{"data":{"id":"10.6084/m9.figshare.c.4034702","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.4034702","prefix":"10.6084","suffix":"m9.figshare.c.4034702","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Yichen Wu","affiliation":[],"nameIdentifiers":[]},{"name":"Rivenson, Yair","nameType":"Personal","givenName":"Yair","familyName":"Rivenson","affiliation":[],"nameIdentifiers":[]},{"name":"Yibo Zhang","affiliation":[],"nameIdentifiers":[]},{"name":"Zhensong Wei","affiliation":[],"nameIdentifiers":[]},{"name":"Günaydın, Harun","nameType":"Personal","givenName":"Harun","familyName":"Günaydın","affiliation":[],"nameIdentifiers":[]},{"name":"Lin, Xing","nameType":"Personal","givenName":"Xing","familyName":"Lin","affiliation":[],"nameIdentifiers":[]},{"name":"Ozcan, Aydogan","nameType":"Personal","givenName":"Aydogan","familyName":"Ozcan","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Extended depth-of-field in holographic image reconstruction using deep learning based auto-focusing and phase-recovery"}],"publisher":"Figshare","container":{},"publicationYear":2018,"subjects":[{"subject":"Uncategorized"},{"subject":"90606 Photonics and Electro-Optical Engineering (excl. Communications)","subjectScheme":"FOR"},{"subject":"FOS: Electrical engineering, electronic engineering, information engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"}],"contributors":[],"dates":[{"date":"2018-03-18","dateType":"Created"},{"date":"2018-05-25","dateType":"Updated"},{"date":"2018","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsSupplementTo","relatedIdentifier":"10.1364/optica.5.000704","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC BY 4.0","rightsUri":"https://creativecommons.org/licenses/by/4.0"}],"descriptions":[{"description":"Holography encodes the three dimensional (3D) information of a sample in the form of an intensity-only recording. However, to decode the original sample image from its hologram(s), auto-focusing and phase-recovery are needed, which are in general cumbersome and time-consuming to digitally perform. Here we demonstrate a convolutional neural network (CNN) based approach that simultaneously performs auto-focusing and phase-recovery to significantly extend the depth-of-field (DOF) in holographic image reconstruction. For this, a CNN is trained by using pairs of randomly de-focused back-propagated holograms and their corresponding in-focus phase-recovered images. After this training phase, the CNN takes a single back-propagated hologram of a 3D sample as input to rapidly achieve phase-recovery and reconstruct an in focus image of the sample over a significantly extended DOF. This deep learning based DOF extension method is non-iterative, and significantly improves the algorithm time-complexity of holographic image reconstruction from O(nm) to O(1), where n refers to the number of individual object points or particles within the sample volume, and m represents the focusing search space within which each object point or particle needs to be individually focused. These results highlight some of the unique opportunities created by data-enabled statistical image reconstruction methods powered by machine learning, and we believe that the presented approach can be broadly applicable to computationally extend the DOF of other imaging modalities.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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