% % This file was created by the TYPO3 extension % bib % --- Timezone: CET % Creation date: 2024-03-29 % Creation time: 16-00-05 % --- Number of references % 40 % @Article { KokDWE2023, title = {Virtual experiments for the assessment of data analysis and uncertainty quantification methods in scatterometry}, journal = {Metrologia}, year = {2023}, month = {5}, day = {19}, tags = {8.4,8.42,Messunsicherheit,Form}, state = {accepted}, DOI = {10.1088/1681-7575/acd6fd}, author = {Kok, G and Dijk, v M and W{\"u}bbeler, G and Elster, C} } @Phdthesis { HarrenneeHoffmann2022, title = {Investigating deep ensembles for the tilted-wave interferometer}, year = {2022}, month = {8}, day = {15}, keywords = {publiziert}, tags = {8.4,8.42,ML,Form}, url = {https://depositonce.tu-berlin.de/bitstream/11303/17264/4/harren_lara.pdf}, school = {TU Berlin}, type = {PhD Thesis}, DOI = {10.14279/depositonce-16044}, author = {Harren n{\'e}e Hoffmann, L} } @Article { KokWE2022, title = {Impact of Imperfect Artefacts and the Modus Operandi on Uncertainty Quantification Using Virtual Instruments}, journal = {Metrology}, year = {2022}, month = {6}, day = {12}, volume = {2}, pages = {311--319}, tags = {8.4,8.42,Messunsicherheit,Form}, DOI = {10.3390/metrology2020019}, author = {Kok, G and W{\"u}bbeler, G and Elster, C} } @Article { WubbelerMKHHE2022, title = {GUM-Compliant Uncertainty Evaluation Using Virtual Experiments}, journal = {Metrology}, year = {2022}, month = {3}, day = {1}, volume = {2}, number = {1}, pages = {114--127}, tags = {8.42,8.4,Form}, DOI = {10.3390/metrology2010008}, author = {W{\"u}bbeler, G and Marschall, M and Kniel, K and Hei{\ss}elmann, D and H{\"a}rtig, F and Elster, C} } @Article { ScholzFMSSE2022, title = {Experimental Design for Virtual Experiments in Tilted-Wave Interferometry}, journal = {Metrology}, year = {2022}, month = {2}, day = {17}, volume = {2}, pages = {84--97}, tags = {8.4,8.42,Form}, DOI = {doi.org/10.3390/metrology2010006}, author = {Scholz, G and Fortmeier, I and Marschall, M and Stavridis, M and Schulz, M and Elster, C} } @Article { FortmeierS2022, title = {Development of a metrological reference system for the form measurement of aspheres and freeform surfaces based on a tilted-wave interferometer}, journal = {Measurement Science and Technology}, year = {2022}, month = {1}, day = {24}, volume = {33}, number = {4}, tags = {8.4,8.42,Form}, state = {accepted}, DOI = {10.1088/1361-6501/ac47bd}, author = {Fortmeier, I and Stavridis, M and Schulz, M and Elster, C} } @Article { HoffmannFE2021_2, title = {Deep learning for tilted-wave interferometry}, journal = {tm - Technisches Messen}, year = {2021}, month = {11}, day = {20}, keywords = {publiziert}, tags = {8.4,8.42,Form,ML}, DOI = {10.1515/teme-2021-0103}, author = {Hoffmann, L and Fortmeier, I and Elster, C} } @Article { FischedickSBE2020, title = {Investigation of the uncertainty contributions of the alignment of PTB's double-ended interferometer by virtual experiments}, journal = {Metrologia}, year = {2021}, month = {10}, day = {12}, volume = {58}, number = {6}, pages = {064001}, tags = {8.4,8.42,Form}, DOI = {10.1088/1681-7575/ac2724}, author = {Fischedick, Markus and Stavridis, Manuel and Bartl, Guido and Elster, Clemens} } @Article { HoffmannFE2021, title = {Uncertainty Quantification by Ensemble Learning for Computational Optical Form Measurements}, journal = {Machine Learning: Science and Technology}, year = {2021}, month = {5}, day = {24}, keywords = {publiziert}, tags = {8.4,8.42,ML,Form}, DOI = {10.1088/2632-2153/ac0495}, author = {Hoffmann, L and Fortmeier, I and Elster, C} } @Article { HoffmannE2020, title = {Deep Neural Networks for Computational Optical Form Measurements}, journal = {Journal of Sensors and Sensor Systems}, year = {2020}, month = {9}, day = {24}, volume = {9}, pages = {301--307}, keywords = {publiziert}, tags = {8.4,8.42,ML,Form}, DOI = {10.5194/jsss-9-301-2020}, author = {Hoffmann, L and Elster, C} } @Article { SchenkerSST2020, title = {Effects of misalignments on the modulation transfer function measurement of camera lenses analyzed in optomechanical simulations}, journal = {Opt. Eng.