{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:18:00Z","timestamp":1785403080075,"version":"3.56.0"},"reference-count":55,"publisher":"Optica Publishing Group","issue":"10","license":[{"start":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T00:00:00Z","timestamp":1773187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T00:00:00Z","timestamp":1773187200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research","doi-asserted-by":"crossref","award":["03\/1492\/23\/EMR-II"],"award-info":[{"award-number":["03\/1492\/23\/EMR-II"]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/021wm7p51","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001412","name":"Council of Scientific and Industrial Research","doi-asserted-by":"crossref","award":["09\/1023(13663)\/2022-EMR-I"],"award-info":[{"award-number":["09\/1023(13663)\/2022-EMR-I"]}],"id":[{"id":"10.13039\/501100001412","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/021wm7p51","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2026,4,1]]},"abstract":"<jats:p>\n                    This study presents an application of the non-recursive\n\t\t\t\t\tapproach after combining the\n\t\t\t\t\ttransport of intensity equation (TIE) and the transport of phase\n\t\t\t\t\tequation (TPE), as proposed by Zhou\n                    <jats:italic toggle=\"yes\">et\u00a0al<\/jats:italic>\n                    . [\n                    <jats:mixed-citation publication-type=\"journal\">\n                      <jats:source>Appl. Opt.<\/jats:source>\n                      <jats:volume>61<\/jats:volume>\n                      ,\n                      <jats:fpage>B190<\/jats:fpage>\n                      (\n                      <jats:year>2022<\/jats:year>\n                      )\n                      <jats:pub-id pub-id-type=\"coden\">APOPAI<\/jats:pub-id>\n                      <jats:issn>0003-6935<\/jats:issn>\n                      <jats:pub-id pub-id-type=\"doi\">10.1364\/AO.444454<\/jats:pub-id>\n                    <\/jats:mixed-citation>\n                    ] for quantitative phase\n\t\t\t\t\timaging. Their method introduced a spatially varying propagation\n\t\t\t\t\tconstant\n                    <jats:italic>k<\/jats:italic>\n                    (\n                    <jats:italic>x<\/jats:italic>\n                    ,\n                    <jats:italic>y<\/jats:italic>\n                    )=\n                    <jats:italic>k<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    \u00d7\n                    <jats:italic>n<\/jats:italic>\n                    (\n                    <jats:italic>x<\/jats:italic>\n                    ,\n                    <jats:italic>y<\/jats:italic>\n                    ), allowing the TIE to be reformulated\n\t\t\t\t\tas a Poisson-type equation, where\n                    <jats:italic>n<\/jats:italic>\n                    (\n                    <jats:italic>x<\/jats:italic>\n                    ,\n                    <jats:italic>y<\/jats:italic>\n                    ) is the effective (virtual) refractive\n\t\t\t\t\tindex. By integrating the TPE into the TIE framework, the fast Fourier\n\t\t\t\t\ttransform TIE-TPE method effectively corrects errors\n\t\t\t\t\tcaused by the conventional assumption of uniform intensity at the\n\t\t\t\t\timage plane. The method is validated through numerical simulation and\n\t\t\t\t\toptical experiments. Gaussian phase functions with varying amplitudes\n\t\t\t\t\tunder perturbation have been used for numerical simulation. The\n\t\t\t\t\texperimental validation using an onion peel demonstrates a significant\n\t\t\t\t\timprovement in phase resolution. Additionally, the robustness of the\n\t\t\t\t\tmethod is demonstrated through phase reconstruction using the glass\n\t\t\t\t\tmicrobead powder sample. The concept of the virtual refractive index\n\t\t\t\t\tis also explored for qualitative analysis.\n                  <\/jats:p>","DOI":"10.1364\/ao.584896","type":"journal-article","created":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T14:00:08Z","timestamp":1771423208000},"page":"D46","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Application of transport of intensity and phase equations for quantitative phase imaging using a non-recursive method"],"prefix":"10.1364","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6006-8072","authenticated-orcid":true,"given":"Ram","family":"Kumar","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01ft5vz71","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9021-155X","authenticated-orcid":true,"given":"Shilpa","family":"Kanjilal","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01ft5vz71","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anurag","family":"Gupta","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01ft5vz71","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8458-6840","authenticated-orcid":true,"given":"Partha P.","family":"Banerjee","sequence":"additional","affiliation":[{"name":"University of Dayton"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7032-3946","authenticated-orcid":true,"given":"Naveen K.","family":"Nishchal","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01ft5vz71","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,3,11]]},"reference":[{"key":"ao-65-10-D46-R1","doi-asserted-by":"publisher","first-page":"4409","DOI":"10.1038\/s41598-021-83537-x","type":"journal-article","volume":"11","author":"Aknoun","year":"2021","journal-title":"Sci. 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All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}