Iterative parallel registration of strongly misaligned wavefront segments

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.

Freeform optics: introduction

This feature issue of Optics Express highlights 28 state-of-the-art articles that capture a snapshot of the recent developments in the field of freeform optics. As an introduction, the editors provide an overview of all published articles, which cover a broad range of topics in freeform optics. The wide variety of applications presented here demonstrates that freeform optics is a growing and vibrant field with many more innovations to come.