The classical Beer-Lambert law (BLL) can be applied for extraction of optical properties of a sample (mu_a or mu_extinction in a more general case) under known and controlled illumination & detection conditions as for example in a conventional cuvette spectroscopy.
For turbid media applications, it has to be modified to account for scattering and increased optical pathlength. So, it transforms to the modified Beer-Lambert law (MBLL). Then, it is usually applied to get information about optical properties of chromophore(s) that are distributed in turbid media. For example, hemoglobin in tissues etc.
Does anybody know if MBLL (or BLL) was applied to obtain optical properties of a localized chromophore inclusion embedded in turbid media? Imagine doing spectroscopic cuvette measurements with the cuvette filled with a certain chromophore and detector embedded in a biological tissue, for example and trying to extract its mu_a. Has anybody tried to adopt MBLL for this purpose by accounting for absorbed and scattered photons?
Dear Serge! I believe You know that exist 2 type of light scattering: one-fold or single and multiple in dependence of scattering centers concetration. Between them intermidiate state with mixed type of scattering. For the first type scattering media with absorption I guess it is possible to work with BLL and MBLL measuring some effective scattering-absorption coefficient. Nothing similar can be done with case of multiple scattering. Maybe possible to modify for your case the old known Kobelka-Munk aproximation...
Yes, but instead of the TOTAL average path length ( =DPF *d) you have to consider the partial average path length in the inclusion
where PDPF is the partial differential path length factor.
Delta-I/Io= -Sum(i=1,n)
which is valid under ANY situation (the medium does not even to be scattering).
Delta-I/Io is the change of detected intensity normalized to the baseline value, while Delta-mua(i) is the change of the absorption coefficient in the voxel (i).
Angelo,
I've looked briefly at the articles you suggested. Perhaps, too briefly because I couldn't see how or where you'd use the BLL (or MBLL) to calculate the absorption coefficient, i.e.:
mu_a=ln(I_0/I)/L, where I_0 is the incident intensity, I is the transmitted intensity in the presence of the defect, L - the optical path inside the defect or some other related quantity.
What am I missing here?
Dear Serge,
if you're asking about how to calculate the CHANGE in absorption in a focal region in a diffusing medium, by measuring the CHANGE of intensity (or absorbance), I repeat that what you need to know is
I don't understand the other example of the cuvette: if the medium is homogeneous and you change only the absorption of the entire medium of course you can apply MBLL. This is what MBLL is for, but you have to know the DPF (or ) which depends on the geometry of the medium, its optical properties etc.
Dear Angelo,
Thanks! I see that it's not that simple... Regarding the example, that's exactly what I had in mind - changing the absorption in the local volume only (i.e., the cuvette) while keeping the absorption of the background medium intact and being able to apply MBLL or its modification to recover mu_a of the volume.
Dear Serge,
It depends how optically dense your samples are (mean free path ell) and how thick (L). If ell
Dear Willem,
Thanks for the tips! A case I'm interested in involves very strong multiple scattering in thick biological tissues, like muscles. What articles on this subject should I look up at your website?
It's nice to reconnect with you after Crete...
Cheers,
Serge
I repeat that MBLL is a very GENERAL law valid within RADIATIVE TRANSPORT EQUATION (i.e. the medium does not even to be scattering.....in this case MBLL reduces to BLL). I published in 2004 "Comment on the modified Beer Lambert law for scattering media (Phys. Med. Biol. 49 N255-N257) , where I showed how to derive MBLL from the Radiative Transport Equation. When the change in absorption is focal you should read carefully what I wrote in the JOSA A paper I indicated above, The laws (both for homogeneous and focal change in the absorption coefficient) are valid within Radiative Transport Equation, but in order to apply them you need to know the total or the partial mean path length(s) which I don't know to calculate unless I can make the assumption of a diffusive medium where Diffusion Equation holds.
Angelo,
I know that very concise but elegant article in PMB. Regarding the JOSA A paper, looks like I'd need to look more closely at it:)
Please look at our recent paper( particularly the Introduction) published in Applied Optics and available in Biomedical express infobase of OSA :
"Red/blue spectral shifts of laser-induced fluorescence emission due to different nanoparticle suspensions in various dye solutions", Applied Optics, Vol. 53, Issue 24, pp. 5398-5409 (2014)
links:
http://dx.doi.org/10.1364/AO.53.005398
http://www.opticsinfobase.org/vjbo/virtual_issue.cfm
The models for propagation of light in hybrid media is reviewed. The LB law and the effects of dense fluorophores and dense nanoparticle suspensions are studied too. Mont Caro can show the deviation from LB law when the multiple scattering is dominant.
How much is the density of scatterers, photon transport regime (Ballistic, diffusive or localization) is determined and proper model for calculating the transport mean free path should be used to determine the absorption. in diffusion regime RTE or Monte Carlo method are vastly used:
"Monte Carlo simulation of photon densities inside the dermis in LLLT (low level laser therapy)", Parviz Parvin, Somayeh Eftekharnoori, Hamid Reza Dehghanpour, Optics and Spectroscopy 01/2009; 107(3):486-490.
But in localized regime, diffusion theory fails because interference effects are significant in this case and may modulate the intensity of propagating light.
Parvin et al., have shown that "spectral shift spectroscopy" is another useful and simple method to be adopted for characterization and detection in turbid media:
http://dx.doi.org/10.1364/AO.53.005398
1- The deviation from Beer-Lambert Law in gain media:
When incident beam in tensity exceeds saturation intensity ;
Iout= I0exp( G0x) , I > Is
Where Is is Saturation Intensity.
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2- The deviation from BL Law in highly scattering media due to Backscattering and Multiple scattering where scattering coefficient is much greater than absorption coefficient.
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3-- The diviation from BL Law at high intesity- incident beams where nonlinear effects become dominant.
Dear Serge,
Here are links to the papers that I meant:
1) Leung et al, Opt. Expr (2014), first link included below (hope this system works?)
2) WLV et al, Appl. Opt (2013), second link below. (Yes, I did all measurements and analysis for this paper; like if I was the postdoc on duty :-)
You might also find useful material in the PhD thesis of Gijs van Soest (also on our website, defended in 2001).
I hope these sources will be helpful for you (if you somehow cannot access them, send me an email.)
Yes, Crete is a great place and Costas organized a nice meeting :-)
Best wishes,
Willem
http://cops.nano-cops.com/publications/interplay-between-multiple-scattering-emission-and-absorption-light-phosphor-white-ligh
http://cops.nano-cops.com/publications/broadband-mean-free-path-diffuse-light-polydisperse-ensembles-scatterers-white-led-lighnull
Sorry, for the second paper, something went wrong with including the link. Here is the correct one.
Oh yes, and on each page you can find a pdf for downloading.
Cheers, W
http://cops.nano-cops.com/publications/broadband-mean-free-path-diffuse-light-polydisperse-ensembles-scatterers-white-led-ligh
We've demonstrated an application of the original Beer-Lambert law for extraction of optical properties of a localized target composed of Au NPs embedded in bulk biological tissues:
https://www.researchgate.net/publication/272350657_Interstitial_diffuse_radiance_spectroscopy_of_gold_nanocages_and_nanorods_in_bulk_muscle_tissues?ev=prf_pub
Article Interstitial diffuse radiance spectroscopy of gold nanocages...
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