{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:59:35Z","timestamp":1760234375613,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,5,15]],"date-time":"2021-05-15T00:00:00Z","timestamp":1621036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Optical satellite communication has received considerable attention as a promising alternative to radio frequency communication because of its potential advantages including higher data rates and license free spectrum. Many studies have conducted performance analyses of optical communication channels, but few have investigated beacon tracking channels under atmospheric turbulence. The centroid accuracy of beacon tracking channels is limited by not only noise sources, but also a finite delay time, which also fluctuates due to atmospheric turbulence. Consequently, the centroid error is an important figure of merit when evaluating the performance of a beacon tracking system. In this study, the closed-form expressions were derived for average centroid error and fade probability, based on received photoelectron counts depending on exposure time, taking into account the log-normal tracking channels. We analyzed the angular positioning performance of beacon tracking detectors onboard small satellites in the presence of atmospheric turbulence, in terms of centroid error and fade probability. We found that an optimal exposure time exists, which minimizes the centroid error, and that fade probability is inversely proportional to the exposure time. These are significant properties to consider in the design of beacon tracking systems.<\/jats:p>","DOI":"10.3390\/rs13101931","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T02:31:34Z","timestamp":1621218694000},"page":"1931","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Centroid Error Analysis of Beacon Tracking under Atmospheric Turbulence for Optical Communication Links"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5266-1335","authenticated-orcid":false,"given":"Hyung-Chul","family":"Lim","sequence":"first","affiliation":[{"name":"Korea Astronomy and Space Science Institute, Space Science Division, Daejeon 34055, Korea"}]},{"given":"Chul-Sung","family":"Choi","sequence":"additional","affiliation":[{"name":"Korea Astronomy and Space Science Institute, Space Science Division, Daejeon 34055, Korea"}]},{"given":"Ki-Pyoung","family":"Sung","sequence":"additional","affiliation":[{"name":"Korea Astronomy and Space Science Institute, Space Science Division, Daejeon 34055, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8060-6050","authenticated-orcid":false,"given":"Jong-Uk","family":"Park","sequence":"additional","affiliation":[{"name":"Korea Astronomy and Space Science Institute, Space Science Division, Daejeon 34055, Korea"}]},{"given":"Mansoo","family":"Choi","sequence":"additional","affiliation":[{"name":"Korea Astronomy and Space Science Institute, Space Science Division, Daejeon 34055, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,15]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Comparison of microwave and light wave communication systems in space application","volume":"46","author":"Toyoshima","year":"2005","journal-title":"Opt. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2381","DOI":"10.1364\/OE.19.002381","article-title":"Analytical expression and optimization of spatial acquisition for intersatellite optical communications","volume":"19","author":"Li","year":"2011","journal-title":"Opt. Exp."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7575","DOI":"10.1364\/AO.54.007575","article-title":"Performance analysis of satellite-to-ground downlink coherent optical communications with spatial diversity over Gamma- Gamma atmospheric turbulence","volume":"54","author":"Ma","year":"2015","journal-title":"Appl. Opt."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1109\/COMST.2016.2603518","article-title":"Optical communication in space: Challenges and mitigation techniques","volume":"19","author":"Kaushal","year":"2016","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.5140\/JASS.2020.37.1.11","article-title":"Performance analysis of DPSK optical communication for LEO-to-Ground Relay link via a GEO Satellite","volume":"37","author":"Lim","year":"2020","journal-title":"J. Astron. Space Sci."},{"key":"ref_6","unstructured":"Meynants, G., Lepage, G., Bogaerts, J., Vanhorebeek, G., and Wang, X. (2009, January 22\u201328). Limitations to the frame rate of high speed image sensors. Proceedings of the 2009 International Image Sensor Workshop, Bergen, Norway."},{"key":"ref_7","unstructured":"Cierny, O. (2017). Precision Closed-Loop Laser Pointing System for the Nanosatellite Optical Downlink Experiment. [Master\u2019s Thesis, Lulea University of Technology]."