{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T10:29:41Z","timestamp":1774434581351,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,9,30]],"date-time":"2021-09-30T00:00:00Z","timestamp":1632960000000},"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":["61871031, 61875012, and 61905014"],"award-info":[{"award-number":["61871031, 61875012, and 61905014"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Funding of foundation enhancement program under Grant","award":["2020-JCJQ-JJ-030"],"award-info":[{"award-number":["2020-JCJQ-JJ-030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Single-pixel imaging, with the advantages of a wide spectrum, beyond-visual-field imaging, and robustness to light scattering, has attracted increasing attention in recent years. Fourier single-pixel imaging (FSI) can reconstruct sharp images under sub-Nyquist sampling. However, the conventional FSI has difficulty balancing imaging quality and efficiency. To overcome this issue, we proposed a novel approach called complementary Fourier single-pixel imaging (CFSI) to reduce the number of measurements while retaining its robustness. The complementary nature of Fourier patterns based on a four-step phase-shift algorithm is combined with the complementary nature of a digital micromirror device. CFSI only requires two phase-shifted patterns to obtain one Fourier spectral value. Four light intensity values are obtained by loading the two patterns, and the spectral value is calculated through differential measurement, which has good robustness to noise. The proposed method is verified by simulations and experiments compared with FSI based on two-, three-, and four-step phase shift algorithms. CFSI performed better than the other methods under the condition that the best imaging quality of CFSI is not reached. The reported technique provides an alternative approach to realize real-time and high-quality imaging.<\/jats:p>","DOI":"10.3390\/s21196544","type":"journal-article","created":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T21:26:20Z","timestamp":1633728380000},"page":"6544","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Complementary Fourier Single-Pixel Imaging"],"prefix":"10.3390","volume":"21","author":[{"given":"Dong","family":"Zhou","sequence":"first","affiliation":[{"name":"Key Laboratory of Biomimetic Robots and Systems, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Cao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Biomimetic Robots and Systems, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huan","family":"Cui","sequence":"additional","affiliation":[{"name":"Key Laboratory of Biomimetic Robots and Systems, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qun","family":"Hao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Biomimetic Robots and Systems, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing-kun","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Biomimetic Robots and Systems, School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Lin","sequence":"additional","affiliation":[{"name":"Beijing Fisheries Research Institute, Beijing 100068, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"R3429","DOI":"10.1103\/PhysRevA.52.R3429","article-title":"Optical imaging by means of two-photon quantum entanglement","volume":"52","author":"Pittman","year":"1995","journal-title":"Phys. Rev. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"061802","DOI":"10.1103\/PhysRevA.78.061802","article-title":"Computational ghost imaging","volume":"78","author":"Shapiro","year":"2008","journal-title":"Phys. Rev. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3379","DOI":"10.1021\/acsphotonics.8b00653","article-title":"Time-Resolved Nonlinear Ghost Imaging","volume":"5","author":"Olivieri","year":"2018","journal-title":"ACS Photonics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2998","DOI":"10.1364\/OE.25.002998","article-title":"Real-time imaging of methane gas leaks using a single-pixel camera","volume":"25","author":"Gibson","year":"2017","journal-title":"Opt. Express"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3452","DOI":"10.1364\/OL.40.003452","article-title":"Sinusoidal ghost imaging","volume":"40","author":"Khamoushi","year":"2015","journal-title":"Opt. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1364\/OPTICA.1.000285","article-title":"Single-pixel infrared and visible microscope","volume":"1","author":"Radwell","year":"2014","journal-title":"Optica"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"253603","DOI":"10.1103\/PhysRevLett.104.253603","article-title":"Differential Ghost Imaging","volume":"104","author":"Ferri","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"16892","DOI":"10.1364\/OE.20.016892","article-title":"Normalized ghost imaging","volume":"20","author":"Sun","year":"2012","journal-title":"Opt. Express"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15118","DOI":"10.1364\/OE.25.015118","article-title":"Adaptive regional single-pixel imaging based on the Fourier slice theorem","volume":"25","author":"Jiang","year":"2017","journal-title":"Opt. Express"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1364\/OPTICA.3.000698","article-title":"Computational temporal ghost imaging","volume":"3","author":"Devaux","year":"2016","journal-title":"Optica"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1126\/science.1234454","article-title":"3-D Computational imaging with single-pixel detectors","volume":"340","author":"Sun","year":"2013","journal-title":"Science"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"12010","DOI":"10.1038\/ncomms12010","article-title":"Single-pixel three-dimensional imaging with time-based depth resolution","volume":"7","author":"Sun","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2497","DOI":"10.1364\/OL.41.002497","article-title":"Three-dimensional single-pixel imaging with far fewer measurements than effective image pixels","volume":"41","author":"Zhang","year":"2016","journal-title":"Opt. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1364\/OPTICA.5.000315","article-title":"Simultaneous spatial, spectruml, and 3D compressive imaging via efficient Fourier single-pixel measurements","volume":"5","author":"Zhang","year":"2018","journal-title":"Optica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1038\/nphoton.2014.139","article-title":"Terahertz compressive imaging with metamaterial spatial light modulators","volume":"8","author":"Watts","year":"2014","journal-title":"Nat. Photonics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"121105","DOI":"10.1063\/1.2989126","article-title":"A single-pixel terahertz imaging system based on compressed sensing","volume":"93","author":"Chan","year":"2008","journal-title":"Appl. Phys. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"e1600190","DOI":"10.1126\/sciadv.1600190","article-title":"Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector","volume":"2","author":"Stantchev","year":"2016","journal-title":"Sci. Adv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"10669","DOI":"10.1038\/srep10669","article-title":"Simultaneous real-time visible and infrared video with single-pixel detectors","volume":"5","author":"Edgar","year":"2015","journal-title":"Sci. Rep."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"24752","DOI":"10.1038\/srep24752","article-title":"Multispectral imaging using a single bucket detector","volume":"6","author":"Bian","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"23068","DOI":"10.1364\/OE.21.023068","article-title":"Fast full-color computational imaging with single-pixel detectors","volume":"21","author":"Welsh","year":"2013","journal-title":"Opt. Express"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"17466","DOI":"10.1364\/OE.25.017466","article-title":"Object classification through scattering media with deep learning on time resolved measurement","volume":"25","author":"Satat","year":"2017","journal-title":"Opt. Express"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1038\/nphoton.2014.189","article-title":"Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations","volume":"8","author":"Katz","year":"2014","journal-title":"Nat. Photonics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1364\/OL.36.000394","article-title":"Correlated imaging in scattering media","volume":"36","author":"Gong","year":"2011","journal-title":"Opt. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"16547","DOI":"10.1364\/OE.26.016547","article-title":"Computational-weighted Fourier single-pixel imaging via binary illumination","volume":"26","author":"Huang","year":"2018","journal-title":"Opt. Express"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6225","DOI":"10.1038\/ncomms7225","article-title":"Single-pixel imaging by means of Fourier spectrum acquisition","volume":"6","author":"Zhang","year":"2015","journal-title":"Nat. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/MSP.2007.914730","article-title":"Single-pixel imaging via compressive sampling","volume":"25","author":"Duarte","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"19619","DOI":"10.1364\/OE.25.019619","article-title":"Hadamard single-pixel imaging versus Fourier single-pixel imaging","volume":"25","author":"Zhang","year":"2017","journal-title":"Opt. Express"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.optlastec.2015.12.009","article-title":"Single pixel sensing for THz laser beam profiler based on Hadamard Transform","volume":"79","author":"Vasile","year":"2016","journal-title":"Opt. Laser Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"221906","DOI":"10.1063\/1.5097901","article-title":"Fourier single-pixel imaging using fewer illumination patterns","volume":"114","author":"Deng","year":"2019","journal-title":"Appl. Phys. Lett."},{"key":"ref_30","unstructured":"Luo, B., Tsai, K., and Liu, J. (2018, January 25\u201327). Computational ghost imaging by using complementary illumination patterns. Proceedings of the SPIE 10711: Biomedical Imaging and Sensing Conference, Yokohama, Japan."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"034035","DOI":"10.1103\/PhysRevApplied.15.034035","article-title":"Ghost Difference Imaging Using One Single-Pixel Detector","volume":"15","author":"Ye","year":"2021","journal-title":"Phys. Rev. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12029","DOI":"10.1038\/s41598-017-12228-3","article-title":"Fast Fourier single-pixel imaging via binary illumination","volume":"7","author":"Zhang","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"e1701477","DOI":"10.1126\/sciadv.1701477","article-title":"Single-pixel computational ghost imaging with helicity-dependent metasurface hologram","volume":"3","author":"Liu","year":"2017","journal-title":"Sci. Adv."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Takhar, D., Laska, J.N., Wakin, M.B., Duarte, M.F., Baron, D., Sarvotham, S., Kelly, K.F., and Baraniuk, R.G. (2006, January 15\u201319). A new compressive imaging camera architecture using optical-domain compression. Proceedings of the SPIE 6065: Computational Imaging IV, San Jose, CA, USA.","DOI":"10.1117\/12.659602"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1364\/AO.56.001353","article-title":"Single-pixel compressive diffractive imaging","volume":"56","author":"Horisaki","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"4085","DOI":"10.1364\/AO.56.004085","article-title":"Single-pixel compressive diffractive imaging with structured illumination","volume":"56","author":"Horisaki","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2524","DOI":"10.1364\/OL.38.002524","article-title":"Compressive holography with a single-pixel detector","volume":"38","author":"Clemente","year":"2013","journal-title":"Opt. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/19\/6544\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:08:04Z","timestamp":1760166484000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/19\/6544"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,30]]},"references-count":37,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["s21196544"],"URL":"https:\/\/doi.org\/10.3390\/s21196544","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,30]]}}}