WO2005008195A2 - Quantification de proprietes optiques dans des milieux de dispersion fondee sur l'analyse fractale de mesures de la repartition de photons - Google Patents

Quantification de proprietes optiques dans des milieux de dispersion fondee sur l'analyse fractale de mesures de la repartition de photons Download PDF

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Publication number
WO2005008195A2
WO2005008195A2 PCT/IB2004/002303 IB2004002303W WO2005008195A2 WO 2005008195 A2 WO2005008195 A2 WO 2005008195A2 IB 2004002303 W IB2004002303 W IB 2004002303W WO 2005008195 A2 WO2005008195 A2 WO 2005008195A2
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medium
distribution
light
photon
optical property
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PCT/IB2004/002303
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English (en)
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WO2005008195A3 (fr
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David H. Burns
Claudia E. W. Gributs
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Mcgill University
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Publication of WO2005008195A3 publication Critical patent/WO2005008195A3/fr

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Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N21/49—Scattering, i.e. diffuse reflection within a body or fluid
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N21/4795—Scattering, i.e. diffuse reflection spatially resolved investigating of object in scattering medium
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N2021/4704—Angular selective
    • G01N2021/4707—Forward scatter; Low angle scatter
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N2021/4704—Angular selective
    • G01N2021/4709—Backscatter
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N2021/4792—Polarisation of scatter light
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N21/4795—Scattering, i.e. diffuse reflection spatially resolved investigating of object in scattering medium
    • G01N2021/4797—Scattering, i.e. diffuse reflection spatially resolved investigating of object in scattering medium time resolved, e.g. analysis of ballistic photons
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
    • G01N21/47—Scattering, i.e. diffuse reflection
    • G01N21/4785—Standardising light scatter apparatus; Standards therefor

