Lambert Law

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Mamoru Tamura - One of the best experts on this subject based on the ideXlab platform.

  • relationship between time resolved and non time resolved beer Lambert Law in turbid media
    Physics in Medicine and Biology, 1997
    Co-Authors: Yasutomo Nomura, Osamu Hazeki, Mamoru Tamura
    Abstract:

    The time-resolved Beer-Lambert Law proposed for oxygen monitoring using pulsed light was extended to the non-time-resolved case in a scattered medium such as living tissues with continuous illumination. The time-resolved Beer-Lambert Law was valid for the phantom model and living tissues in the visible and near-infrared regions. The absolute concentration and oxygen saturation of haemoglobin in rat brain and thigh muscle could be determined. The temporal profile of rat brain was reproduced by Monte Carlo simulation. When the temporal profiles of rat brain under different oxygenation states were integrated with time, the absorbance difference was linearly related to changes in the absorption coefficient. When the simulated profiles were integrated, there was a linear relationship within the absorption coefficient which was predicted for fractional inspiratory oxygen concentration from 10 to 100% and, in the case beyond the range of the absorption coefficient, the deviation from linearity was slight. We concluded that an optical pathlength which is independent of changes in the absorption coefficient is a good approximation for near-infrared oxygen monitoring.

  • quantitation of absolute concentration change in scattering media by the time resolved microscopic beer Lambert Law
    Advances in Experimental Medicine and Biology, 1994
    Co-Authors: M Oda, Yutaka Yamashita, Goro Nishimura, Mamoru Tamura
    Abstract:

    In a scattering media like living tissue, there have been two lines of critical argument concerning the effect of optical absorption on the distribution of’ the optical pathlength. One is that the optical pathlength is constant when the absorption changes, though it differs markedly from the physical pathlength, such as the thickness of the tissue because of considerable scattering. The other is that the distribution of the path-length depends on the absorption (1,2). Previously, we have shown the validity of the Beer-Lambert Law in rat heads (3) and thigh muscles (4). The requirement of’ the Beer-Lambert Law is the independence of the attenuation of incident light by absorption from that by scattering. This was confirmed by measuring the time of flight of picosecond length light pulses in several rat tissues (5) as well as model systems (6). Equation(1), which was derived from our time-resolved study on the Beer-Lambert Law, shows that light intensity along the non-linear path taken by photons through scattering media is exponentially attenuated by absorption. Monte Carlo simulation also confirmed this (7). The present paper expands equation(1) into time-resolved multiwavelength photometry for determination of the absolute concentration of absorber coexisting in scattering media, by which the optical pathlength was directly estimated.

Jurgen Popp - One of the best experts on this subject based on the ideXlab platform.

  • the bouguer beer Lambert Law shining light on the obscure
    ChemPhysChem, 2020
    Co-Authors: Thomas G Mayerhofer, Susanne Pahlow, Jurgen Popp
    Abstract:

    The Beer-Lambert Law is unquestionably the most important Law in optical spectroscopy and indispensable for the qualitative and quantitative interpretation of spectroscopic data. As such, every spectroscopist should know its limits and potential pitfalls, arising from its application, by heart. It is the goal of this work to review these limits and pitfalls, as well as to provide solutions and explanations to guide the reader. This guidance will allow a deeper understanding of spectral features, which cannot be explained by the Beer-Lambert Law, because they arise from electromagnetic effects/the wave nature of light. Those features include band shifts and intensity changes based exclusively upon optical conditions, i.e. the method chosen to record the spectra, the substrate and the form of the sample. As such, the review will be an essential tool towards a full understanding of optical spectra and their quantitative interpretation based not only on oscillator positions, but also on their strengths and damping constants.

  • employing theories far beyond their limits the case of the boguer beer Lambert Law
    ChemPhysChem, 2016
    Co-Authors: Thomas G Mayerhofer, Jurgen Popp, H Mutschke
    Abstract:

    For spectroscopists, the (Bouguer-)Beer–Lambert Law is unquestionably an essential principle, since it is inseparably linked with one of the most important quantities in spectroscopy, the absorbance. In spite of its importance, a quantitative discussion of the legitimacy of relating the transmittance, the quantity that is usually measured, to the absorbance by assuming a logarithmic relation between both quantities cannot be found in literature. In this contribution, we quantitatively discuss, based on examples, the errors that can be introduced by disregarding the exact solution based on Maxwell's equations and show that these errors can easily exceed one order of magnitude. We also re-derive the Beer–Lambert Law, thereby providing guidance as how to convert transmittance into absorbance properly.

Yutaka Tsuchiya - One of the best experts on this subject based on the ideXlab platform.

