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Forming foci for the ultrasound phased array using the linear synthesis scheme (LSS) is a straightforward technique to induce tactile feeling. The matching phase set for each focal point is calculated separately in LSS, and then they are linearly superimposed to generate multiple focal points. Due to the fact that adding an arbitrary offset to the entire phase pattern has no effect on the generated focus patterns, adjusting the offset in linear summation may result in a superior sound field. In our study, we propose that optimize the offset before linear superposition. These offsets are determined based on the number of focal points, which means it will not cause an explosive increase in computing cost with the increase of transducers. To optimize the offset of each focus pressure generated by LSS, we used a greedy algorithm with a brute-force search optimization method. The computing cost of our proposed method is dictated by the number of foci after calculating the phase sets of LSS once. We demonstrate the proposed method\u2019s optimum performance in varied numbers of foci and transducers in this study.<\/jats:p>","DOI":"10.1007\/978-3-031-06249-0_17","type":"book-chapter","created":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T16:05:38Z","timestamp":1652976338000},"page":"147-154","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sound Pressure Field Reconstruction for Ultrasound Phased Array by Linear Synthesis Scheme Optimization"],"prefix":"10.1007","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-0908-0022","authenticated-orcid":false,"given":"Jianyu","family":"Chen","sequence":"first","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-8431-6664","authenticated-orcid":false,"given":"Shun","family":"Suzuki","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0003-0820-879X","authenticated-orcid":false,"given":"Tao","family":"Morisaki","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-9703-6020","authenticated-orcid":false,"given":"Yutaro","family":"Toide","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-5042-1773","authenticated-orcid":false,"given":"Masahiro","family":"Fujiwara","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-9362-4407","authenticated-orcid":false,"given":"Yasutoshi","family":"Makino","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-3006-430X","authenticated-orcid":false,"given":"Hiroyuki","family":"Shinoda","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,20]]},"reference":[{"key":"17_CR1","doi-asserted-by":"crossref","unstructured":"Iwamoto, T., Tatezono, M., Shinoda, H.: Non-contact method for producing tactile sensation using airborne ultrasound. In: International Conference on Human Haptic Sensing and Touch Enabled Computer Applications, pp. 504\u2013513 (2008)","DOI":"10.1007\/978-3-540-69057-3_64"},{"key":"17_CR2","doi-asserted-by":"publisher","unstructured":"Monnai, Y.: HaptoMime: mid-air haptic interaction with a floating virtual screen. In: The 27th Annual ACM Symposium on User Interface Software and Technology, UIST 2014, pp. 663\u2013667 (2014). https:\/\/doi.org\/10.1145\/2642918.2647407","DOI":"10.1145\/2642918.2647407"},{"key":"17_CR3","doi-asserted-by":"publisher","unstructured":"Inoue, S., Makino, Y., Shinoda, H.: Active touch perception produced by airborne ultrasonic haptic hologram. In: 2015 IEEE World Haptics Conference (WHC), pp. 362\u2013367 (2015). https:\/\/doi.org\/10.1109\/WHC.2015.7177739","DOI":"10.1109\/WHC.2015.7177739"},{"key":"17_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2661229.2661257","volume":"33","author":"B Long","year":"2014","unstructured":"Long, B., Seah, S.A., Carter, T., Subramanian, S.: Rendering volumetric haptic shapes in mid-air using ultrasound. ACM Trans. Graph. (TOG) 33, 1\u201310 (2014). https:\/\/doi.org\/10.1145\/2661229.2661257","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"17_CR5","doi-asserted-by":"publisher","unstructured":"Plasencia, D.M., Hirayama, R., Montano-Murillo, R., Subramanian, S.: GS-PAT: high-speed multi-point sound-fields for phased arrays of transducers. ACM Trans. Graph. Article no. 138 (2020). https:\/\/doi.org\/10.1145\/3386569.3392492","DOI":"10.1145\/3386569.3392492"},{"key":"17_CR6","doi-asserted-by":"publisher","unstructured":"Suzuki, S., Fujiwara, M., Makino, Y., Shinoda, H.: Radiation pressure field reconstruction for ultrasound midair haptics by Greedy algorithm with brute-force search. IEEE Trans. Haptics (Open Access, Early Access). https:\/\/doi.org\/10.1109\/TOH.2021.3076489","DOI":"10.1109\/TOH.2021.3076489"}],"container-title":["Lecture Notes in Computer Science","Haptics: Science, Technology, Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-06249-0_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T11:23:47Z","timestamp":1710242627000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-06249-0_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031062483","9783031062490"],"references-count":6,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-06249-0_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"20 May 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EuroHaptics","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Human Haptic Sensing and Touch Enabled Computer Applications","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Hamburg","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 May 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25 May 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurohaptics2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.eurohaptics2022.org","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"OCS","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"129","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"36","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"28% - 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