Definitions

  • the invention relates to a method of calculating one or more optical properties of a turbid medium from time resolved light measurements, or polarization resolved light measurements, or spatially resolved light measurements.
  • the scattering coefficient, ⁇ s is a measure of the number of scattering events per millimeter.
  • the scattering anisotropy, g is the average cosine of the angle that light is scattered at each scattering event.
  • Both the media and the scattering centers in a sample will have an index of refraction, n m and n s .
  • a sample can contain optically active, chiral molecules, which can rotate the polarization and can be described by a degree of polarization, ⁇ .
  • Both ⁇ a and ⁇ s can be obtained from time-resolved measurement of light traversing a sample, since the time spent by an individual photons in a medium before exiting it or be absorbed by it is a function of the number of scattering events as well as the absorption properties of said medium. They can also be determined by a space-resolved or angle-resolved measurement of light exiting a medium since the distance traveled by a photon in a medium is also a function of the number of scattering events and of the absorption properties of said medium.
  • a polarization resolved measurement of light traversing a sample can as well be used to determine the scattering and the absorption coefficients of a medium.
  • the other optical properties may also be determined using the above method as a model of light propagation.
  • One approach is to use the diffusion approximation to the radiative transport equation which is based on the two optical coefficients to model the time-resolved measurements.
  • One of the limiting factors of this model is the description of the short photon paths through the sample, i.e. those photons that experience little scattering. Such photons have not undergone large multiple angle scattering and their behavior is inadequately described by the diffusion equation. This approach can also be mathematically quite involved.
  • a data analysis method involving one element of fractal analysis of a photon distribution.
  • the invention also provides an optical property measurement apparatus, operating as an imaging device or spectrometer, that measures the photon distribution and analyses it using an element of fractal analysis to obtain optical parameter data of a turbid medium.
  • a method of determining an optical property of a turbid medium to be tested comprising obtaining a photon distribution in respect to a parameter from the measurements of exiting light from the medium, selecting a series of partition element sizes wherein each partition element corresponds to an area of the distribution, counting a number of points of the distribution in the partition element for each data point in the distribution, for each of the partition element sizes, and establishing a relationship between the number for each partition element size and the partition element size.
  • the preceding steps are to be repeated for a plurality of calibration media having a known optical property.
  • an apparatus for determining an optical property of a turbid medium to be tested A light measurement device is used to obtain photon distribution data regarding a parameter from light exiting from the medium.
  • a fractal element analyzer receives the distribution data and produces a count of a number of points of the distribution in a partition element for each data point in the distribution, for each of the partition element sizes.
  • An optical property estimator receives the count and compares characteristics of a relationship of the optical property of the medium to be tested to characteristics of a relationship of the optical property obtained for a plurality of calibration media to output a value for the optical property of the medium.
  • One example of the photon distribution data is a time-of-flight intensity distribution.
  • FIG. 1 is a schematic drawing illustrating the instrumentation set-up of a preferred embodiment of the present invention.
  • BS beam splitter
  • PD photodiode
  • CFD constant fraction discriminator
  • DL delay line
  • ND neutral density filter
  • S sample
  • MCP-PMT microchannel plate photomultiplier tube
  • TAC time-to- amplitude converter
  • PC personal computer
  • FIG 2A is a graph illustrating several photon time of flight distributions (TOF) that were obtained for samples having different absorption coefficients but same scattering coefficient
  • FIG. 1 is a schematic drawing illustrating the instrumentation set-up of a preferred embodiment of the present invention.
  • BS beam splitter
  • PD photodiode
  • CFD constant fraction discriminator
  • DL delay line
  • ND neutral density filter
  • S sample
  • MCP-PMT microchannel plate photomultiplier tube
  • TAC time-to- amplitude converter
  • PC personal computer
  • FIG 2A is a graph illustrating several photon time
  • FIG. 2B is a graph illustrating several photon time of flight distributions (TOF) that were obtained for samples having different scattering coefficients but same absorption coefficient;
  • FIG. 3 is a flowchart illustrating a method to determine at least one of /.a and // s .
  • Fig. 4 is a flowchart illustrating a method to calculate some fractal characteristics of photon TOF profiles ;
  • Fig. 5 is a schematic drawing illustrating a method to compute a correlation sum;
  • Fig. 6 is a graph illustrating the logarithm of a correlation sum with respect to the logarithm of a partition element size;
  • Fig. 7 is a schematic drawing illustrating a matrix of calibration samples;
  • Fig. 8 is a flowchart illustrating a method to determine relations between some regressions parameters and ⁇ s and ⁇ a ;
  • Fig. 9 is a schematic drawing illustrating the instrumentation set-up of a second embodiment fo the present invention.
  • a method for estimating optical parameters such as scattering and absorption coefficients ( ⁇ a and ⁇ s ) in turbid media from photon time of flight distributions using fractal dimension analysis of the signal.
  • This new method greatly simplifies the analysis of the data
  • FIGS. 1 through 8 like numerals being used for corresponding parts of the various drawings. Measurements of the photon time of flight distributions are made using a single photon counting instrument.
  • an ultrafast laser 1 produces repeated light pulses 2 that are split via a beam splitter 3 into two portions: approximately 4% of the light pulse intensity is sent to a PIN photodiode 5 and the remaining light is injected in a turbid medium 7 after going through a neutral density filter 4.
  • Light injected in the turbid medium -referred therein as sample - is scattered and partly absorbed, and a cooled micro-channel plate photomultiplier tube (MCP-PMT) 6 detects photons individually coming out from the sample.
  • MCP-PMT micro-channel plate photomultiplier tube
  • the said PMT detects photons that are "reflected" by the sample and this detection geometry is therefore called a reflectance measurement.
  • the time spent in the sample by each detected photon is determined by measuring the time delay between the PIN photodiode and the PMT signals.
  • the signals detected are sent respectively to two constant fraction discriminators 8 that send two logic signals (a start signal and a stop signal) to a time-to amplitude converter 9.
  • the time difference between the start and stop pulses which is related to the time spent by a photon in the sample, is converted to a corresponding dc voltage sent to the measurement controller 11.
  • a photon time of flight distribution can be constructed this way.
  • FIG.2A is a graph illustrating several photon time of flight distributions
  • FIG. 2B presents the total number of photons measured 13 at a specific time delay 14.
  • the samples had the same absorption coefficient but different scattering coefficients.