  • photon path distribution and optical responses of turbid media theoretical analysis based on the microscopic beer Lambert Law
    Physics in Medicine and Biology, 2001
    Co-Authors: Yutaka Tsuchiya
    Abstract:

    A concise theoretical treatment has been developed to describe the optical responses of a highly scattering inhomogeneous medium using functions of the photon path distribution (PPD). The treatment is based on the microscopic Beer-Lambert Law and has been found to yield a complete set of optical responses by time- and frequency-domain measurements. The PPD is defined for possible photons having a total zigzag pathlength of l between the points of light input and detection. Such a distribution is independent of the absorption properties of the medium and can be uniquely determined for the medium under quantification. Therefore, the PPD can be calculated with an imaginary reference medium having the same optical properties as the medium under quantification except for the absence of absorption. One of the advantages of this method is that the optical responses, the total attenuation, the mean pathlength, etc are expressed by functions of the PPD and the absorption distribution.

  • tissue spectroscopy with a newly developed phase modulation system based on the microscopic beer Lambert Law
    BiOS 2001 The International Symposium on Biomedical Optics, 2001
    Co-Authors: Hidenao Iwai, Mitsuharu Miwa, Tsuneyuki Urakami, Mitsunori Nishizawa, Yutaka Tsuchiya
    Abstract:

    We have developed a phase and intensity-modulated spectroscopy system (PMS) using a newly developed algorithm based on the microscopic Beer-Lambert Law. Experiments with phantoms and the human body demonstrate the feasibility and reliability of the system as well as the new algorithm. Our goal is to develop compact, cost-effective, highly reliable, and user-friendly medical equipment for the quantitative monitoring of oxygen metabolism, and so on. The PMS system consists of three time-shared wavelength laser diodes with a 70MHz modulation frequency as sources and a 3mm diameter silicon PIN photodiode as a detector with an in-phase quadrature demodulator (IQD) for AC amplitude and phase detection. The PIN photodiode is operated at a low voltage and is durable against strong extraneous light. In addition, a specially designed low-noise amplifier is achieve a high S/N and reliable measurement. Our algorithm is independent of boundary conditions, exterior shape, scattering properties of the medium, and optode separation for measurement. We can therefore quantify the absolute concentration for oxy- deoxy-hemoglobin and hemoglobin saturation in living tissue of various shapes precisely.

  • applicability of time integrated spectroscopy based on the microscopic beer Lambert Law to finite turbid media with curved boundaries
    Optical Review, 2000
    Co-Authors: Hedong Zhang, Yutaka Tsuchiya
    Abstract:

    Finite curved boundaries are unavoidable in the practical field of non-invasive tissue spectroscopy. This being the case, a technique derived from the microscopic Beer-Lambert Law (MBL) can be applied regardless of what geometry is assumed. Here, experimental tests on a type of time integrated spectroscopy based on the MBL for a tissue-like phantom with curved boundaries are presented. The experiments employed a cylindrical liquid phantom 56 mm in diameter, which resembles a human forearm. Two independent measurements were made on the surface of the phantom at various absorption levels (the absorption coefficients of the phantom were from 2.45 × 10−3 to 4.12 × 10−2 mm−1 at 782 nm), one in the direction along the circumference and the other along the long axis of symmetry. In both cases, the absorber concentrations were successfully recovered within error values of a few percent using a single equation.

  • time integrated spectroscopy of turbid media based on the microscopic beer Lambert Law consideration of the wavelength dependence of scattering properties
    Optics Communications, 1998
    Co-Authors: Hedong Zhang, Mitsuharu Miwa, Yutaka Tsuchiya, Tsuneyuki Urakami, Yutaka Yamashita
    Abstract:

    Abstract A simple expression is proposed to describe the dependence of the mean pathlength on scattering properties. Based on this expression and the microscopic Beer–Lambert Law, a dual-wavelength time integrated spectroscopy (TIS) method in which the influence of wavelength dependence of scattering properties on both mean pathlength and intensity is taken into consideration, is developed to determine the absolute concentration of an absorber in highly scattering media. The validity and the accurate performance of the method are well demonstrated by measuring the transmission through a slab-like phantom and reflection from a semi-infinite phantom. In both cases, with a single equation, the absorber concentrations were determined within errors of a few percent.

  • quantitation of absorbers in turbid media using time integrated spectroscopy based on microscopic beer Lambert Law
    Japanese Journal of Applied Physics, 1998
    Co-Authors: Hedong Zhang, Yutaka Yamashita, Mitsuharu Miwa, Yutaka Tsuchiya
    Abstract:

    Based on the microscopic Beer-Lambert Law, two practical time-integrated spectroscopy (TIS) methods, called dual-wavelength spectroscopy method, and dual-wavelength and dual-site spectroscopy method, are described to determine the absolute concentration of an absorber in variously shaped turbid media. We demonstrate, for the first time, the validity of the TIS methods by means of experiments in which the absolute concentrations of an absorber in a tissue-like phantom were determined with errors less than several percent. The advantages and disadvantages of both methods are also discussed.

