{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:27:41Z","timestamp":1785403661397,"version":"3.56.0"},"reference-count":32,"publisher":"Optica Publishing Group","issue":"12","license":[{"start":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T00:00:00Z","timestamp":1780531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T00:00:00Z","timestamp":1780531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100003246","name":"Dutch Research Council","doi-asserted-by":"crossref","award":["19405"],"award-info":[{"award-number":["19405"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/04jsz6e67","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,6,15]]},"abstract":"<jats:p>Ptychography is a widely used computational imaging technique capable of reconstructing both the complex object and the illumination field. However, as a scanning-based imaging method, its acquisition speed is inherently limited, and in high-flux regimes, the total measurement time is often dominated by sample positioning and settling overhead rather than exposure time. To overcome this limitation, fly-scan ptychography was introduced, in which the sample is translated continuously during each exposure. This approach maximizes acquisition duty cycle but introduces motion-induced blurring of the diffraction patterns, which is typically addressed using probe-mode or object-mode decomposition. In existing implementations, these methods require precise synchronization between sample motion and detector acquisition, relying on accurate knowledge of the fly-scan trajectory. In this work, we introduce a modified ptychographic forward model that leverages automatic differentiation to simultaneously reconstruct not only the object and probe, but also the fly-scan trajectory directly from the measured data, without requiring precise synchronization or prior knowledge of the sample path. We demonstrate, through both numerical simulations and experimental measurements, accurate fly-scan path retrieval for extended scan lengths, achieving diffraction-limited resolution. We show that trajectory retrieval significantly improves reconstruction quality compared to approaches based on spline-interpolated scan paths. By directly comparing retrieved fly-scan trajectories with independently measured ground-truth paths, we confirm good agreement. This approach eliminates the need for high-speed position tracking and tight hardware synchronization, reducing experimental complexity and cost, and enabling fly-scan operation to be readily implemented in conventional step-scan ptychography setups.<\/jats:p>","DOI":"10.1364\/oe.597690","type":"journal-article","created":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T05:00:08Z","timestamp":1779685208000},"page":"21563","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["High-speed computational imaging achieved by fly-scan ptychography"],"prefix":"10.1364","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7741-4883","authenticated-orcid":true,"given":"Augustas","family":"Karpavicius","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02e2c7k09","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Advanced Research Center for Nanolithography"},{"name":"Vrije Universiteit Amsterdam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3441-0943","authenticated-orcid":true,"given":"Matthias","family":"Gouder","sequence":"additional","affiliation":[{"name":"Advanced Research Center for Nanolithography"},{"name":"Vrije Universiteit Amsterdam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1899-4395","authenticated-orcid":true,"given":"Stefan","family":"Witte","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02e2c7k09","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Advanced Research Center for Nanolithography"},{"name":"Vrije Universiteit Amsterdam"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,6,4]]},"reference":[{"key":"oe-34-12-21563-R1","doi-asserted-by":"publisher","first-page":"826","DOI":"10.1126\/science.abg2533","type":"journal-article","volume":"372","author":"Chen","year":"2021","journal-title":"Science"},{"key":"oe-34-12-21563-R2","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1038\/s41586-018-0298-5","type":"journal-article","volume":"559","author":"Jiang","year":"2018","journal-title":"Nature"},{"key":"oe-34-12-21563-R3","doi-asserted-by":"publisher","first-page":"12532","DOI":"10.1038\/ncomms12532","type":"journal-article","volume":"7","author":"Yang","year":"2016","journal-title":"Nat. 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Further distribution of this work must maintain attribution to the author(s) and the published article\u2019s title, journal citation, and DOI.","name":"copyright","label":"Copyright"}]}}