}, year = {2020}, month = {3}, day = {3}, volume = {59}, number = {3}, pages = {034101}, tags = {8.4,8.42,Form}, DOI = {10.1117/1.OE.59.3.034101}, author = {Schenker, M and Stavridis, M and Schulz, M and Tutsch, R} } @Article { FortmeierSLMSHBBKSE2019, title = {Round robin comparison study on the form measurement of optical freeform surfaces}, journal = {Journal of the European Optical Society-Rapid Publications}, year = {2020}, month = {1}, day = {8}, volume = {16}, number = {2}, tags = {8.4,8.42,Form}, DOI = {10.1186/s41476-019-0124-1}, author = {Fortmeier, Ines and Schachtschneider, Reyko and Ledl, Vit and Matousek, Ondrej and Siepmann, Jens and Harsch, Antonia and Beisswanger, Rolf and Bitou, Youichi and Kondo, Yohan and Schulz, Michael and Elster, Clemens} } @Article { SchachtschneiderSFSE2019, title = {SimOptDevice: a library for virtual optical experiments}, journal = {Journal of Sensors and Sensor Systems}, year = {2019}, month = {2}, day = {27}, volume = {8}, number = {1}, pages = {105--110}, tags = {8.4, 8.42, Form}, DOI = {10.5194/jsss-8-105-2019}, author = {Schachtschneider, R and Stavridis, M and Fortmeier, I and Schulz, M and Elster, C} } @Article { SchachtschneiderFSABBBBKKLLMPRSSWWSE2018, title = {Interlaboratory comparison measurements of aspheres}, journal = {Measurement Science and Technology}, year = {2018}, month = {4}, day = {9}, volume = {29}, number = {5}, pages = {055010}, tags = {8.4, 8.42, KC, Form}, DOI = {10.1088/1361-6501/aaae96}, author = {Schachtschneider, R and Fortmeier, I and Stavridis, M and Asfour, J and Berger, G and Bergmann, R B and Beutler, A and Bl{\"u}mel, T and Klawitter, H and Kubo, K and Liebl, J and L{\"o}ffler, F and Mee{\ss}, R and Pruss, C and Ramm, D and Sandner, M and Schneider, G and Wendel, M and Widdershoven, I and Schulz, M and Elster, C} } @Phdthesis { Fortmeier2016, title = {Zur Optimierung von Auswerteverfahren f{\"u}r Tilted-Wave Interferometer}, journal = {Institut f{\"u}r Technische Optik, Universit{\"a}t Stuttgart}, year = {2016}, month = {7}, day = {31}, volume = {Berichte aus dem Institut f{\"u}r Technische Optik}, number = {82}, keywords = {8.42,Form}, tags = {8.42,Form}, address = {Stuttgart}, school = {Institut f{\"u}r Technische Optik, Universit{\"a}t Stuttgart}, type = {Berichte aus dem Institut f{\"u}r Technische Optik}, DOI = {10.18419/opus-8878}, author = {Fortmeier, I} } @Article { Fortmeier:16, title = {Evaluation of absolute form measurements using a tilted-wave interferometer}, journal = {Opt. Express}, year = {2016}, month = {1}, day = {8}, volume = {24}, number = {4}, pages = {3393--3404}, abstract = {Tilted-wave interferometry is a promising measurement technique for the highly accurate measurement of aspheres and freeform surfaces. However, the interferometric fringe evaluation of the sub-apertures causes unknown patch offsets, which currently prevent this measurement technique from providing absolute measurements. Simple strategies, such as constructing differences of optical path length differences (OPDs) or ignoring the piston parameter, can diminish the accuracy resulting from the absolute form measurement. Additional information is needed instead; in this paper, the required accuracy of such information is explored in virtual experiments. Our simulation study reveals that, when one absolute OPD is known within a range of 500 nm, the accuracy of the final measurement result is significantly enhanced.