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Comment on the modified Beer–Lambert law for scattering media
Open accessAbstract
We present a concise overview of the modified Beer-Lambert law, which has been extensively used in the literature of near-infrared spectroscopy (NIRS) of scattering media. In particular, we discuss one form of the modified Beer-Lambert law that is commonly found in the literature and that is not strictly correct. However, this incorrect form of the modified Beer-Lambert law still leads to the correct expression for the changes in the continuous wave optical signal associated with changes in the absorption coefficient of the investigated medium. Here we propose a notation for the modified Beer-Lambert law that keeps the typical form commonly found in the literature without introducing any incorrect assumptions.
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“When absorption and multiple scattering is present, the situation is more complicated because the total propagation path of the detected photons is generally larger than l (the penetration depth).”
From Effect of skin color on optical properties and the implications for medical optical technologies: a review (2024) · cites this paper as [54]
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Estimation of optical pathlength through tissue from direct time of flight measurement
Delpy, D. T., Cope, M., van der Zee, P., Arridge, S., Wray, S., & Wyatt, J. S. (1988) · Physics in Medicine and Biology · doi:10.1088/0031-9155/33/12/008 · Cited by 2,251
Hiraoka, M., Firbank, M., Essenpreis, M., Cope, M., Arridge, S., van der Zee, P., & Delpy, D. T. (1993) · Physics in Medicine and Biology · doi:10.1088/0031-9155/38/12/011 · Cited by 375
Matcher, S. J., Cope, M., & Delpy, D. T. (1994) · Physics in Medicine and Biology · doi:10.1088/0031-9155/39/1/011 · Cited by 323
Franceschini, M. A., Fantini, S., Paunescu, L. A., Maier, J. S., & Gratton, E. (1998) · Applied Optics · doi:10.1364/ao.37.007447 · Cited by 172
Self-citationWobst, P., Wenzel, R., Kohl‐Bareis, M., Obrig, H., & Villringer, A. (2001) · NeuroImage · doi:10.1006/nimg.2000.0706 · Cited by 117
Kohl‐Bareis, M., Nolte, C. H., Heekeren, H. R., Horst, S., Scholz, U., Obrig, H., & Villringer, A. (1998) · Physics in Medicine and Biology · doi:10.1088/0031-9155/43/6/028 · Cited by 112
Tsuchiya, Y. (2001) · Physics in Medicine and Biology · doi:10.1088/0031-9155/46/8/303 · Cited by 43
Research works printed but not linked: 2
- Boas D, Franceschini M A, Dunn A K and Strangman G 2002 Noninvasive imaging of cerebral activation with diffuse optical tomography In Vivo Optical Imaging of Brain Function ed D Ron Frostig (Boca Raton, FL: CRC Press) chapter 8, pp 193-211
- Duderstadt J J 1979 Transport Theory (New York: Wiley)
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Metadata
- Authors
- Sassaroli, A., & Fantini, S.
- Affiliations
- Tufts University (US)
- Venue
- Physics in Medicine and Biology
- Publisher
- IOP Publishing
- Published
- 2004-07-06
- Volume
- 49
- Issue
- 14
- Pages
- N255-N257
- ISSN
- 0031-9155 (ISSN-L)
- 1361-6560
- OpenAlex
- W2108329838
- Cited by
- 352
- References
- 7
- Citations by year
- 2026: 16 · 2025: 24 · 2024: 21 · 2023: 25 · 2022: 22 · 2021: 30 · 2020: 29 · 2019: 33 · 2018: 25 · 2017: 20 · 2016: 24 · 2015: 10 · 2014: 11 · 2013: 10 · 2012: 13
- FWCI
- 3.07
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physics in Medicine and Biology (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation
- National Institutes of Health
- National Institute on Drug Abuse (DA14178, R01DA014178)
- Topics
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Optical Imaging and Spectroscopy Techniques
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Biophysics › Spectroscopy Techniques in Biomedical and Chemical Research
- Physical Sciences › Chemistry › Analytical Chemistry › Spectroscopy and Chemometric Analyses
- Keywords
- modified Beer-Lambert law, turbid media, near-infrared spectroscopy, optical loss, absorption coefficient
- MeSH terms
- Biophysics, Image Processing, Computer-Assisted, Models, Theoretical, Scattering, Radiation, Statistics as Topic, Models, Statistical, Photons, Spectroscopy, Near-Infrared
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