Jeanmichel Roger - One of the best experts on this subject based on the ideXlab platform.

  • relating near infrared light path length modifications to the water content of scattering media in near infrared spectroscopy toward a new bouguer beer Lambert Law
    Analytical Chemistry, 2021
    Co-Authors: Alexandre Mallet, Roumiana Tsenkova, Jelena Muncan, Cyrille Charnier, Eric Latrille, Ryad Bendoula, Jeanphilippe Steyer, Jeanmichel Roger
    Abstract:

    In near-infrared spectroscopy (NIRS), the linear relationship between absorbance and an absorbing compound concentration has been strictly defined by the Bouguer-Beer-Lambert Law only for the case of transmission measurements of nonscattering media. However, various quantitative calibrations have been successfully built both on reflectance measurements and for scattering media. Although the lack of linearity for scattering media has been observed experimentally, the sound multivariate statistics and signal processing involved in chemometrics have allowed us to overcome this problem in most cases. However, in the case of samples with varying water content, important modifications of scattering levels still make calibrations difficult to build due to nonlinearities. Moreover, even when calibration procedures are successfully developed, many preprocessing methods used do not guarantee correct spectroscopic assignments (in the sense of a pure chemical absorbance). In particular, this may prevent correct modeling and interpretation of the structure of water. In this study, dynamic near-infrared spectra acquired during a drying process allow the study of the physical effects of water content variations, with a focus on the first overtone OH absorbance region. A model sample consisting of aluminum pellets mixed with water allowed us to study this specifically, without any other absorbing interaction terms related to the dry mass-absorbing constituents. A new formulation of the Bouguer-Beer-Lambert Law is proposed, by expressing path length as a power function of water content. Through this new formulation, it is shown that a better and simpler prediction model of water content may be developed, with more precise and accurate identification of water absorbance bands.

Arjun G Yodh - One of the best experts on this subject based on the ideXlab platform.

  • modified beer Lambert Law for blood flow
    Proceedings of SPIE, 2015
    Co-Authors: Wesley B Baker, Ashwin B Parthasarathy, David R Busch, Rickson C Mesquita, Joel H Greenberg, Arjun G Yodh
    Abstract:

    The modified Beer-Lambert Law is among the most widely used approaches for analysis of near-infrared spectroscopy (NIRS) reflectance signals for measurements of tissue blood volume and oxygenation. Briefly, the modified Beer-Lambert paradigm is a scheme to derive changes in tissue optical properties based on continuous-wave (CW) diffuse optical intensity measurements. In its simplest form, the scheme relates differential changes in light transmission (in any geometry) to differential changes in tissue absorption. Here we extend this paradigm to the measurement of tissue blood flow by diffuse correlation spectroscopy (DCS). In the new approach, differential changes of the intensity temporal auto-correlation function at a single delay-time are related to differential changes in blood flow. The key theoretical results for measurement of blood flow changes in any tissue geometry are derived, and we demonstrate the new method to monitor cerebral blood flow in a pig under conditions wherein the semi-infinite geometry approximation is fairly good. Specifically, the drug dinitrophenol was injected in the pig to induce a gradual 200% increase in cerebral blood flow, as measured with MRI velocity flow mapping and by DCS. The modified Beer-Lambert Law for flow accurately recovered these flow changes using only a single delay-time in the intensity auto-correlation function curve. The scheme offers increased DCS measurement speed of blood flow. Further, the same techniques using the modified Beer-Lambert Law to filter out superficial tissue effects in NIRS measurements of deep tissues can be applied to the DCS modified Beer-Lambert Law for blood flow monitoring of deep tissues.

  • modified beer Lambert Law for blood flow
    Biomedical Optics Express, 2014
    Co-Authors: Wesley B Baker, Ashwin B Parthasarathy, David R Busch, Rickson C Mesquita, Joel H Greenberg, Arjun G Yodh
    Abstract:

    We develop and validate a Modified Beer-Lambert Law for blood flow based on diffuse correlation spectroscopy (DCS) measurements. The new formulation enables blood flow monitoring from temporal intensity autocorrelation function data taken at single or multiple delay-times. Consequentially, the speed of the optical blood flow measurement can be substantially increased. The scheme facilitates blood flow monitoring of highly scattering tissues in geometries wherein light propagation is diffusive or non-diffusive, and it is particularly well-suited for utilization with pressure measurement paradigms that employ differential flow signals to reduce contributions of superficial tissues.