{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T02:18:11Z","timestamp":1780625891745,"version":"3.54.1"},"reference-count":41,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2024,8,4]],"date-time":"2024-08-04T00:00:00Z","timestamp":1722729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100014188","name":"MSIT (Ministry of Science and ICT), Korea","doi-asserted-by":"publisher","award":["IITP 2024-2021-0-01810"],"award-info":[{"award-number":["IITP 2024-2021-0-01810"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]},{"name":"GIST","award":["IITP 2024-2021-0-01810"],"award-info":[{"award-number":["IITP 2024-2021-0-01810"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of \u03c0\/N in resolution.<\/jats:p>","DOI":"10.3390\/s24155041","type":"journal-article","created":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T13:57:28Z","timestamp":1722866248000},"page":"5041","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Intensity-Product-Based Optical Sensing to Beat the Diffraction Limit in an Interferometer"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3609-8508","authenticated-orcid":false,"given":"Byoung S.","family":"Ham","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology, Gwangju 61005, Republic of Korea"},{"name":"Qu-Lidar, Gwangju 61005, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"083001","DOI":"10.1088\/2040-8986\/aa7419","article-title":"Roadmap on optical sensors","volume":"19","author":"Ferreira","year":"2017","journal-title":"J. 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