{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T05:34:12Z","timestamp":1773812052137,"version":"3.50.1"},"reference-count":47,"publisher":"AIP Publishing","issue":"12","funder":[{"DOI":"10.13039\/100006132","name":"Office of Science","doi-asserted-by":"publisher","award":["DE-SC0014229"],"award-info":[{"award-number":["DE-SC0014229"]}],"id":[{"id":"10.13039\/100006132","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006132","name":"Office of Science","doi-asserted-by":"publisher","award":["DE-SC0016154"],"award-info":[{"award-number":["DE-SC0016154"]}],"id":[{"id":"10.13039\/100006132","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018708","name":"Euratom Research and Training Program","doi-asserted-by":"publisher","award":["101052200 - EUROfusion"],"award-info":[{"award-number":["101052200 - EUROfusion"]}],"id":[{"id":"10.13039\/100018708","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,12,1]]},"abstract":"<jats:p>We present an improved diffraction model for phase contrast imaging (PCI), relevant to the measurement of electron density fluctuations in magnetically confined fusion plasmas. The model applies to optical systems containing multiple special components, such as phase plates, localization masks, and apertures, connected by segments describable in terms of ray transfer matrices. Fresnel diffraction in the connecting segments may be described using linear canonical transforms, while the special components are characterized by their respective transfer functions. For a PCI system with ideal placement of the phase plate and localization mask, deviations between the Fresnel and Fraunhofer diffraction models are entirely determined by the distance from the diffraction plane to the object plane of the optical system. Application of the developed model to the synthetic PCI diagnostic at the Wendelstein 7-X (W7-X) stellarator shows minimal impact of diffraction on the DC detector power. However, significant amplitude modifications due to phase scintillation from diffraction are expected for high-wavenumber PCI sound wave calibration signals at W7-X, in qualitative agreement with the experimental observations. In contrast to previous expectations, diffraction is found to have only a small impact on the localization mask response characteristics at W7-X. Based on this observation, we show that the synthetic PCI mask response at W7-X can be reproduced by a model which only considers the signal at the beam center in the image plane without diffraction. We further use a similar model to reproduce the experimentally observed mask response from the DIII-D tokamak, indicating the general applicability of such models.<\/jats:p>","DOI":"10.1063\/5.0287939","type":"journal-article","created":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T13:46:06Z","timestamp":1765374366000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Improved description of diffraction effects for phase contrast imaging with applications to magnetically confined fusion plasmas"],"prefix":"10.1063","volume":"96","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5146-1056","authenticated-orcid":false,"given":"S. K.","family":"Hansen","sequence":"first","affiliation":[{"name":"Plasma Science and Fusion Center, Massachusetts Institute of Technology 1 , Cambridge, Massachusetts 02139,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9518-4097","authenticated-orcid":false,"given":"M.","family":"Porkolab","sequence":"additional","affiliation":[{"name":"Plasma Science and Fusion Center, Massachusetts Institute of Technology 1 , Cambridge, Massachusetts 02139,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4501-8995","authenticated-orcid":false,"given":"J. C.","family":"Rost","sequence":"additional","affiliation":[{"name":"Plasma Science and Fusion Center, Massachusetts Institute of Technology 1 , Cambridge, Massachusetts 02139,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5828-2747","authenticated-orcid":false,"given":"J.-P.","family":"B\u00e4hner","sequence":"additional","affiliation":[{"name":"Plasma Science and Fusion Center, Massachusetts Institute of Technology 1 , Cambridge, Massachusetts 02139,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9729-9069","authenticated-orcid":false,"given":"M. R.","family":"Major","sequence":"additional","affiliation":[{"name":"Plasma Science and Fusion Center, Massachusetts Institute of Technology 1 , Cambridge, Massachusetts 02139,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0277-4600","authenticated-orcid":false,"given":"A.","family":"von Stechow","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Plasmaphysik 2 , D-17491 