scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Determining the optical properties of turbid media by using the adding–doubling method

01 Feb 1993-Applied Optics (Optical Society of America)-Vol. 32, Iss: 4, pp 559-568
TL;DR: A method is described for finding the optical properties of a slab of turbid material by using total reflection, unscattered transmission, and total transmission measurements and the intrinsic error in the method is < 3% when four quadrature points are used.
Abstract: A method is described for finding the optical properties (scattering, absorption, and scattering anisotropy) of a slab of turbid material by using total reflection, unscattered transmission, and total transmission measurements. This method is applicable to homogeneous turbid slabs with any optical thickness, albedo, or phase function. The slab may have a different index of refraction from its surroundings and may or may not be bounded by glass. The optical properties are obtained by iterating an adding–doubling solution of the radiative transport equation until the calculated values of the reflection and transmission match the measured ones. Exhaustive numerical tests show that the intrinsic error in the method is <3% when four quadrature points are used.

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI
TL;DR: In this article, the optical properties of human skin, subcutaneous adipose tissue and human mucosa were measured in the wavelength range 400-2000 nm using a commercially available spectrophotometer with an integrating sphere.
Abstract: The optical properties of human skin, subcutaneous adipose tissue and human mucosa were measured in the wavelength range 400–2000 nm. The measurements were carried out using a commercially available spectrophotometer with an integrating sphere. The inverse adding–doubling method was used to determine the absorption and reduced scattering coefficients from the measurements.

1,446 citations

Journal ArticleDOI
TL;DR: This review describes optical interactions pursued for biomedical applications (fluorescence, fluorescence lifetime, phosphorescence, and Raman from cells, cultures, and tissues) and provides a descriptive framework for light interaction based upon tissue absorption and scattering properties.
Abstract: The interaction of light within tissue has been used to recognize disease since the mid-1800s. The recent developments of small light sources, detectors, and fiber optic probes provide opportunities to quantitatively measure these interactions, which yield information for diagnosis at the biochemical, structural, or (patho)physiological level within intact tissues. However, because of the strong scattering properties of tissues, the reemitted optical signal is often influenced by changes in biochemistry (as detected by these spectroscopic approaches) and by physiological and pathophysiological changes in tissue scattering. One challenge of biomedical optics is to uncouple the signals influenced by biochemistry, which themselves provide specificity for identifying diseased states, from those influenced by tissue scattering, which are typically unspecific to a pathology. In this review, we describe optical interactions pursued for biomedical applications (fluorescence, fluorescence lifetime, phosphorescence, and Raman from cells, cultures, and tissues) and then provide a descriptive framework for light interaction based upon tissue absorption and scattering properties. Finally, we review important endogenous and exogenous biological chromophores and describe current work to employ these signals for detection and diagnosis of disease.

1,230 citations

Journal ArticleDOI
TL;DR: The absorption and transport scattering coefficients of c Caucasian and negroid dermis, subdermal fat and muscle have been measured for all wavelengths between 620 and 1000 nm and the optical properties of caucasian dermis were found to be approximately twice those of the underlying fat layer.
Abstract: The absorption and transport scattering coefficients of caucasian and negroid dermis, subdermal fat and muscle have been measured for all wavelengths between 620 and 1000 nm. Samples of tissue 2 mm thick were measured ex vivo to determine their reflectance and transmittance. A Monte Carlo model of the measurement system and light transport in tissue was then used to recover the optical coefficients. The sample reflectance and transmittance were measured using a single integrating sphere 'comparison' method. This has the advantage over conventional double-sphere techniques in that no corrections are required for sphere properties, and so measurements sufficiently accurate to recover the absorption coefficient reliably could be made. The optical properties of caucasian dermis were found to be approximately twice those of the underlying fat layer. At 633 nm, the mean optical properties over 12 samples were 0.033 mm(-1) and 0.013 mm(-1) for absorption coefficient and 2.73 mm(-1) and 1.26 mm(-1) for transport scattering coefficient for caucasian dermis and the underlying fat layer respectively. The transport scattering coefficient for all biological samples showed a monotonic decrease with increasing wavelength. The method was calibrated using solid tissue phantoms and by comparison with a temporally resolved technique.

701 citations

Journal ArticleDOI
TL;DR: An overview of published absorption and scattering properties of skin and subcutaneous tissues measured in wide wavelength range is presented and basic principles of measurements of the tissue optical properties and techniques used for processing of the measured data are outlined.
Abstract: The development of optical methods in modern medicine in the areas of diagnostics, therapy, and surgery has stimulated the investigation of optical properties of various biological tissues, since the efficacy of laser treatment depends on the photon propagation and fluence rate distribution within irradiated tissues. In this work, an overview of published absorption and scattering properties of skin and subcutaneous tissues measured in wide wavelength range is presented. Basic principles of measurements of the tissue optical properties and techniques used for processing of the measured data are outlined.

585 citations


Cites methods from "Determining the optical properties ..."