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1093\/mnras\/sty223","article-title":"Methods for multiple-telescope beam imaging and guiding in the near-infrared","volume":"476","author":"Anugu","year":"2018","journal-title":"MNRAS"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"16771","DOI":"10.3390\/s121216771","article-title":"High dynamics and precision optical measurement using a position sensitive Detector (PSD) in reflection-mode: Application to 2D object tracking over a smart surface","volume":"12","author":"Ivan","year":"2012","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1364\/JON.4.000300","article-title":"Trends in satellite communications and the role of optical free-space communications","volume":"4","author":"Toyoshima","year":"2005","journal-title":"J. Opt. Netw."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Buske, I., and Riede, W. (2006). Sub-\u03bcrad laser beam tracking. Technologies for Optical Countermeasures III, Proceedings of the Optics\/Photonics in Security and Defence, Stockholm, Sweden, 11\u201314 September 2016, SPIE.","DOI":"10.1117\/12.690424"},{"key":"ref_12","unstructured":"Hemmati, H. (2009). Near-Earth Laser Communications, CRC Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"804","DOI":"10.2184\/lsj.28.804","article-title":"Space laser communications: Systems, technologies, and applications","volume":"28","author":"Leeb","year":"2000","journal-title":"Rev. Laser Eng."},{"key":"ref_14","unstructured":"Kaminow, I.P., Li, T., and Willner, A.E. (2013). Optical Fiber Telecommunications VIB, Elsevier Inc."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Carrasco-Casado, A., Biswas, A., Fields, R., Grefenstette, B., Harrison, F., Sburlan, S., and Toyoshima, M. (2017, January 14\u201316). Optical communication on CubeSats\u2014Enabling the next era in space science. Proceedings of the 2017 IEEE International Conference on Space Optical Systems and Applications (ICSOS), Okinawa, Japan.","DOI":"10.1109\/ICSOS.2017.8357210"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3866","DOI":"10.1364\/AO.43.003866","article-title":"Scintillation and beam-wander analysis in an optical ground station-satellite uplink","volume":"43","author":"Dios","year":"2004","journal-title":"Appl. Opt."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6313","DOI":"10.1364\/OE.23.006313","article-title":"Analysis of angle of arrival fluctuations for optical wave\u2019s propagation through weak anisotropic non-Kolmogorov turbulence","volume":"23","author":"Cui","year":"2015","journal-title":"Opt. Exp."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lim, H.-C., Zhang, Z.-P., Sung, K.-P., Park, J.U., Kim, S., Choi, C.-S., and Choi, M. (2020). Modeling and analysis of an echo laser pulse waveform for the orientation determination of space debris. Remote Sens., 12.","DOI":"10.3390\/rs12101659"},{"key":"ref_19","unstructured":"Nguyen, T.N. (2013). Laser Beacon Tracking for Free-space Optical Communication on Small-Satellite Platforms in Low-Earth Orbit. [Master\u2019s Thesis, Massachusetts Institute of Technology]."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"804","DOI":"10.1364\/JOSA.72.000804","article-title":"Image-position error associated with a quadrant detector","volume":"72","author":"Tyler","year":"1982","journal-title":"J. Opt. Soc. Am."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Lee, S. (2002). Pointing accuracy improvement using model-based noise reduction method. Free-Space Laser Communication Technologies XIV, Proceedings of the High-Power Lasers and Applications, San Jose, CA, USA, 20\u201325 January 2002, SPIE.","DOI":"10.1117\/12.464110"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Hemmati, H. (2005). Deep Space Optical Communications, Jet Propulsion Laboratory.","DOI":"10.1002\/0470042419"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1364\/JOSAA.11.000925","article-title":"Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes","volume":"11","author":"Sandler","year":"1994","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1086\/133484","article-title":"A reflective shack-hartmann wave-front sensor for adaptive optics","volume":"106","author":"Colucci","year":"1994","journal-title":"Publ. Astron. Soc. Pac."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1111\/j.1365-2966.2006.10661.x","article-title":"Comparison of centroid computation algorithms in a Shack-Hartmann sensor","volume":"371","author":"Thomas","year":"2006","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"071413","DOI":"10.1117\/1.OE.52.7.071413","article-title":"Shack-Hartmann wavefront sensor image analysis: A comparison of centroiding methods and image-processing techniques","volume":"52","author":"Nightingale","year":"2013","journal-title":"Opt. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2243","DOI":"10.1080\/09500340802082426","article-title":"Measuring statistical error of Shack\u2013Hartmann wavefront sensor with discrete detector arrays","volume":"55","author":"Li","year":"2008","journal-title":"J. Mod. Opt."