{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T16:25:09Z","timestamp":1773246309717,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T00:00:00Z","timestamp":1687219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62205100"],"award-info":[{"award-number":["62205100"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Optical neural networks can effectively address hardware constraints and parallel computing efficiency issues inherent in electronic neural networks. However, the inability to implement convolutional neural networks at the all-optical level remains a hurdle. In this work, we propose an optical diffractive convolutional neural network (ODCNN) that is capable of performing image processing tasks in computer vision at the speed of light. We explore the application of the 4f system and the diffractive deep neural network (D2NN) in neural networks. ODCNN is then simulated by combining the 4f system as an optical convolutional layer and the diffractive networks. We also examine the potential impact of nonlinear optical materials on this network. Numerical simulation results show that the addition of convolutional layers and nonlinear functions improves the classification accuracy of the network. We believe that the proposed ODCNN model can be the basic architecture for building optical convolutional networks.<\/jats:p>","DOI":"10.3390\/s23125749","type":"journal-article","created":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T02:30:51Z","timestamp":1687314651000},"page":"5749","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Optical Diffractive Convolutional Neural Networks Implemented in an All-Optical Way"],"prefix":"10.3390","volume":"23","author":[{"given":"Yaze","family":"Yu","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Hebei University of Technology, Tianjin 300401, China"},{"name":"Center for Advanced Laser Technology, Hebei University of Technology, Tianjin 300401, China"},{"name":"Hebei Key Laboratory of Advanced Laser Technology and Equipment, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Cao","sequence":"additional","affiliation":[{"name":"Center for Advanced Laser Technology, Hebei University of Technology, Tianjin 300401, China"},{"name":"Hebei Key Laboratory of Advanced Laser Technology and Equipment, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gong","family":"Wang","sequence":"additional","affiliation":[{"name":"Center for Advanced Laser Technology, Hebei University of Technology, Tianjin 300401, China"},{"name":"Hebei Key Laboratory of Advanced Laser Technology and Equipment, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yajun","family":"Pang","sequence":"additional","affiliation":[{"name":"Center for Advanced Laser Technology, Hebei University of Technology, Tianjin 300401, China"},{"name":"Hebei Key Laboratory of Advanced Laser Technology and Equipment, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liying","family":"Lang","sequence":"additional","affiliation":[{"name":"Center for Advanced Laser Technology, Hebei University of Technology, Tianjin 300401, China"},{"name":"Hebei Key Laboratory of Advanced Laser Technology and Equipment, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,20]]},"reference":[{"key":"ref_1","first-page":"8930","article-title":"This looks like that: Deep learning for interpretable image recognition","volume":"32","author":"Chen","year":"2019","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.neucom.2016.11.100","article-title":"On the application of reservoir computing networks for noisy image recognition","volume":"277","author":"Jalalvand","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3923","DOI":"10.1038\/s41467-020-17419-7","article-title":"Improving the accuracy of medical diagnosis with causal machine learning","volume":"11","author":"Richens","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5088","DOI":"10.1038\/s41467-020-18685-1","article-title":"Development and evaluation of an artificial intelligence system for COVID-19 diagnosis","volume":"11","author":"Jin","year":"2020","journal-title":"Nat. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1109\/MNET.2019.1900120","article-title":"Autonomous driving cars in smart cities: Recent advances, requirements, and challenges","volume":"34","author":"Yaqoob","year":"2019","journal-title":"IEEE Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.cell.2015.09.029","article-title":"Reconstruction and simulation of neocortical microcircuitry","volume":"163","author":"Markram","year":"2015","journal-title":"Cell"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/2943.692532","article-title":"Electronic lighting interference","volume":"4","author":"Schwabe","year":"1998","journal-title":"IEEE Ind. Appl. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6380","DOI":"10.1364\/AO.44.006380","article-title":"Analysis of optical channel cross talk for free-space optical interconnects in the presence of higher-order transverse modes","volume":"44","author":"Tsai","year":"2005","journal-title":"Appl. Opt."