Method and apparatus for measuring locally and superficially the scattering and absorption properties of turbid media
First Claim
1. A method for local and superficial characterization of a turbid medium using the following parameters:
- 1) the refractive index n of the turbid medium 2) the absorption coefficient μ
a of the turbid medium 3) the reduced scattering coefficient μ
s′
of the turbid medium 4) the phase function parameter γ
=(1−
g2)/(1−
g1) of the turbid media, where g1 and g2 are the first two moments of the Legendre polynomial development of the phase function p, the method comprising the steps of;
measuring the spatially-resolved reflectance R(ρ
) of the turbid medium (ρ
being the source-detector distance) using an illumination beam as a source and an optical detector, mathematically processing R(ρ
) to compute at least one of the said parameters;
n, μ
a, μ
s′
, γ and
/or the variations, in time and/or space, of at least one of the said parameters;
Δ
n, Δ
μ
a, Δ
μ
s′
, Δ
γ
, whereby an “
inverse problem”
, which comprises extracting the optical coefficients from the spatially resolved reflectance data is solved, and whereby a “
direct problem”
comprises computing the spatially resolved reflectance from the values of the optical coefficients n, μ
a, μ
s′
, γ
involved in a model of propagation of the light in turbid medium and whereby the said “
model”
incorporates a Legendre polynomial development to the second order of the said “
phase function”
, and whereby the said “
phase parameter”
γ
is introduced in the computation as an independent parameter.
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Abstract
We present a method and apparatus for local and superficial measurement of the optical properties of turbid media. The depth probed is on the order of 1 transport mean free path of the photon. The absorption coefficient, reduced scattering coefficient and the phase function parameter γ=(1−g2)/(1−g1) are optical parameters computed from a single measurement of the spatially resolved reflectance close to the source. Images of superficial structures of the medium can be obtained by performing multi-site measurements. An important application of this technique is the characterization of biological tissues, for example for medical diagnostic purposes. Measurements on biological tissues can be achieved using a probe of diameter less than 2 mm, and the average volume probed is on the order of 1 mm3. Separate images of absorption and tissue structure can be achieved with a resolution of approximately one transport mean free path of the considered tissue.
39 Citations
21 Claims
-
1. A method for local and superficial characterization of a turbid medium using the following parameters:
-
1) the refractive index n of the turbid medium 2) the absorption coefficient μ
a of the turbid medium3) the reduced scattering coefficient μ
s′
of the turbid medium4) the phase function parameter γ
=(1−
g2)/(1−
g1) of the turbid media, where g1 and g2 are the first two moments of the Legendre polynomial development of the phase function p, the method comprising the steps of;
measuring the spatially-resolved reflectance R(ρ
) of the turbid medium (ρ
being the source-detector distance) using an illumination beam as a source and an optical detector,mathematically processing R(ρ
) to compute at least one of the said parameters;
n, μ
a, μ
s′
, γ and
/or the variations, in time and/or space, of at least one of the said parameters;
Δ
n, Δ
μ
a, Δ
μ
s′
, Δ
γ
, whereby an “
inverse problem”
, which comprises extracting the optical coefficients from the spatially resolved reflectance data is solved, and whereby a “
direct problem”
comprises computing the spatially resolved reflectance from the values of the optical coefficients n, μ
a, μ
s′
, γ
involved in a model of propagation of the light in turbid medium and whereby the said “
model”
incorporates a Legendre polynomial development to the second order of the said “
phase function”
, and whereby the said “
phase parameter”
γ
is introduced in the computation as an independent parameter. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21)
-
-
18. A test, where the control of the homogeneity of the sample over the probed area is performed with the apparatus of 16, which can be carried out according to the following procedure:
- in the apparatus, disposing two illuminating fibers symmetrically in regard to the collecting fibers;
comparing the reflectance curves for each illuminating fiber to detect the heterogeneity of the investigated region or obstructions beneath the fibers; and
, if the two curves are sufficiently close, validating the measurement and calculating the average of the two curves.
- in the apparatus, disposing two illuminating fibers symmetrically in regard to the collecting fibers;
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