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1109\/TWC.2009.071318","article-title":"Optical wireless links with spatial diversity over strong atmospheric turbulence channels","volume":"8","author":"Tsiftsis","year":"2009","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Mishra, N., and Kumar, D.S. (2016, January 3\u20135). Outage analysis of relay assisted FSO systems over K-distribution turbulence channel. Proceedings of the 2016 International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT), Chennei, India.","DOI":"10.1109\/ICEEOT.2016.7755243"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1117\/1.1386641","article-title":"Mathematical model for the irradiance probability density function of a laser beam propagating through turbulent media","volume":"40","author":"Andrews","year":"2001","journal-title":"Opt. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1455","DOI":"10.1109\/TCOMM.2005.855009","article-title":"Performance of APD-based, PPM free-space optical communication systems in atmospheric turbulence","volume":"53","author":"Kiasaleh","year":"2005","journal-title":"IEEE Trans. Commun."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Andrews, L.C., and Phillips, R.L. (2005). Laser Beam Propagation through Random Media, SPIE Press.","DOI":"10.1117\/3.626196"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.1049\/iet-com.2008.0212","article-title":"Performance analysis of free-space optical communication systems over atmospheric turbulence channels","volume":"3","author":"Nistazakis","year":"2009","journal-title":"IET Commun."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"033564","DOI":"10.1117\/1.3271047","article-title":"Effect of target surface orientation on the range precision of laser detection and ranging systems","volume":"3","author":"Johnson","year":"2009","journal-title":"J. Appl. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1029\/GD025p0133","article-title":"Milimeter accuracy satellite laser ranging: A review","volume":"25","author":"Degnan","year":"1993","journal-title":"Geodyn. Ser."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.optcom.2014.05.039","article-title":"Temporal spectrum of atmospheric scintillation and the effects of aperture averaging and time averaging","volume":"330","author":"Shen","year":"2014","journal-title":"Opt. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Ghassemlooy, Z., Popoola, W., and Rajbhandari, S. (2018). Optical Wireless Communications: System and Channel Modelling with MATLAB., CRC Press.","DOI":"10.1201\/9781315151724"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"3308","DOI":"10.1109\/TGRS.2006.880623","article-title":"A Laser altimeter performance model and its application to BELA","volume":"44","author":"Gunderson","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"8525","DOI":"10.1364\/OE.17.008525","article-title":"Error analysis of CCD-based point source centroid computation under the background light","volume":"17","author":"Ma","year":"2009","journal-title":"Opt. Exp."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1117\/12.7973628","article-title":"Beam pointing error as a significant design parameter for satellite-borne, free-space optical communication systems","volume":"24","author":"Barry","year":"1985","journal-title":"Opt. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1364\/JOSAA.11.000358","article-title":"Bandwidth considerations for tracking through turbulence","volume":"11","author":"Tyler","year":"1994","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0079-6638(08)70204-X","article-title":"The effects of atmospheric turbulence in optical astronomy","volume":"19","author":"Roddier","year":"1981","journal-title":"Prog. Opt."},{"key":"ref_43","unstructured":"Riesing, K.M. (2013). Development of a Pointing, Acquisition, and Tracking System for a Nanosatellite Laser Communication Module. [Master\u2019s Thesis, Massachusetts Institute of Technology]."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1117\/1.1418222","article-title":"Measurement of the characteristics of a quadrant avalanche photodiode and its application to a laser tracking system","volume":"41","author":"Toyoda","year":"2002","journal-title":"Opt. Eng."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/10\/1931\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:01:53Z","timestamp":1760162513000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/10\/1931"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,15]]},"references-count":44,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["rs13101931"],"URL":"https:\/\/doi.org\/10.3390\/rs13101931","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,5,15]]}}}