}, keywords = {Interferometry; Metrology; Surface measurements, figure; Aspherics}, tags = {8.42,Form,EMRP-Form}, web_url = {http://www.opticsexpress.org/abstract.cfm?URI=oe-24-4-3393}, publisher = {OSA}, DOI = {10.1364/OE.24.003393}, author = {Fortmeier, I and Stavridis, M and Wiegmann, A and Schulz, M and Osten, W and Elster, C} } @Article { Fortmeier2014, title = {Analytical Jacobian and its application to tilted-wave interferometry}, journal = {Optics express}, year = {2014}, volume = {22}, number = {18}, pages = {21313--25}, abstract = {Tilted-wave interferometry (TWI) is a novel optical measurement principle for the measurement of aspherical surfaces. For the reconstruction of the wavefront and the surface under test, respectively, perturbation methods are applied, which require the calculation of the Jacobian matrix. For the practical use of the instrument, a fast and exact calculation of the Jacobian matrices is crucial, since this strongly influences the calculation times of the TWI. By applying appropriate approaches in optical perturbation methods we are able to calculate the required Jacobian matrices analytically when the nominal optical path through the system is given. As a result, calculation times for the TWI can be considerably reduced. We finally illustrate the improved TWI procedure and apply methods of optimal design to determine optimal positions of the surface under test. For such applications the fast calculation of the Jacobian matrices is essential.}, keywords = {Aspherics,Interferometry,Mathematical methods (general),Metrology,Surface measurements,TWI,figure,tilted-wave}, tags = {8.42,EMRP_Form,Form,SimOpt}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=oe-22-18-21313{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, language = {EN}, ISSN = {1094-4087}, DOI = {10.1364/OE.22.021313}, author = {Fortmeier, I and Stavridis, M and Wiegmann, A and Schulz, M and Osten, W and Elster, C} } @Article { Schmahling2014, title = {Virtual experiment for near-field goniophotometric measurements}, journal = {Applied optics}, year = {2014}, volume = {53}, number = {7}, pages = {1481--7}, abstract = {Near-field goniometric measurements are employed to determine the photometric characteristics of light sources, i.e., the spatial and angular distribution of the emitted light. To this end, a complex measurement system consisting of a goniometer and a CCD-based imaging photometer is employed. In order to gain insight into the measurement system and to enable characterization of the whole measurement setup, we propose to apply a computer model to conduct virtual experiments. Within the computer model, the current state of all parts of the virtual experiment can be easily controlled. The reliability of the computer model is demonstrated by a comparison to actual measurement results. As an example for the application of the virtual experiment, we present an analysis of the impact of axial malpositions of the goniometer and camera.}, keywords = {Gonio,Light-emitting diodes,Mathematical methods (general),Metrological instrumentation,Metrology,Photometry,virtual experiment}, tags = {8.4,8.42,Form}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=ao-53-7-1481{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, language = {EN}, ISSN = {1539-4522}, DOI = {10.1364/AO.53.001481}, author = {Schm{\"a}hling, F and W{\"u}bbeler, G and Lopez, M and Gassmann, F and Kr{\"u}ger, U and Schmidt, F and Sperling, A and Elster, C} } @Article { Ehret2013, title = {Optical measurement of absolute flatness with the deflectometric measurement systems at PTB}, journal = {Journal of Physics: Conference Series}, year = {2013}, volume = {425}, number = {15}, pages = {152016}, tags = {8.42, Form, SimOpt}, web_url = {http://iopscience.iop.org/article/10.1088/1742-6596/425/15/152016}, publisher = {IOP Publishing}, language = {en}, ISSN = {1742-6588}, DOI = {10.1088/1742-6596/425/15/152016}, author = {Ehret, G and Schulz, M and Baier, M and Fitzenreiter, A} } @Article { Wiegmann2011, title = {Absolute Profilmessung optischer Oberfl{\"a}chen mit Mehrfachsensorsystemen}, journal = {tm - Technisches Messen}, year = {2011}, volume = {78}, number = {4}, pages = {184--189}, tags = {8.42,Form,SimOpt}, web_url = {http://www.degruyter.com/view/j/teme.2011.78.issue-4/teme.2011.0102/teme.2011.0102.xml}, ISSN = {0171-8096}, DOI = {10.1524/teme.2011.0102}, author = {Wiegmann, A and Schulz, M and Elster, C} } @Article { Wiegmann2011a, title = {Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments}, journal = {Precision Engineering}, year = {2011}, volume = {35}, number = {2}, pages = {183--190}, abstract = {We present a virtual experiment for the accuracy assessment of the sub-aperture interferometric measurement of a synchrotron mirror involving several thousand sub-aperture topographies. The virtual experiment simulates the measurement process and accounts for the influence of positioning device errors, interferometer errors, non-perfect calibration of machine geometry as well as errors in the interferometer reference. Two principles are considered for reconstructing the form of a test specimen from the conducted sub-aperture topographies, a stitching procedure and a direct measurement method. The virtual experiments are applied to the task of absolute form measurement (including its radius of curvature) of a synchrotron mirror with a length of 30cm, a width of 4cm, a maximum curvature of about 44mm{\^a}ˆ’1 and a peak-to-valley of 5mm. As a result, reconstruction accuracies can be expected to be in the range of 100nm when the stitching method is applied, which outperforms the direct measurement method by a factor of about 3.}, keywords = {Interferometry,Simulation,Stitching,Virtual experiment,virtual experiment}, tags = {8.42,Form,SimOpt}, web_url = {http://www.sciencedirect.com/science/article/pii/S014163591000125X}, ISSN = {01416359}, DOI = {10.1016/j.precisioneng.2010.08.007}, author = {Wiegmann, A and Stavridis, M and Walzel, M and Siewert, F and Zeschke, T and Schulz, M and Elster, C} } @Article { Schulz2010, title = {Concept, design and capability analysis of the new Deflectometric Flatness Reference at PTB}, journal = {Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment}, year = {2010}, volume = {616}, number = {2-3}, pages = {134--139}, abstract = {At PTB, a new setup for the highly accurate topography measurement of nearly flat optical surfaces is now under construction. The so-called Deflectometric Flatness Reference (DFR) is designed to measure in the direct deflectometric mode by applying an autocollimator and a scanning pentaprism, and in the difference deflectometric mode corresponding to the Extended Shear Angle Difference (ESAD) principle invented by PTB. With the new DFR instrument, horizontally as well as vertically orientated specimens with dimensions of up to 1m and a mass of up to 120kg will be measurable. The design of the new instrument is supported by employing a comprehensive simulation environment developed for dimensional measuring machines. The mechanical and optical concept is illustrated together with the current design of the DFR setup. Results from the simulations are presented to derive requirements for tolerated mechanical stage deviations and alignment accuracies.}, keywords = {ESAD,Flatness measurement,Nanometrology,Simulation}, tags = {8.42,Deflectometry,Form,SimOpt}, web_url = {http://www.sciencedirect.com/science/article/pii/S0168900209020592}, ISSN = {01689002}, DOI = {10.1016/j.nima.2009.10.108}, author = {Schulz, M and Ehret, G and Stavridis, M and Elster, C} } @Article { Wiegmann2010, title = {Improving the lateral resolution of a multi-sensor profile measurement method by non-equidistant sensor spacing}, journal = {Optics express}, year = {2010}, volume = {18}, number = {15}, pages = {15807--19}, abstract = {We present a method to enhance the achievable lateral resolution of a multi-sensor scanning profile measurement method. The relationship between the profile measurement method considered and established shearing techniques is illustrated. Simulation and measurement results show that non-equidistant sensor spacing can improve the lateral resolution significantly.