{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:25:55Z","timestamp":1760235955287,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T00:00:00Z","timestamp":1633910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 2274","SPP2013 SCHU 3227\/2"],"award-info":[{"award-number":["GRK 2274","SPP2013 SCHU 3227\/2"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"European Research Council","doi-asserted-by":"publisher","award":["AdG 695045"],"award-info":[{"award-number":["AdG 695045"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Federal Ministry of Education and Research","doi-asserted-by":"publisher","award":["05K16WO8"],"award-info":[{"award-number":["05K16WO8"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>Grating-based phase-contrast and dark-field imaging systems create intensity modulations that are usually modeled with sinusoidal functions to extract transmission, differential-phase shift, and scatter information. Under certain system-related conditions, the modulations become non-sinusoidal and cause artifacts in conventional processing. To account for that, we introduce a piecewise-defined periodic polynomial function that resembles the physical signal formation process, modeling convolutions of binary periodic functions. Additionally, we extend the model with an iterative expectation-maximization algorithm that can account for imprecise grating positions during phase-stepping. We show that this approach can process a higher variety of simulated and experimentally acquired data, avoiding most artifacts.<\/jats:p>","DOI":"10.3390\/jimaging7100209","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T21:45:32Z","timestamp":1633988732000},"page":"209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Signal Retrieval from Non-Sinusoidal Intensity Modulations in X-ray and Neutron Interferometry Using Piecewise-Defined Polynomial Function"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3552-2418","authenticated-orcid":false,"given":"Simon","family":"Pinzek","sequence":"first","affiliation":[{"name":"Chair of Biomedical Physics, Department of Physics, School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany"},{"name":"Munich Institute of Biomedical Engineering, Technical University of Munich, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1559-5495","authenticated-orcid":false,"given":"Alex","family":"Gustschin","sequence":"additional","affiliation":[{"name":"Chair of Biomedical Physics, Department of Physics, School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany"},{"name":"Munich Institute of Biomedical Engineering, Technical University of Munich, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9858-1194","authenticated-orcid":false,"given":"Tobias","family":"Neuwirth","sequence":"additional","affiliation":[{"name":"Heinz Maier-Leibnitz Zentrum (MLZ), Technical University of Munich, 85748 Garching, Germany"},{"name":"Physik-Department E21, Technical University of Munich, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Backs","sequence":"additional","affiliation":[{"name":"Heinz Maier-Leibnitz Zentrum (MLZ), Technical University of Munich, 85748 Garching, Germany"},{"name":"Physik-Department E21, Technical University of Munich, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0811-9589","authenticated-orcid":false,"given":"Michael","family":"Schulz","sequence":"additional","affiliation":[{"name":"Heinz Maier-Leibnitz Zentrum (MLZ), Technical University of Munich, 85748 Garching, Germany"},{"name":"Physik-Department E21, Technical University of Munich, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9456-1591","authenticated-orcid":false,"given":"Julia","family":"Herzen","sequence":"additional","affiliation":[{"name":"Chair of Biomedical Physics, Department of Physics, School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany"},{"name":"Munich Institute of Biomedical Engineering, Technical University of Munich, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Franz","family":"Pfeiffer","sequence":"additional","affiliation":[{"name":"Chair of Biomedical Physics, Department of Physics, School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany"},{"name":"Munich Institute of Biomedical Engineering, Technical University of Munich, 85748 Garching, Germany"},{"name":"Department of Diagnostic and Interventional Radiology, School of Medicine, Klinikum Rechts der Isar, Technical University of Munich, 81675 M\u00fcnchen, Germany"},{"name":"Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1063\/1.1754212","article-title":"An X-ray Interferometer","volume":"6","author":"Bonse","year":"1965","journal-title":"Appl. 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