefront exceeds the sensor aperture or the dynamic range of the sensor, a Shack-Hartmann sensor can measure only segments of an optical wavefront. The algorithm registers the wavefront segments in parallel, where they are simultaneously transformed to minimize their overlap mismatch for precise reconstruction of the entire wavefront. The original nonlinear optimization problem is approximated by a convex optimization problem that can be solved more efficiently. A simulation-based analysis of the algorithm and a comparison to a previously proposed parallel registration (PR) algorithm as well as to the iterative closest point (ICP) algorithm are presented. It is shown that despite measurement noise, the algorithm can precisely register plane as well as divergent wavefronts with root mean square registration errors smaller than 10 nm. Particularly for the divergent wavefront, this enables a reduction of the registration error by a factor of up to 750 as compared to the established algorithms. Analysis and comparison to the ICP and PR algorithm also show that the computation time of the proposed algorithm can be from one to three orders of magnitude smaller.