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1364\/JOSAA.27.000200","article-title":"Crosstalk analysis of aligned and misaligned free-space optical interconnect systems","volume":"27","author":"Hu","year":"2010","journal-title":"JOSA A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1126\/science.aaw2498","article-title":"Inverse-designed metastructures that solve equations","volume":"363","author":"Edwards","year":"2019","journal-title":"Science"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"32911","DOI":"10.1038\/srep32911","article-title":"Graphene-assisted multiple-input high-base optical computing","volume":"6","author":"Hu","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1038\/nature22986","article-title":"On-chip generation of high-dimensional entangled quantum states and their coherent control","volume":"546","author":"Kues","year":"2017","journal-title":"Nature"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1038\/nphoton.2017.95","article-title":"Quantum transport simulations in a programmable nanophotonic processor","volume":"11","author":"Harris","year":"2017","journal-title":"Nat. Photonics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1038\/nphoton.2017.93","article-title":"Deep learning with coherent nanophotonic circuits","volume":"11","author":"Shen","year":"2017","journal-title":"Nat. Photonics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1126\/science.aat8084","article-title":"All-optical machine learning using diffractive deep neural networks","volume":"361","author":"Lin","year":"2018","journal-title":"Science"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1364\/OL.442970","article-title":"Modeling and simulation of all-optical diffractive neural network based on nonlinear optical materials","volume":"47","author":"Sun","year":"2022","journal-title":"Opt. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1364\/OL.389696","article-title":"Residual D 2 NN: Training diffractive deep neural networks via learnable light shortcuts","volume":"45","author":"Dou","year":"2020","journal-title":"Opt. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"LeCun, Y., Kavukcuoglu, K., and Farabet, C. (June, January 30). Convolutional networks and applications in vision. Proceedings of the Proceedings of 2010 IEEE International Symposium on Circuits and Systems, Paris, France.","DOI":"10.1109\/ISCAS.2010.5537907"},{"key":"ref_20","unstructured":"Gupta, P., and Li, S. (February, January 22). 4F optical neural network acceleration: An architecture perspective. Proceedings of the AI and Optical Data Sciences III, San Francisco, CA, USA."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12324","DOI":"10.1038\/s41598-018-30619-y","article-title":"Hybrid optical-electronic convolutional neural networks with optimized diffractive optics for image classification","volume":"8","author":"Chang","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3179","DOI":"10.1364\/AO.58.003179","article-title":"Optical frontend for a convolutional neural network","volume":"58","author":"Colburn","year":"2019","journal-title":"Appl. Opt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3789","DOI":"10.1364\/AO.50.003789","article-title":"Enlarging the angle of view in Michelson-interferometer-based shearography by embedding a 4f system","volume":"50","author":"Wu","year":"2011","journal-title":"Appl. Opt."},{"key":"ref_24","first-page":"1095","article-title":"Introduction to Fourier optics","volume":"8","author":"Goodman","year":"1996","journal-title":"Quantum Semiclassical-Opt.-J. Eur. Opt. Soc. Part B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1109\/JQE.1978.1069864","article-title":"Optics of the atmosphere: Scattering by molecules and particles","volume":"14","author":"McCartney","year":"1978","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_26","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1364\/OPTICA.6.001132","article-title":"All-optical neural network with nonlinear activation functions","volume":"6","author":"Zuo","year":"2019","journal-title":"Optica"},{"key":"ref_28","unstructured":"Glorot, X., Bordes, A., and Bengio, Y. (2011, January 11\u201313). Deep sparse rectifier neural networks. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, Fort Lauderdale, FL, USA. JMLR Workshop and Conference Proceedings."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5877","DOI":"10.1364\/OE.415542","article-title":"Optronic convolutional neural networks of multi-layers with different functions executed in optics for image classification","volume":"29","author":"Gu","year":"2021","journal-title":"Opt. Express"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"023901","DOI":"10.1103\/PhysRevLett.123.023901","article-title":"Fourier-space diffractive deep neural network","volume":"123","author":"Yan","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1038\/s41566-021-00796-w","article-title":"Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit","volume":"15","author":"Zhou","year":"2021","journal-title":"Nat. Photonics"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/12\/5749\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:57:07Z","timestamp":1760126227000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/12\/5749"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,20]]},"references-count":31,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,6]]}},"alternative-id":["s23125749"],"URL":"https:\/\/doi.org\/10.3390\/s23125749","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,20]]}}}