{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T01:25:24Z","timestamp":1770081924374,"version":"3.49.0"},"reference-count":23,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T00:00:00Z","timestamp":1769990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Free-space optical (FSO) communication enables high-bandwidth license-free data transmission and is particularly attractive for maritime point-to-point links. However, FSO performance is strongly affected by atmospheric conditions. This work presents a semi-empirical model quantifying the impact of fine particulate matter (PM2.5) on received optical power in a maritime FSO link. The model is derived from long-term experimental measurements collected over a 2.96 km horizontal optical path above the sea surface, combining received signal strength indicator (RSSI) data with co-located PM2.5 observations. Statistical analysis reveals a strong negative correlation between PM2.5 concentration and received optical power (Pearson coefficient \u22120.748). Using a logarithmic attenuation formulation, the PM2.5-induced attenuation is estimated to increase by approximately 0.0026 dB\/km per \u00b5g\/m3 of PM2.5 concentration. A second-order semi-empirical model captures the observed nonlinear attenuation behavior with a coefficient of determination of R2 = 0.57. The proposed model provides a practical tool for link budgeting, performance forecasting, and adaptive design of maritime FSO systems operating in aerosol-rich environments.<\/jats:p>","DOI":"10.3390\/computation14020039","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T12:49:44Z","timestamp":1770036584000},"page":"39","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Semi-Empirical Estimation of Aerosol Particle Influence at the Performance of Terrestrial FSO Links over the Sea"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2764-0599","authenticated-orcid":false,"given":"Argyris N.","family":"Stassinakis","sequence":"first","affiliation":[{"name":"Section of Battle Systems, Naval Operations, Sea Studies, Navigation, Electronics and Telecommunications, Hellenic Naval Academy, Hadjikyriakou Ave., 18539 Piraeus, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Efstratios V.","family":"Chatzikontis","sequence":"additional","affiliation":[{"name":"Section of Electronic Physics and Systems, Department of Physics, National and Kapodistrian University of Athens, 15784 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kyle R.","family":"Drexler","sequence":"additional","affiliation":[{"name":"Naval Information Warfare Center Pacific, San Diego, CA 92152, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8247-3930","authenticated-orcid":false,"given":"Andreas D.","family":"Tsigopoulos","sequence":"additional","affiliation":[{"name":"Section of Battle Systems, Naval Operations, Sea Studies, Navigation, Electronics and Telecommunications, Hellenic Naval Academy, Hadjikyriakou Ave., 18539 Piraeus, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gratchia","family":"Mkrttchian","sequence":"additional","affiliation":[{"name":"Centre of Excellence for Applied Research & Training\u2014CERT, Higher Colleges of Technology, Abu Dhabi P.O. Box 5464, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hector E.","family":"Nistazakis","sequence":"additional","affiliation":[{"name":"Section of Electronic Physics and Systems, Department of Physics, National and Kapodistrian University of Athens, 15784 Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2231","DOI":"10.1109\/COMST.2014.2329501","article-title":"Survey on free space optical communication: A communication theory perspective","volume":"16","author":"Ali","year":"2014","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_2","first-page":"203","article-title":"An introduction to free-space optical communications","volume":"19","author":"Hennes","year":"2010","journal-title":"Radioengineering"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1049\/iet-opt.2014.0150","article-title":"Performance of quadrature amplitude modulation orthogonal frequency division multiplexing-based free space optical links with non-linear clipping effect over gamma\u2013gamma modelled turbulence channels","volume":"9","author":"Stassinakis","year":"2015","journal-title":"IET Optoelectron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1364\/AO.54.001453","article-title":"Coherent free space optics communications over the maritime atmosphere with use of adaptive optics for beam wavefront correction","volume":"54","author":"Ming","year":"2015","journal-title":"Appl. Opt."