}, keywords = {Image recognition,Instrumentation,Interferometry,Metrology,Surface measurements,algorithms and filters,and metrology,figure,measurement}, tags = {8.42, Form, SimOpt}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=oe-18-15-15807{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, language = {EN}, ISSN = {1094-4087}, DOI = {10.1364/OE.18.015807}, author = {Wiegmann, A and Schulz, M and Elster, C} } @Phdthesis { Wiegmann2009a, title = {Multiple Sensorsysteme zur Topographiebestimmung optischer Oberfl{\"a}chen}, year = {2009}, tags = {8.42,Form, SimOpt}, url = {http://dx.doi.org/10.14279/depositonce-2278}, school = {TU Berlin}, type = {PhD Thesis}, author = {Wiegmann, A} } @Article { Wiegmann2009, title = {Suppression of aliasing in multi-sensor scanning absolute profile measurement}, journal = {Optics Express}, year = {2009}, volume = {17}, number = {13}, pages = {11098}, abstract = {The task of anti-aliasing in absolute profile measurement by multi-sensor scanning techniques is considered. Simulation results are presented which demonstrate that aliasing can be highly reduced by a suitable choice of the scanning steps. The simulation results were confirmed by results obtained for interferometric measurements (Nyquist frequency 1/646 \(\mu\)m-1) on a specifically designed chirp specimen with sinusoidal waves of amplitude 100 nm and wavelengths from 2.5 mm down to 19 \(\mu\)m.}, keywords = {Image recognition,Instrumentation,Interferometry,Metrology,Surface measurements,algorithms and filters,and metrology,figure,measurement}, tags = {8.42, Form, SimOpt}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=oe-17-13-11098{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, language = {EN}, ISSN = {1094-4087}, DOI = {10.1364/OE.17.011098}, author = {Wiegmann, A and Schulz, M and Elster, C} } @Inproceedings { Schulz2009b, title = {Direkte Kalibrierung fl{\"a}chenmessender Interferometer mit dem TMS-Verfahren}, year = {2008}, tags = {8.42, Form, SimOpt}, url = {http://www.dgao-proceedings.de/download/109/109_a6.pdf}, booktitle = {DGaO Proceedings}, event_name = {DGaO 2008}, author = {Schulz, M and Marquez, A and Wiegmann, A and Elster, C} } @Inproceedings { Wiegmann2008b, title = {Absolute Topographievermessung gekr{\"u}mmter optischer Oberfl{\"a}chen mit hoher lateraler Aufl{\"o}sung}, year = {2008}, tags = {8.42, Form, SimOpt}, url = {http://www.dgao-proceedings.de/download/109/109_p28.pdf}, booktitle = {DGaO Proceedings}, event_name = {DGaO 2008}, author = {Wiegmann, A and Elster, C and Schulz, M and Stavridis, M} } @Article { Schulz2008, title = {Optical flatness metrology: 40 years of progress}, journal = {Opt. Pura Apl}, year = {2008}, volume = {41}, pages = {325}, abstract = {Optical flatness metrology has improved significantly in the last decades due to novel measurement tools and new math-based methods. An overview is given summarizing the most important optical techniques for flatness metrology at the nanometer level. The capabilities of modern methods such as the interferometric three-flat test accompanied by a computer-aided evaluation, the Traceable Multi Sensor method as an improved stitching method, and difference deflectometry represented by the Extended Shear Angle Difference method are reviewed.}, note = {Open Access}, keywords = {Deflectometry, Interferometry, Mathematical methods, Metrology, Optical inspection}, tags = {8.42, SimOpt, Form}, url = {http://www.sedoptica.es/Menu_Volumenes/pdfs/314.pdf}, booktitle = {Opt. Pura Apl}, DOI = {10.2971/jeos.2010.10011}, author = {Schulz, M and Wiegmann, A and Marquez, A and Elster, C} } @Article { Wiegmann2008, title = {Absolute profile measurement of large moderately flat optical surfaces with high dynamic range}, journal = {Optics Express}, year = {2008}, volume = {16}, number = {16}, pages = {11975}, abstract = {We present a novel procedure for absolute, highly-accurate profile measurement with high dynamic range for large, moderately flat optical surfaces. The profile is reconstructed from many sub-profiles measured by a small interferometer which is scanned along the specimen under test. Additional angular and lateral distance measurements are used to account for the tilt of the interferometer and its precise lateral location during the measurements. Accurate positioning of the interferometer is not required. The algorithm proposed for the analysis of the data allows systematic errors of the interferometer and height offsets of the scanning stage to be eliminated and it does not reduce the resolution. By utilizing a realistic simulation scenario we show that accuracies in the nanometer range can be reached.