{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T04:11:16Z","timestamp":1776312676063,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,3,7]],"date-time":"2022-03-07T00:00:00Z","timestamp":1646611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002367","name":"Chinese Academy of Sciences","doi-asserted-by":"publisher","award":["M.IF.A.QOP18098"],"award-info":[{"award-number":["M.IF.A.QOP18098"]}],"id":[{"id":"10.13039\/501100002367","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004189","name":"Max Planck Society","doi-asserted-by":"publisher","award":["M.IF.A.QOP18098"],"award-info":[{"award-number":["M.IF.A.QOP18098"]}],"id":[{"id":"10.13039\/501100004189","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["434617780, SFB 1464"],"award-info":[{"award-number":["434617780, SFB 1464"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Clusters of Excellence \u201cQuantumFrontiers: Light and Matter at the Quantum Frontier: Foundations and Applications in Metrology\u201d","award":["EXC-2123, project number: 390837967"],"award-info":[{"award-number":["EXC-2123, project number: 390837967"]}]},{"name":"PhoenixD: \u201cPhotonics, Optics, and Engineering \u2013 Innovation Across Disciplines\u201d","award":["EXC-2122, project number: 322 390833453"],"award-info":[{"award-number":["EXC-2122, project number: 322 390833453"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The laser ranging interferometer onboard the Gravity Recovery and Climate Experiment Follow-On mission proved the feasibility of an interferometric sensor for inter-satellite length tracking with sub-nanometer precision, establishing an important milestone for space laser interferometry and the general expectation that future gravity missions will employ heterodyne laser interferometry for satellite-to-satellite ranging. In this paper, we present the design of an on-axis optical bench for next-generation laser ranging which enhances the received optical power and the transmit beam divergence, enabling longer interferometer arms and relaxing the optical power requirement of the laser assembly. All design functionalities and requirements are verified by means of computer simulations. A thermal analysis is carried out to investigate the robustness of the proposed optical bench to the temperature fluctuations found in orbit.<\/jats:p>","DOI":"10.3390\/s22052070","type":"journal-article","created":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T01:50:53Z","timestamp":1646790653000},"page":"2070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["On-Axis Optical Bench for Laser Ranging Instruments in Future Gravity Missions"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0553-4362","authenticated-orcid":false,"given":"Yichao","family":"Yang","sequence":"first","affiliation":[{"name":"Max\u2013Planck-Institut f\u00fcr Gravitationsphysik (Albert\u2013Einstein\u2013Institut) and Institut f\u00fcr Gravitationsphysik, Leibniz Universit\u00e4t Hannover, Callinstrasse 38, D-30167 Hannover, Germany"},{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5064-4619","authenticated-orcid":false,"given":"Kohei","family":"Yamamoto","sequence":"additional","affiliation":[{"name":"Max\u2013Planck-Institut f\u00fcr Gravitationsphysik (Albert\u2013Einstein\u2013Institut) and Institut f\u00fcr Gravitationsphysik, Leibniz Universit\u00e4t Hannover, Callinstrasse 38, D-30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6300-5226","authenticated-orcid":false,"given":"Miguel","family":"Dovale \u00c1lvarez","sequence":"additional","affiliation":[{"name":"Max\u2013Planck-Institut f\u00fcr Gravitationsphysik (Albert\u2013Einstein\u2013Institut) and Institut f\u00fcr Gravitationsphysik, Leibniz Universit\u00e4t Hannover, Callinstrasse 38, D-30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5409-926X","authenticated-orcid":false,"given":"Daikang","family":"Wei","sequence":"additional","affiliation":[{"name":"Max\u2013Planck-Institut f\u00fcr Gravitationsphysik (Albert\u2013Einstein\u2013Institut) and Institut f\u00fcr Gravitationsphysik, Leibniz Universit\u00e4t Hannover, Callinstrasse 38, D-30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7613-3681","authenticated-orcid":false,"given":"Juan Jos\u00e9","family":"Esteban Delgado","sequence":"additional","affiliation":[{"name":"Max\u2013Planck-Institut f\u00fcr Gravitationsphysik (Albert\u2013Einstein\u2013Institut) and Institut f\u00fcr Gravitationsphysik, Leibniz Universit\u00e4t Hannover, Callinstrasse 38, D-30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vitali","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Max\u2013Planck-Institut f\u00fcr Gravitationsphysik (Albert\u2013Einstein\u2013Institut) and Institut f\u00fcr Gravitationsphysik, Leibniz Universit\u00e4t Hannover, Callinstrasse 38, D-30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianjun","family":"Jia","sequence":"additional","affiliation":[{"name":"Key Laboratory of Space Active Opto-Electronics Technology, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China"},{"name":"School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1661-7868","authenticated-orcid":false,"given":"Gerhard","family":"Heinzel","sequence":"additional","affiliation":[{"name":"Max\u2013Planck-Institut f\u00fcr Gravitationsphysik (Albert\u2013Einstein\u2013Institut) and Institut f\u00fcr Gravitationsphysik, Leibniz Universit\u00e4t Hannover, Callinstrasse 38, D-30167 Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"L09607","DOI":"10.1029\/2004GL019920","article-title":"The gravity recovery and climate experiment: Mission overview and early results","volume":"31","author":"Tapley","year":"2004","journal-title":"Geophys. 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