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Juarez Juan, C., Sluz, J.E., Nelson, C., Airola, M.B., Fitch, M.J., Young, D.W., Terry, D., Davidson, F.M., Rottier, J.R., and Sova, R.M. (2010). Free-space optical channel characterization in the maritime environment. Atmospheric Propagation VII, SPIE.","DOI":"10.1117\/12.852645"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"13769","DOI":"10.1364\/OE.518363","article-title":"Maritime free space optical communications field test and link budget statistics","volume":"32","author":"Willitsford","year":"2024","journal-title":"Opt. Express"},{"key":"ref_7","first-page":"66","article-title":"Estimating maritime free space optical link performance using models based on experimental measurements","volume":"Volume 12691","author":"Rabinovich","year":"2023","journal-title":"Laser Communication and Propagation through the Atmosphere and Oceans XII"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3525","DOI":"10.1109\/JIOT.2022.3219674","article-title":"Maritime communications: A survey on enabling technologies, opportunities, and challenges","volume":"10","author":"Alqurashi","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"10217","DOI":"10.1364\/OE.484922","article-title":"Optical scintillation in a maritime environment","volume":"31","author":"Rabinovich","year":"2023","journal-title":"Opt. Express"},{"key":"ref_10","first-page":"355","article-title":"Terrestrial free-space optical communications","volume":"Volume 17","author":"Zabih","year":"2010","journal-title":"Mobile and Wireless Communications Network Layer and Circuit Level Design"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"128508","DOI":"10.1016\/j.optcom.2022.128508","article-title":"Optical turbulence measurements and modeling over Monterey Bay","volume":"520","author":"Lionis","year":"2022","journal-title":"Opt. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1080\/02786826.2015.1131809","article-title":"A light-weight, high-sensitivity particle spectrometer for PM2.5 aerosol measurements","volume":"50","author":"Gao","year":"2016","journal-title":"Aerosol Sci. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.atmosenv.2017.09.023","article-title":"Satellite-based PM2.5 estimation using fine-mode aerosol optical thickness over China","volume":"170","author":"Xing","year":"2017","journal-title":"Atmos. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1364\/JOCN.551182","article-title":"Modeling the physical layer of air-to-space optical communication networks using the modified multi-scale method","volume":"17","author":"Helsdingen","year":"2025","journal-title":"J. Opt. Commun. Netw."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Galaktionov, I., and Toporovsky, V. (2025). Performance Analysis of an Optical System for FSO Communications Utilizing Combined Stochastic Gradient Descent Optimization Algorithm. Appl. Syst. Innov., 8.","DOI":"10.3390\/asi8050143"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Schiavon, M., Vanzo, A., Campaci, K., Marulanda Acosta, V., and Bonora, S. (2025). Multi-Actuator Lens Systems for Turbulence Correction in Free-Space Optical Communications. Photonics, 12.","DOI":"10.3390\/photonics12090870"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"93","DOI":"10.3390\/telecom2010007","article-title":"Experimental model development for the attenuation coefficient estimation of terrestrial optical wireless links over the sea","volume":"2","author":"Papavgeris","year":"2021","journal-title":"Telecom"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"117410","DOI":"10.1016\/j.atmosenv.2020.117410","article-title":"Observation of PM2.5 using a combination of satellite remote sensing and low-cost sensor network in Siberian urban areas with limited reference monitoring","volume":"227","author":"Lin","year":"2020","journal-title":"Atmos. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1080\/10408340500526766","article-title":"The correlation coefficient: An overview","volume":"36","author":"Garcia","year":"2006","journal-title":"Crit. Rev. Anal. Chem."},{"key":"ref_20","unstructured":"Marko, S., and Mooi, E. (2019). Regression analysis. A Concise Guide to Market Research: The Process, Data, and Methods Using IBM SPSS Statistics, Springer."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"e623","DOI":"10.7717\/peerj-cs.623","article-title":"The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation","volume":"7","author":"Chicco","year":"2021","journal-title":"PeerJ Comput. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"79","DOI":"10.3354\/cr030079","article-title":"Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance","volume":"30","author":"Willmott","year":"2005","journal-title":"Clim. Res."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, W., and Lu, Y. (2018). Analysis of the mean absolute error (MAE) and the root mean square error (RMSE) in assessing rounding model. IOP Conference Series: Materials Science and Engineering, Proceedings of the 2017 the 5th International Conference on Mechanical Engineering, Materials Science and Civil Engineering, Kuala Lumpur, Malaysia, 15\u201316 December 2017, IOP Publishing.","DOI":"10.1088\/1757-899X\/324\/1\/012049"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/14\/2\/39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T13:08:05Z","timestamp":1770037685000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/14\/2\/39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,2]]},"references-count":23,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2]]}},"alternative-id":["computation14020039"],"URL":"https:\/\/doi.org\/10.3390\/computation14020039","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,2]]}}}