Greifswald,","place":["Germany"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7879-8671","authenticated-orcid":false,"given":"O.","family":"Grulke","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Plasmaphysik 2 , D-17491 Greifswald,","place":["Germany"]},{"name":"Department of Physics, Technical University of Denmark 3 , DK-2800 Kgs. Lyngby,","place":["Denmark"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5320-4996","authenticated-orcid":false,"given":"E. M.","family":"Edlund","sequence":"additional","affiliation":[{"name":"State University of New York College at Cortland 4 , Cortland, New York 13045,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Wendelstein 7-X Team","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2025,12,10]]},"reference":[{"key":"2025121008460035800_c1","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1016\/s0031-8914(34)80259-5","volume":"1","year":"1934","journal-title":"Physica"},{"key":"2025121008460035800_c2","doi-asserted-by":"publisher","first-page":"1563","DOI":"10.1063\/1.1720602","volume":"38","year":"1967","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c3","doi-asserted-by":"publisher","first-page":"1544","DOI":"10.1063\/1.1140193","volume":"59","year":"1988","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c4","doi-asserted-by":"publisher","first-page":"10E105","DOI":"10.1063\/1.5038804","volume":"89","year":"2018","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c5","doi-asserted-by":"publisher","first-page":"P01014","DOI":"10.1088\/1748-0221\/16\/01\/p01014","volume":"16","year":"2021","journal-title":"J.\u00a0Instrum."},{"key":"2025121008460035800_c6","doi-asserted-by":"publisher","first-page":"10E702","DOI":"10.1063\/1.2988821","volume":"79","year":"2008","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c7","doi-asserted-by":"publisher","first-page":"C12019","DOI":"10.1088\/1748-0221\/18\/12\/c12019","volume":"18","year":"2023","journal-title":"J.\u00a0Instrum."},{"key":"2025121008460035800_c8","doi-asserted-by":"publisher","first-page":"6492","DOI":"10.1143\/jjap.34.6492","volume":"34","year":"1995","journal-title":"Jpn. J. Appl. Phys."},{"key":"2025121008460035800_c9","unstructured":"S.\n            Coda\n          , \u201cAn experimental study of turbulence by phase-contrast imaging in the DIII-D tokamak,\u201d Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, 1997."},{"key":"2025121008460035800_c10","doi-asserted-by":"publisher","first-page":"023503","DOI":"10.1063\/1.3065094","volume":"80","year":"2009","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c11","unstructured":"J. R.\n            Dorris\n          , \u201cPhase contrast imaging measurements and modeling of short wavelength turbulence in the DIII\u2013D tokamak,\u201d Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, 2010."},{"key":"2025121008460035800_c12","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1063\/1.1147717","volume":"68","year":"1997","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c13","doi-asserted-by":"publisher","first-page":"1206","DOI":"10.1063\/1.1147883","volume":"68","year":"1997","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c14","doi-asserted-by":"publisher","first-page":"10E918","DOI":"10.1063\/1.2228623","volume":"77","year":"2006","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c15","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1016\/j.fusengdes.2019.01.015","volume":"139","year":"2019","journal-title":"Fusion Eng. Des."},{"key":"2025121008460035800_c16","doi-asserted-by":"publisher","first-page":"025005","DOI":"10.1088\/1361-6587\/aca4f7","volume":"65","year":"2023","journal-title":"Plasma Phys. Controlled Fusion"},{"key":"2025121008460035800_c17","doi-asserted-by":"publisher","first-page":"106022","DOI":"10.1088\/1741-4326\/ac2081","volume":"61","year":"2021","journal-title":"Nucl. Fusion"},{"key":"2025121008460035800_c18","doi-asserted-by":"publisher","first-page":"115340","DOI":"10.1016\/j.fusengdes.2025.115340","volume":"220","year":"2025","journal-title":"Fusion Eng. Des."},{"key":"2025121008460035800_c19","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1038\/s41567-021-01460-4","volume":"18","year":"2022","journal-title":"Nat. Phys."},{"key":"2025121008460035800_c20","doi-asserted-by":"publisher","first-page":"235101","DOI":"10.1103\/physrevlett.132.235101","volume":"132","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"2025121008460035800_c21","doi-asserted-by":"publisher","first-page":"025103","DOI":"10.1103\/physrevlett.134.025103","volume":"134","year":"2025","journal-title":"Phys. Rev. Lett."