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.

Compact scanning confocal chromatic sensor enabling precision 3-D measurements.

This paper proposes a compact and lightweight scanning confocal chromatic sensor (SCCS) for robot-based precision three-dimensional (3-D) surface measurement applications. The integrated system design includes a 2-D fast steering mirror (FSM) to manipulate the optical path of a high precision 1-D confocal chromatic sensor (CCS). A data-driven calibration procedure is used to accurately combine the FSM deflection angles and the correspondingly measured distances to the sample surface in order to obtain a correctly reconstructed 3-D image. Lissajous scan trajectories are applied to enable efficient scans of the sample surface. The SCCS provides 3-D images at frame rates of up to 1 fps and a measurement volume of 0.35×0.25×1.8mm3, as well as the measurement of arbitrary regions of interest. Using a calibration standard including structures with defined sizes, the lateral and axial resolutions are determined to 2.5 µm and 76 nm, respectively.

Robust wavefront segment registration based on a parallel approach.

This paper presents a robust registration algorithm for wavefront reconstruction from multiple partial measurements. Wavefronts exceeding the dynamic range or size of the Shack-Hartmann sensor can be measured as a set of segments. The wavefront is reconstructed by parallel registration of these wavefront segments, enabling compensation for sensor misalignment as well as for phase differences. For registration, a global mismatch metric is minimized by rigid body transformations and propagation of the wavefront segments. Apart from the description of the algorithm, a simulation-based evaluation and comparison to the iterative closest point (ICP) algorithm is performed. It is shown that in the case of a noisy data set, the parallel approach enables reconstruction errors that are a factor of 10 smaller than the result obtained with the ICP algorithm.

High-speed scanning chromatic confocal sensor for 3-D imaging with modeling-free learning control.

This paper presents a scanning system that integrates a chromatic confocal displacement sensor for topography measurement of a surface. To take an advantage of its compactness and reliability, an off-the-shelf chromatic confocal displacement sensor is integrated. Instead of moving the sensor, a galvanometer scanner reflects the optical point to increase the scan speed, and fast and accurate scanning motion is realized by learning without a model. The resulting images are corrected based on a geometric model to compensate for image distortion.

Confocal chromatic sensor with an actively tilted lens for 3D measurement.

Confocal chromatic displacement sensors are versatile and precise sensors for measuring the distance to a single point. In order to obtain a 3D measurement device, this paper presents an integrated scanning sensor design that employs a tilting lens mechanism for manipulating the light path of the sensor. The optical implications of the design are analytically modeled and simulated. An experimental setup is constructed to evaluate the system design and to test its performance on a variety of samples. Results show good agreement with the simulations and modeling; with maximal tip/tilt angles of ±2.5∘, the setup is capable of measuring a volume of 1.7×1.7×1mm3 with a lateral resolution of 24.8 µm and an axial resolution of 3 µm.

Integrated compensation-based laser sensor system for in-plane and out-of-plane target tracking.

This paper presents the development of a compensation-based laser sensor system, capable of sensing in-plane as well as out-of-plane displacements of a target. The sensor design integrates principles of laser triangulation and objective laser speckle measurement into a single device and provides an in-plane and out-of-plane resolution of 3 µm and 1 µm, respectively. The compensation-based operation keeps the variation of distance and lateral position relative to the target close to zero by actively following the target motion using feedback control. This enables a large operation range of the resulting sensing and tracking system, limited only by the range of the actuation system. Accurate tracking of target motions is demonstrated in an area of 1×1mm2 with a small remaining spatial rms tracking error between 8.75 µm and 13.25 µm.

Optical scanning of laser line sensors for 3D imaging.

In scanning laser triangulation sensors for 3D imaging, the achievable throughput is strongly limited by the moving mass. By realizing an optical scanning approach rather than repositioning the entire sensor, this limitation could be reduced, leading to a reduced measurement time. This work presents sensor system geometries in which only the optical path of a line triangulation sensor is manipulated by a tip-tilt mirror. In the proposed rotational scanning systems, either the illumination path or both the illumination and the reflection path are manipulated. By using ray-tracing simulation, the performance of the scanning systems are optimized and possible disadvantages can be determined up front. Using geometric relations, the surface profile can be reconstructed from the measured sensor data, the mirror position, and the model parameters. Experimental results show that the image quality of the proposed rotational scanning systems is comparable to systems based on classical translational scanning motion.