Average optical path length estimation in a slab of arbitrary finite thickness
A method for determining the average photon path length in a slab of multiple scattering material is presented. Radiances can be obtained from the radiative transfer equation and subsequently differentiated to obtain the average photon path length. These radiances can be obtained via multiple method...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-06-01
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| Series: | Frontiers in Remote Sensing |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/frsen.2025.1565245/full |
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| author | Tim Kindervatter Wei Li Nan Chen Yuping Huang Yongxiang Hu Snorre Stamnes Xiaomei Lu Børge Hamre Jakob J. Stamnes Tomonori Tanikawa Jennifer Lee Carl Weimer Xubin Zeng Charles K. Gatebe Knut Stamnes |
| author_facet | Tim Kindervatter Wei Li Nan Chen Yuping Huang Yongxiang Hu Snorre Stamnes Xiaomei Lu Børge Hamre Jakob J. Stamnes Tomonori Tanikawa Jennifer Lee Carl Weimer Xubin Zeng Charles K. Gatebe Knut Stamnes |
| author_sort | Tim Kindervatter |
| collection | DOAJ |
| description | A method for determining the average photon path length in a slab of multiple scattering material is presented. Radiances can be obtained from the radiative transfer equation and subsequently differentiated to obtain the average photon path length. These radiances can be obtained via multiple methods including Monte Carlo simulations, analytic two-stream approximations, and multi-stream numerical solutions such as the AccuRT computational tool. Average path lengths obtained via numerical differentiation of these radiances are found to agree closely with path length estimates predicted by existing methods found in the literature. The average photon path length is further considered for a slab of finite physical thickness. It was found that for a slab consisting of non-absorbing material there is a linear relationship between the slab thickness and the average photon path length, but that for materials with nonzero absorption, this linear relationship breaks down as the slab thickness increases. Average path lengths may be converted to time spans to determine the amount of time a photon spends in a multiple scattering medium, which may be used to quantify the impact of multiple scattering on pulse stretching in lidar/radar applications. |
| format | Article |
| id | doaj-art-d8a188a6239f4096b69628b2ffed31f6 |
| institution | Kabale University |
| issn | 2673-6187 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Remote Sensing |
| spelling | doaj-art-d8a188a6239f4096b69628b2ffed31f62025-08-20T03:47:04ZengFrontiers Media S.A.Frontiers in Remote Sensing2673-61872025-06-01610.3389/frsen.2025.15652451565245Average optical path length estimation in a slab of arbitrary finite thicknessTim Kindervatter0Wei Li1Nan Chen2Yuping Huang3Yongxiang Hu4Snorre Stamnes5Xiaomei Lu6Børge Hamre7Jakob J. Stamnes8Tomonori Tanikawa9Jennifer Lee10Carl Weimer11Xubin Zeng12Charles K. Gatebe13Knut Stamnes14Light and Life Laboratory, Department of Physics, Stevens Institute of Technology, Hoboken, NJ, United StatesLight and Life Laboratory, Department of Physics, Stevens Institute of Technology, Hoboken, NJ, United StatesLight and Life Laboratory, Department of Physics, Stevens Institute of Technology, Hoboken, NJ, United StatesLight and Life Laboratory, Department of Physics, Stevens Institute of Technology, Hoboken, NJ, United StatesRadiation and Aerosol Branch, NASA Langley Research Center, Hampton, VA, United StatesRadiation and Aerosol Branch, NASA Langley Research Center, Hampton, VA, United StatesRadiation and Aerosol Branch, NASA Langley Research Center, Hampton, VA, United StatesDepartment of Physics and Technology, University of Bergen, Bergen, NorwayDepartment of Physics and Technology, University of Bergen, Bergen, NorwayMeteorological Research Institute, Japan Meteorological Agency, Tsukuba, JapanBAE Systems, Boulder, CO, United StatesBAE Systems, Boulder, CO, United StatesDepartment of Atmospheric Sciences, University of Arizona, Tucson, AZ, United StatesAtmospheric Science Branch, NASA Ames Research Center, Moffett Field, CA, United StatesLight and Life Laboratory, Department of Physics, Stevens Institute of Technology, Hoboken, NJ, United StatesA method for determining the average photon path length in a slab of multiple scattering material is presented. Radiances can be obtained from the radiative transfer equation and subsequently differentiated to obtain the average photon path length. These radiances can be obtained via multiple methods including Monte Carlo simulations, analytic two-stream approximations, and multi-stream numerical solutions such as the AccuRT computational tool. Average path lengths obtained via numerical differentiation of these radiances are found to agree closely with path length estimates predicted by existing methods found in the literature. The average photon path length is further considered for a slab of finite physical thickness. It was found that for a slab consisting of non-absorbing material there is a linear relationship between the slab thickness and the average photon path length, but that for materials with nonzero absorption, this linear relationship breaks down as the slab thickness increases. Average path lengths may be converted to time spans to determine the amount of time a photon spends in a multiple scattering medium, which may be used to quantify the impact of multiple scattering on pulse stretching in lidar/radar applications.https://www.frontiersin.org/articles/10.3389/frsen.2025.1565245/fullradiative transfertwo stream approximationphoton path lengthmultiple scatteringradarlidar |
| spellingShingle | Tim Kindervatter Wei Li Nan Chen Yuping Huang Yongxiang Hu Snorre Stamnes Xiaomei Lu Børge Hamre Jakob J. Stamnes Tomonori Tanikawa Jennifer Lee Carl Weimer Xubin Zeng Charles K. Gatebe Knut Stamnes Average optical path length estimation in a slab of arbitrary finite thickness Frontiers in Remote Sensing radiative transfer two stream approximation photon path length multiple scattering radar lidar |
| title | Average optical path length estimation in a slab of arbitrary finite thickness |
| title_full | Average optical path length estimation in a slab of arbitrary finite thickness |
| title_fullStr | Average optical path length estimation in a slab of arbitrary finite thickness |
| title_full_unstemmed | Average optical path length estimation in a slab of arbitrary finite thickness |
| title_short | Average optical path length estimation in a slab of arbitrary finite thickness |
| title_sort | average optical path length estimation in a slab of arbitrary finite thickness |
| topic | radiative transfer two stream approximation photon path length multiple scattering radar lidar |
| url | https://www.frontiersin.org/articles/10.3389/frsen.2025.1565245/full |
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