}, keywords = {Image recognition,Instrumentation,Interferometry,Metrology,Surface measurements,algorithms and filters,and metrology,figure,measurement}, tags = {8.42, Form, SimOpt}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=oe-16-16-11975{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, language = {EN}, ISSN = {1094-4087}, DOI = {10.1364/OE.16.011975}, author = {Wiegmann, A and Schulz, M and Elster, C} } @Inproceedings { Schulz2007, title = {Weiterentwicklung des TMS-Verfahrens zur hochaufl{\"o}senden und hochgenauen optischen Formmessung}, year = {2007}, tags = {8.42, Form, SimOpt}, url = {http://www.dgao-proceedings.de/download/108/108_a4.pdf}, booktitle = {DGaO Proceedings}, event_name = {DGaO 2007}, author = {Schulz, M and Wiegmann, A and Elster, C} } @Inproceedings { Wiegmann2007, title = {Stabilit{\"a}tsanalyse f{\"u}r das TMS-Verfahren: Einfluss hoher Ortsfrequenzen des Pr{\"u}flings}, year = {2007}, tags = {8.42, Form, SimOpt}, url = {http://www.dgao-proceedings.de/download/108/108_p34.pdf}, booktitle = {DGaO Proceedings}, event_name = {DGaO 2007}, author = {Wiegmann, A and Elster, C and Geckeler, R D and Schulz, M} } @Article { Elster2006, title = {Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors}, journal = {Precision Engineering}, year = {2006}, volume = {30}, number = {1}, pages = {32--38}, abstract = {Scanning topography measurements using systems of coupled distance sensors suffer from the presence of scanning stage and systematic sensor errors. While scanning stage errors can be estimated for suitably-designed sensor systems, it is usually not possible to simultaneously estimate both scanning stage and systematic sensor errors. Additional angular scanning stage measurements can solve this problem, and potentials and limitations of such a proceeding will be assessed. It is shown that perfect topography reconstruction can be achieved in the presence of systematic sensor and certain scanning stage errors provided that the measurements are noise-free and no further systematic errors emerge. In general, the topography is reconstructed by the application of least-squares, and the uncertainty associated with the reconstructed topography is derived. Resulting topography accuracies are evaluated for different noise levels of the distance sensor and angular scanning stage measurements, and practical considerations are discussed. The gain in accuracy due to accounting for scanning stage and systematic sensor errors can be large, and high accuracies can be reached.}, keywords = {Angular measurement,Distance sensor,High accuracy,High resolution,Least-squares,Topography,Uncertainty}, tags = {8.42,Form,SimOpt}, web_url = {http://www.sciencedirect.com/science/article/pii/S0141635905000504}, ISSN = {01416359}, DOI = {10.1016/j.precisioneng.2005.04.001}, author = {Elster, C and Weing{\"a}rtner, I and Schulz, M} } @Article { Schulz2006, title = {Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution}, journal = {Optical Engineering}, year = {2006}, volume = {45}, number = {6}, tags = {8.42,Form,SimOpt}, DOI = {10.1117/1.2208568}, author = {Schulz, M and Elster, C} } @Article { Weingärtner2004, title = {System of four distance sensors for high-accuracy measurement of topography}, journal = {Precision Engineering}, year = {2004}, volume = {28}, number = {2}, pages = {164 - 170}, abstract = {A novel sensor system consisting of four distance sensors is proposed for the scanning measurement of topography. The system achieves high accuracy and allows high lateral resolution. The configuration of the system can be chosen such that it guarantees perfect reconstruction of the topography in the presence of offset and pitch errors of the scan system provided the sensor measurements are error-free. Moreover, a favorable propagation of the random and systematic errors of the sensor measurements is achieved. The error influences are investigated and the sensor system is compared to a previously proposed three-sensor system by analyzing simulated data.