  • These measured photon time of flight distributions contain information on both the absorption and scattering properties of the sample, as it can be seen from these graphs that a change of ⁇ a or ⁇ s modified the shape of the TOF 12.
  • the time of flight distribution 12 is then analyzed with in view to determine its fractal characteristics 16.
  • FIG. 3 is a flowchart illustrating how this method is implemented.
  • Fig. 4 gives more details on the method 27 that is used in the preferred embodiment to calculate some TOF fractal characteristics.
  • the first step 19 is to calculate a greatest distance, ⁇ M AX > between any two data points of the TOF.
  • the second step 20 is to select a' series of different values of partition element size smaller than r MA X- A partition element size is then selected from these values in third step 21.
  • a correlation sum of the TOF for this selected partition element size is computed 22.
  • the correlation sum C(r) is defined as: c( r ) (1)
  • ⁇ is the number of points in the TOF distribution
  • H is the Heaviside function
  • ⁇ and ⁇ are the coordinates of two points in the data set
  • r is the partition element size. Practically, the number of points that lie within a distance r of each data point are counted, summed over the data set and normalized.
  • step 5 the logarithm of C(r), log (C(r)), is calculated as well as the logarithm of the partition element size, log(r), 23.
  • the process from step 3 to step 5 is then repeated until the entire series of selected partition element sizes have been scanned 24.
  • Fig. 5 illustrates schematically the above process.
  • step 6 a linear relation is calculated between the logarithm of above computed correlation sums and the logarithm of partition element sizes.
  • the slope, m, and the parameter, b, of the linear relation are calculated as well as a parameter X b which is equal to -b/m.
  • the slope, m is equal to the fractal dimension of the TOF data set.
  • the logarithm of the calculated correlation values can be plotted in respect to the logarithm of the partition element size as shown in Fig. 6. This plot may help to discard points of the curve 30 that are associated to experimental noise, since noisy data points have a fractal dimension different from the fractal dimension of the remaining points.
  • each sample 36 representing a unique combination of ⁇ s and ⁇ a coefficients among 7 different levels of ⁇ s 37 and 8 different levels of ⁇ a 38.
  • a TOF is acquired by applying the same technique previously described.
  • the data analysis previously described is carried out and the values of m 31, b33, and x 32 for each calibration sample are this way obtained.
  • regression parameters 47 will be therein referred to as regression parameters 47.
  • Several data analysis steps 48 are then performed in order to find which combination of regression parameters gives the most parsimonious estimation of the scattering coefficient ⁇ s and the absorption coefficient ⁇ a 46.
  • Fig. 8 illustrates how this method 48 can be implemented.
  • a combination of the regression parameters 47 is chosen 41.
  • a series of samples having the same known ⁇ s coefficient are selected as a first validation set 39, the remaining samples constituting a . calibration set.
  • the best linear relation between the chosen regression parameters 47 and the known ⁇ s values is calculated 43 (step 3).
  • step 4 estimated values of the scattering coefficient, / S EST > are obtained 44 by inserting the m.b.and xb values of the samples of the validation set into equation (2). Step 2 to step 4 are repeated for all possible validation sets so that at the end of the process we can compare the estimated scattering values / J S ESTJ obtained with (2) to their known values. This is done in step 5 45 where the coefficient of variation, C.V. 47, of the model represented by equation (2) is computed. C.V is given by equation (3): C.V.
  • SEE is the standard error of estimation given by: ⁇ is -isEst 'j ' (4) N ⁇ #param with ⁇ is : known scattering coefficient of the i validation set Pis E stj : estimated scattering coefficient obtained with the j sample of the i validation set N: number of ⁇ s estimates #param: number of parameters (m, b or xb) used in the model (2)
  • steps 1 to 5 are repeated 49.
  • the best relation is determined in step 6 46.
  • the best relation is the one that uses the smallest number of regression parameters 47 and that has a corresponding C.V. that is not significantly larger than the smallest one found overall.
  • this best relation can be used as a pre-established relation 17 to determine ⁇ s of an unknown sample.
  • the pre-established relation to determine ⁇ a of an unknown sample can be found by following the calibration method 48 just described with the following changes: at step 3 the regression parameters of each sample k of the validation set L are divided by the value of its best estimated scattering coefficient previously calculated.
  • the validation sets are naturally also different and Fig.
  • FIG. 7 illustrates a possible validation set 40 use to obtain a relation to determine ⁇ a .
  • the following examples are given to illustrate the accuracy level this preferred embodiment can provide in the determination of the of ⁇ a and ⁇ s coefficients.
  • Two independent sets of samples with a combination of 7 scattering and 8 absorption levels were analyzed at separate times and in random order.
  • the scattering coefficients values of these samples were ranging from 100 mm "1 to 250 mm "1 and the absorption coefficients values were ranging form 0 to 0.035 mm "1 .
  • the C.V. value increases slightly to about 4% when only one regression parameter is used.
  • the absorption coefficients were determine with a C.V. value less than 10%. It is understood that the method that has been described in details can equally be used in the case of a transmittance measurement. It is also understood that the data analysis just described can be applied as well to photon distributions obtained from polarization-resolved measurement where linear or circular polarization light is injected in a medium and scattered light at a series of states of polarization is detected and measured. Since the properties of the medium have the ability to change the state of polarization of the incoming light, the time dimension in Fig.2A and 2B is replaced by a state of polarization dimension.
  • Fig.9 illustrates schematically an experimental system that could be used to obtain a polarized-resolved photon distribution measurement.
  • a He-Ne laser is launched onto the turbid medium after having been intensity modulated by a chopper and after polarization modulated by a photo-elastic modulator (PEM).
  • PEM photo-elastic modulator
  • the reflected light is collected via a beam splitter and a state of polarization ⁇ (the electric field vector makes an angle ⁇ with the horizontal) of the reflected light is selected via the rotating polarizer .
  • This light intensity, ⁇ ( ⁇ ) is detected by a photomultiplier and an electrical signal proportional to the light intensity is sent to a lock-in amplifier.
  • the lock-in amplifier also receives a signal from the chopper.
  • a phase resolved measurement of the backscattered light is measured using an interferometric technique comparing the phase of the backscattered light an unscattered beam. Since the properties of the medium change the relative distance of the incoming light, the time dimension in Fig.2A and 2B is replaced by a phase or distance state dimension. It is understood that the method that has been described in detail can equally be used on photon distributions obtained from an angle resolved optical system measuring the backscattered light at different angles in respect to the light illumination orientation. Since the properties of the medium change the relative angle distribution of the incoming light, the time dimension in Fig.2A and 2B is replaced by an angle dimension.