  • ...An error of 3% or less is considered acceptable.(30) Also, the method may be used to directly correct experimental ̄ndings obtained with the aid of integrating spheres....

    [...]

  • ...The term \adding" indicates that the doubling procedure may be extended to heterogeneous layers for modeling multilayer tissues or taking into account internal re°ections related to abrupt change in refractive index.(30) The adding-doubling technique is a numerical method for solving the 1D transport equation in slab geometry....

    [...]

Journal ArticleDOI
TL;DR: From the measured optical properties, it was found that a 2% Intralipid solution provides a suitable skin tissue phantom and in vitro results show that values for mua) follow 70% of the absorption coefficient of water.
Abstract: In this paper we present the absorption coefficient mu(a) and the isotropic scattering coefficient mu(s)(') for 22 human skin samples measured using a double integrating sphere apparatus in the wavelength range of 1000-2200 nm These in vitro results show that values for mua) follow 70% of the absorption coefficient of water and values for mu(s)(') range from 3 to 16 cm(-1) From the measured optical properties, it was found that a 2% Intralipid solution provides a suitable skin tissue phantom

568 citations

References
More filters
Journal ArticleDOI
TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Abstract: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.

27,271 citations

Book
01 Jan 1950

9,085 citations

Book
16 Feb 2013
TL;DR: This well written book is enlarged by the following topics: B-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for theLR and QR algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations and preconditioning techniques.
Abstract: This well written book is enlarged by the following topics: $B$-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for the $LR$ and $QR$ algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations, preconditioning techniques and convergence rate of the conjugate gradient algorithm and multigrid methods for boundary value problems. Cf. also the reviews of the German original editions.

6,270 citations

Journal ArticleDOI
TL;DR: The known optical properties (absorption, scattering, total attenuation, effective attenuation and/or anisotropy coefficients) of various biological tissues at a variety of wavelengths are reviewed in this article.
Abstract: The known optical properties (absorption, scattering, total attenuation, effective attenuation, and/or anisotropy coefficients) of various biological tissues at a variety of wavelengths are reviewed. The theoretical foundations for most experimental approaches are outlined. Relations between Kubelka-Munk parameters and transport coefficients are listed. The optical properties of aorta, liver, and muscle at 633 nm are discussed in detail. An extensive bibliography is provided. >

2,858 citations


"Determining the optical properties ..." refers background or methods in this paper

  • ...(1) and (2) can be used to generate a single set of starting values (a, , g)....

    [...]

  • ...Finally three components of the iteration process are given: (1) the function that defines the distance the calculated values are from the measure values, (2) the initial set of optical properties guessed, and (3) the algorithm used to minimize this function....

    [...]

  • ...(2) Calculate the reflection and transmission by using the addingdoubling method....

    [...]

  • ...In practice the two most common sources of experimental errors are (1) loss of light from the edges of the sample (which thereby invalidates the one-dimensional assumptions and underestimating both RT and TT) and (2) collecting scattered light in the unscattered transmission measurement (which thereby overestimates Tc)....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the Gurevic and Judd formulas were derived from the Kubelka-Munk differential equations, and they are exact under the same conditions as in this paper, that is, when the material is perfectly dull and when the light, is perfectly diffused or if it is parallel and hits the specimen under an angle of 60° from normal.
Abstract: The system of differential equations of Kubelka-Munk, -di=-(S+K)idx+Sjdx, dj=-(S+K)jdx+Sidx(i, j⋯ intensities of the light traveling inside a plane-parallel light-scattering specimen towards its unilluminated and its illuminated surface; x⋯ distance from the unilluminated surface S, K⋯ constants), has been derived from a simplified model of traveling of light in the material. Now, without simplifying assumptions the following exact system is derived: -di=-12(S+K)uidx+12Svjdx,dj=-12(S+K)vjdx+12Suidx,u≡∫0π/2(∂i/i∂φ)(dφ/cosφ), v≡∫0π/2(∂j/j∂φ)(dφ/cosφ), φ≡angle from normal of the light). Both systems become identical when u=v=2, that is, for instance, when the material is perfectly dull and when the light, is perfectly diffused or if it is parallel and hits the specimen under an angle of 60° from normal. Consequently, the different formulas Kubelka-Munk got by integration of their differential equations are exact when these conditions are fulfilled. The Gurevic and Judd formulas, although derived in another way by their authors, may be got from the Kubelka-Munk differential equations too. Consequently, they are exact under the same conditions. The integrated equations may be adapted for practical use by introducing hyperbolic functions and the secondary constants a=12(1/R∞+R∞) and b=12(1/R∞-R∞), (R∞≡reflectivity). Reflectance R, for instance, is then represented by the formula R=1-Rg(a-b ctghbSX)a+b ctghbSX-Rg(Rg≡reflectance of the backing, X=thickness of the specimen) and transmittance T by the formula T=ba sinhbSX+b coshbSX.In many practical cases the exact formulas may be replaced by appropriated approximations.

2,322 citations