}, keywords = {High lateral resolution}, tags = {8.42,Form}, web_url = {http://www.sciencedirect.com/science/article/pii/S0141635903001235}, ISSN = {0141-6359}, DOI = {10.1016/j.precisioneng.2003.10.001}, author = {Weing{\"a}rtner, I and Elster, C} } @Article { Elster2002, title = {Reconstructing surface profiles from curvature measurements}, journal = {Optik - International Journal for Light and Electron Optics}, year = {2002}, volume = {113}, number = {4}, pages = {154 - 158}, abstract = {Summary Recently, the measurement of curvature has been suggested as a promising new technique for the highly accurate determination of large-area surface profiles on the nanometer scale. It was shown that the curvature can be measured with highest accuracy and high lateral resolution. However, the reconstruction of surface profiles from curvature data involves the numerical solution of an ordinary differential equation for which initial or boundary values must be specified. This paper investigates the accuracy with which surface profiles can be reconstructed from curvature data. The stability of the reconstructions is examined with respect to the presence of measurement noise and the accuracy of the initial values. The assessment of the reconstruction accuracy is based on an analytical solution (up to numerical integration) derived for the case when the measurement results are given in Cartesian coordinates, and on numerical results in the polar case. The results presented for the latter case allow, in particular, conclusions to be drawn regarding the minimum accuracy of data and initial values required for reconstructing aspheres from curvature measurements with nanometer accuracy.}, keywords = {Runge-Kutta method}, tags = {8.42, Form}, web_url = {http://www.sciencedirect.com/science/article/pii/S0030402604701345}, ISSN = {0030-4026}, DOI = {10.1078/0030-4026-00138}, author = {Elster, C and Gerhardt, J and Thomsen-Schmidt, P and Schulz, M and Weing{\"a}rtner, I} } @Inbook { Elster2000c, title = {Evaluation of lateral shearing interferograms}, year = {2000}, volume = {Advanced Mathematical \& Computational Tools in Metrology and Testing IV}, pages = {76-87}, tags = {8.42,Form}, editor = {P. Ciarlini, A.B. Forbes, F. Pavese, D. Richter}, publisher = {World Scientific Singapore}, series = {Series on Advances in Mathematics for Applied Sciences}, edition = {53}, chapter = {5}, author = {Elster, C} } @Article { Elster2000, title = {Exact two-dimensional wave-front reconstruction from lateral shearing interferograms with large shears}, journal = {Appl. Opt.}, year = {2000}, volume = {39}, number = {29}, pages = {5353--5359}, abstract = {A method is proposed for exact discrete reconstruction of atwo-dimensional wave front from four suitably designed lateral shearingexperiments. The method reconstructs any wave front at evaluationpoints of a circular aperture exactly up to an arbitrary constant fornoiseless data, and it shows excellent stability properties in the caseof noisy data. Application of large shears is allowed, and highresolution of the reconstructed wave front can be achieved. Resultsof numerical experiments are presented that demonstrate the capabilityof the method.}, keywords = {Interferometry; Optical inspection; Phase measurement}, tags = {8.42,Form}, web_url = {http://ao.osa.org/abstract.cfm?URI=ao-39-29-5353}, publisher = {OSA}, DOI = {10.1364/AO.39.005353}, author = {Elster, C} } @Article { Elster1999, title = {Recovering wavefronts from difference measurements in lateral shearing interferometry}, journal = {Journal of Computational and Applied Mathematics}, year = {1999}, volume = {110}, number = {1}, pages = {177--180}, abstract = {Results of lateral shearing interferograms are difference measurements of a wavefront under study, from which this wavefront is to be reconstructed. Properties of the difference operator associated with a shearing experiment are discussed. It is shown that the Moore{\^a}{\euro}“Penrose generalized inverse is bounded and it is given in an explicit form for suitably chosen shearing parameters.