{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:11:43Z","timestamp":1760134303549,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T00:00:00Z","timestamp":1701043200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2020YFC2200100","XDA1502110201"],"award-info":[{"award-number":["2020YFC2200100","XDA1502110201"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Chinese Academy of Sciences Strategic Pioneer Program on Space Science","award":["2020YFC2200100","XDA1502110201"],"award-info":[{"award-number":["2020YFC2200100","XDA1502110201"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>For space-based gravitational wave detection, a laser interferometric measurement system composed of a three-spacecraft formation offers the most rewarding bandwidth of astrophysical sources. There are no oscillators available that are stable enough so that each spacecraft could use its own reference frequency. The conversion between reference frequencies and their distribution between all spacecrafts for the synchronization of the different metrology systems is the job of the inter-spacecraft frequency setting strategy, which is important for continuously acquiring scientific data and suppressing measurement noise. We propose a hierarchical optimization algorithm to solve the frequency setting strategy. The optimization objectives are minimum total readout displacement noise and maximum beat-note frequency feasible range. Multiple feasible parameter combinations were obtained for the Taiji program. These optimized parameters include lower and upper bounds of the beat note, sampling frequency, pilot tone signal frequency, ultrastable clock frequencies, and modulation depth. Among the 20 Pareto optimal solutions, the minimum total readout displacement noise was 4.12 pm\/Hz, and the maximum feasible beat-note frequency range was 23 MHz. By adjusting the upper bound of beat-note frequency and laser power transmitted by the telescope, we explored the effects of these parameters on the minimum total readout displacement noise and optimal local laser power in greater depth. Our results may serve as a reference for the optimal design of laser interferometry system instrument parameters and may ultimately improve the detection performance and continuous detection time of the Taiji program.<\/jats:p>","DOI":"10.3390\/s23239431","type":"journal-article","created":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T03:48:17Z","timestamp":1701056897000},"page":"9431","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Enhanced Detection Precision of the Taiji Program by Frequency Setting Strategy Based on a Hierarchical Optimization Algorithm"],"prefix":"10.3390","volume":"23","author":[{"given":"Jiafeng","family":"Zhang","sequence":"first","affiliation":[{"name":"Key Laboratory of Electronics and Information Technology for Space System, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhen","family":"Yang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronics and Information Technology for Space System, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoshan","family":"Ma","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronics and Information Technology for Space System, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaodong","family":"Peng","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronics and Information Technology for Space System, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China"},{"name":"Taiji Laboratory for Gravitational Wave Universe, Hangzhou 310024, China"},{"name":"Key Laboratory of Gravitational Wave Precision Measurement of Zhejiang Province, Hangzhou 310024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Gao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronics and Information Technology for Space System, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengyuan","family":"Zhao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronics and Information Technology for Space System, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0126-2542","authenticated-orcid":false,"given":"Wenlin","family":"Tang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Electronics and Information Technology for Space System, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1126\/science.256.5055.325","article-title":"LIGO: The Laser Interferometer Gravitational-Wave Observatory","volume":"256","author":"Abramovici","year":"1992","journal-title":"Science"},{"key":"ref_2","unstructured":"Thorne, K.S. (1995). Gravitational Waves. arXiv."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1016\/S0273-1177(03)90325-5","article-title":"LISA\u2014The Interferometer","volume":"32","author":"Hough","year":"2003","journal-title":"Adv. Space Res."},{"key":"ref_4","unstructured":"Danzmann, K., Prince, T.A., Binetruy, P., Bender, P., Buchman, S., Centrella, J., Cerdonio, M., Cornish, N., Cruise, M., and Cutler, C.J. (2011). Assessment Study Report ESA\/SRE, AEI."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1093\/nsr\/nwx116","article-title":"The Taiji Program in Space for Gravitational Wave Physics and the Nature of Gravity","volume":"4","author":"Hu","year":"2017","journal-title":"Natl. Sci. Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/s00340-021-07637-2","article-title":"A Brief Overview of 8 m Prototype Facility of Laser Interferometer for Taiji Pathfinder Mission","volume":"127","author":"Li","year":"2021","journal-title":"Appl. Phys. B"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102918","DOI":"10.1016\/j.rinp.2019.102918","article-title":"A Brief Analysis to Taiji: Science and Technology","volume":"16","author":"Luo","year":"2020","journal-title":"Results Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"035010","DOI":"10.1088\/0264-9381\/33\/3\/035010","article-title":"TianQin: A Space-Borne Gravitational Wave Detector","volume":"33","author":"Luo","year":"2016","journal-title":"Class. Quantum Grav."},{"key":"ref_9","unstructured":"Otto, M. (2015). Time-Delay Interferometry Simulations for the Laser Interferometer Space Antenna. [Ph.D. Thesis, Gottfried Wilhelm Leibniz Universit\u00e4t Hannover]."},{"key":"ref_10","unstructured":"Brause, N.C. (2018). Auxiliary Function Development for the LISA Metrology System. [Ph.D. Thesis, Gotfried Wilhelm Leibniz Universitmt Hannover]."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"063613","DOI":"10.1103\/PhysRevA.92.063613","article-title":"Laser-Ranging Long-Baseline Differential Atom Interferometers for Space","volume":"92","author":"Chiow","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_12","unstructured":"Wang, Y. (2014). On Inter-Satellite Laser Ranging, Clock Synchronization and Gravitational Wave Data Analysis. [Ph.D. Thesis, Gottfried Wilhelm Leibniz Universit\u00e4t Hannover]."},{"key":"ref_13","unstructured":"Barke, S. (2015). Inter-Spacecraft Frequency Distribution. [Ph.D. Thesis, Gottfried Wilhelm Leibniz Universit\u00e4t Hannover]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4201","DOI":"10.1088\/0264-9381\/23\/12\/015","article-title":"A Demonstration of LISA Laser Communication","volume":"23","author":"Pollack","year":"2006","journal-title":"Class. Quantum Grav."},{"key":"ref_15","unstructured":"Kullmann, J. (2012). Development of a Digital Phase Measuring System with Microradian Precision for LISA. [Ph.D. Thesis, Gottfried Wilhelm Leibniz Universit\u00e4t Hannover]."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1364\/AO.442583","article-title":"Inter-Spacecraft Offset Frequency Setting Strategy in the Taiji Program","volume":"61","author":"Zhang","year":"2022","journal-title":"Appl. Opt."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"094008","DOI":"10.1088\/0264-9381\/28\/9\/094008","article-title":"Auxiliary Functions of the LISA Laser Link: Ranging, Clock Noise Transfer and Data Communication","volume":"28","author":"Heinzel","year":"2011","journal-title":"Class. Quantum Grav."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Klipstein, W., Halverson, P.G., Peters, R., Cruz, R., and Shaddock, D. (2006, January 19\u201323). Clock Noise Removal in LISA. Proceedings of the Laser Interferometer Space Antenna: 6th International LISA Symposium, Greenbelt, MD, USA.","DOI":"10.1063\/1.2405061"},{"key":"ref_19","unstructured":"Barke, S., Brause, N., Bykov, I., Esteban Delgado, J.J., Enggaard, A., Gerberding, O., Heinzel, G., Kullmann, J., Pedersen, S.M., and Rasmussen, T. (2014). LISA Metrology System\u2014Final Report, AEI."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s12217-019-09769-9","article-title":"A Laser Interferometer Prototype with Pico-Meter Measurement Precision for Taiji Space Gravitational Wave Detection Missionin China","volume":"32","author":"Li","year":"2020","journal-title":"Microgravity Sci. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1102011","DOI":"10.3788\/CJL201138.1102011","article-title":"Solid State Tunable Single-Frequency Laser Based on Non-Planar Ring Oscillator","volume":"38","author":"Ren","year":"2011","journal-title":"Chin. J. Lasers"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1364\/OE.408822","article-title":"Automatic, High-Speed, High-Precision Acquisition Scheme with QPD for the Taiji Program","volume":"29","author":"Gao","year":"2021","journal-title":"Opt. Express"},{"key":"ref_23","unstructured":"Zhao, Y. (2021). The Research on the Tilt to Length Coupling Noise in Inter-Satellite Interference Link for the Space-Based Gravitational Wave Detection, Chinese Academy of Sciences."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"05A108","DOI":"10.1093\/ptep\/ptaa083","article-title":"The Taiji Program: A Concise Overview","volume":"2021","author":"Luo","year":"2021","journal-title":"Prog. Theor. Exp. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s12217-021-09875-7","article-title":"Numerical Simulations of Arm-Locking for Taiji Space Gravitational Waves Detection","volume":"33","author":"Liu","year":"2021","journal-title":"Microgravity Sci. Technol."},{"key":"ref_27","unstructured":"Wan, C. (2012). A Study on nW-Level Weak Light Optical Phase-Locking Techniques. [Master\u2019s Thesis, Huazhong University of Science and Technology]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/23\/9431\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:31:06Z","timestamp":1760131866000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/23\/9431"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,27]]},"references-count":27,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["s23239431"],"URL":"https:\/\/doi.org\/10.3390\/s23239431","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,11,27]]}}}