},{"key":"2025121008460035800_c22","doi-asserted-by":"publisher","first-page":"016007","DOI":"10.1088\/1741-4326\/ae15a3","volume":"66","year":"2026","journal-title":"Nucl. Fusion"},{"key":"2025121008460035800_c23","doi-asserted-by":"publisher","first-page":"905870314","DOI":"10.1017\/S0022377821000635","volume":"87","year":"2021","journal-title":"J.\u00a0Plasma Phys."},{"key":"2025121008460035800_c24","doi-asserted-by":"publisher","first-page":"095011","DOI":"10.1088\/1361-6587\/ac7ad2","volume":"64","year":"2022","journal-title":"Plasma Phys. Controlled Fusion"},{"key":"2025121008460035800_c25","article-title":"Characterizing core and edge turbulence regimes with fluctuation imaging diagnostics in Wendelstein 7-X","year":"2025","journal-title":"Nucl. Fusion"},{"key":"2025121008460035800_c26","doi-asserted-by":"publisher","first-page":"062302","DOI":"10.1063\/5.0197958","volume":"31","year":"2024","journal-title":"Phys. Plasmas"},{"key":"2025121008460035800_c27","volume-title":"Principles of Optics","year":"2002","edition":"7"},{"key":"2025121008460035800_c28","volume-title":"Principles of Plasma Diagnostics","year":"2002","edition":"2"},{"key":"2025121008460035800_c29","doi-asserted-by":"publisher","first-page":"062506","DOI":"10.1063\/1.3435217","volume":"17","year":"2010","journal-title":"Phys. Plasmas"},{"key":"2025121008460035800_c30","doi-asserted-by":"publisher","first-page":"1147","DOI":"10.1088\/0741-3335\/28\/8\/007","volume":"28","year":"1986","journal-title":"Plasma Phys. Controlled Fusion"},{"key":"2025121008460035800_c31","volume-title":"Fundamentals of Photonics","year":"2007","edition":"2"},{"key":"2025121008460035800_c32","doi-asserted-by":"publisher","first-page":"1168","DOI":"10.1364\/josa.60.001168","volume":"60","year":"1970","journal-title":"J.\u00a0Opt. Soc. Am."},{"key":"2025121008460035800_c33","doi-asserted-by":"publisher","first-page":"1772","DOI":"10.1063\/1.1665805","volume":"12","year":"1971","journal-title":"J.\u00a0Math. Phys."},{"key":"2025121008460035800_c34"},{"key":"2025121008460035800_c35","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1038\/s41586-020-2649-2","volume":"585","year":"2020","journal-title":"Nature"},{"key":"2025121008460035800_c36","article-title":"PCI calibration speaker pressure field measurement","year":"2024"},{"key":"2025121008460035800_c37","doi-asserted-by":"publisher","first-page":"1235","DOI":"10.1364\/josa.58.001235","volume":"58","year":"1968","journal-title":"J.\u00a0Opt. Soc. Am."},{"key":"2025121008460035800_c38","volume-title":"Handbook of Mathematical Functions","year":"1964"},{"key":"2025121008460035800_c39","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","volume":"17","year":"2020","journal-title":"Nat. Methods"},{"key":"2025121008460035800_c40","volume-title":"Table of Integrals, Series, and Products","year":"2007","edition":"7"},{"key":"2025121008460035800_c41","first-page":"283","volume":"5","year":"1835","journal-title":"Trans. Cambridge Philos."},{"key":"2025121008460035800_c42","volume":"47A","year":"2023","journal-title":"Europhys. Conf. Abstr."},{"key":"2025121008460035800_c43","doi-asserted-by":"publisher","first-page":"112002","DOI":"10.1088\/1741-4326\/ad2f4d","volume":"64","year":"2024","journal-title":"Nucl. Fusion"},{"key":"2025121008460035800_c44","volume-title":"Designing Optics Using Zemax OpticStudio\u00ae","year":"2024"},{"key":"2025121008460035800_c45","doi-asserted-by":"publisher","first-page":"2383","DOI":"10.1109\/tsp.2007.912890","volume":"56","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"2025121008460035800_c46","doi-asserted-by":"publisher","first-page":"093503","DOI":"10.1063\/1.4928668","volume":"86","year":"2015","journal-title":"Rev. Sci. Instrum."},{"key":"2025121008460035800_c47","doi-asserted-by":"publisher","first-page":"1819","DOI":"10.1364\/ao.46.001819","volume":"46","year":"2007","journal-title":"Appl. Opt."}],"container-title":["Review of Scientific Instruments"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/rsi\/article-pdf\/doi\/10.1063\/5.0287939\/20833293\/123507_1_5.0287939.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/rsi\/article-pdf\/doi\/10.1063\/5.0287939\/20833293\/123507_1_5.0287939.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T13:46:07Z","timestamp":1765374367000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/rsi\/article\/96\/12\/123507\/3374507\/Improved-description-of-diffraction-effects-for"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,1]]},"references-count":47,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2025,12,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0287939","relation":{},"ISSN":["0034-6748","1089-7623"],"issn-type":[{"value":"0034-6748","type":"print"},{"value":"1089-7623","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,12,1]]},"published":{"date-parts":[[2025,12,1]]},"article-number":"123507"}}