}, keywords = {Difference operator,Generalized inverse,Shearing interferometry}, tags = {8.42,Form}, web_url = {http://www.sciencedirect.com/science/article/pii/S0377042799002320}, ISSN = {03770427}, DOI = {10.1016/S0377-0427(99)00232-0}, author = {Elster, C} } @Article { Elster1999a, title = {Solution to the Shearing Problem}, journal = {Applied Optics}, year = {1999}, volume = {38}, number = {23}, pages = {5024}, abstract = {Lateral shearing interferometry is a promising reference-free measurement technique for optical wave-front reconstruction. The wave front under study is coherently superposed by a laterally sheared copy of itself, and from the interferogram difference measurements of the wave front are obtained. From these difference measurements the wave front is then reconstructed. Recently, several new and efficient algorithms for evaluating lateral shearing interferograms have been suggested. So far, however, all evaluation methods are somewhat restricted, e.g., assume a priori knowledge of the wave front under study, or assume small shears, and so on. Here a new, to our knowledge, approach for the evaluation of lateral shearing interferograms is presented, which is based on an extension of the difference measurements. This so-called natural extension allows for reconstruction of that part of the underlying wave front whose information is contained in the given difference measurements. The method is not restricted to small shears and allows for high lateral resolution to be achieved. Since the method uses discrete Fourier analysis, the reconstructions can be efficiently calculated. Furthermore, it is shown that, by application of the method to the analysis of two shearing interferograms with suitably chosen shears, exact reconstruction of the underlying wave front at all evaluation points is obtained up to an arbitrary constant. The influence of noise on the results obtained by this reconstruction procedure is investigated in detail, and its stability is shown. Finally, applications to simulated measurements are presented. The results demonstrate high-quality reconstructions for single shearing interferograms and exact reconstructions for two shearing interferograms.}, keywords = {Interferometry,Optical inspection,Phase measurement}, tags = {8.42,Form}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=ao-38-23-5024{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, language = {EN}, ISSN = {0003-6935}, DOI = {10.1364/AO.38.005024}, author = {Elster, C and Weing{\"a}rtner, I} } @Article { Elster1999b, title = {Exact wave-front reconstruction from two lateral shearing interferograms}, journal = {Journal of the Optical Society of America A}, year = {1999}, volume = {16}, number = {9}, pages = {2281}, abstract = {A new method is presented for the reconstruction of a one-dimensional wave front on the basis of difference measurements from two shearing interferograms. The proposed algorithm reconstructs any wave front exactly up to an arbitrary constant. The method is not restricted to small shears. However, the shearing parameters have to be chosen such that certain constraints are satisfied. A procedure for determining such shearing parameters is given. In addition, it is shown that the procedure is stable with respect to noise introduced into the differences.}, keywords = {Interferometry,Optical inspection,Paraxial wave optics,Phase measurement}, tags = {8.42,Form}, web_url = {http://www.osapublishing.org/viewmedia.cfm?uri=josaa-16-9-2281{\&}seq=0{\&}html=true}, publisher = {Optical Society of America}, ISSN = {1084-7529}, DOI = {10.1364/JOSAA.16.002281}, author = {Elster, C and Weing{\"a}rtner, I} }