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Abstract

On détermine une propriété optique d'un milieu trouble à tester. Un dispositif de mesure de la lumière est utilisé pour obtenir des données de répartition de photons, liées à un paramètre, à partir de la lumière émise par le milieu (un exemple est la répartition de l'intensité de temps de vol). Un analyseur d'élément fractal reçoit les données de répartition et génère un décompte d'un certain nombre de points de la répartition dans un élément de séparation pour chaque point de données dans ladite répartition et pour chacune des dimensions de l'élément de séparation. Un estimateur de propriété optique reçoit le décompte et compare des caractéristiques d'un rapport de la propriété optique du milieu à tester et des caractéristiques d'un rapport de la propriété optique obtenue pour une pluralité de milieux d'étalonnage (présentant des propriétés optiques connues), afin de générer une valeur indicative de la propriété optique du milieu.
PCT/IB2004/002303 2003-07-16 2004-07-15 Quantification de proprietes optiques dans des milieux de dispersion fondee sur l'analyse fractale de mesures de la repartition de photons WO2005008195A2 (fr)

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Cited By (4)

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US7224769B2 (en) 2004-02-20 2007-05-29 Aribex, Inc. Digital x-ray camera
US7496178B2 (en) 2004-02-20 2009-02-24 Aribex, Inc. Portable x-ray device
US8892192B2 (en) 2012-11-07 2014-11-18 Modulated Imaging, Inc. Efficient modulated imaging
US9220412B2 (en) 2009-11-19 2015-12-29 Modulated Imaging Inc. Method and apparatus for analysis of turbid media via single-element detection using structured illumination

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US6422998B1 (en) * 1999-09-20 2002-07-23 Ut-Battelle, Llc Fractal analysis of time varying data
US20040038264A1 (en) * 2002-05-14 2004-02-26 Souza Glauco R. Fractal dimension analysis of nanoparticle aggregates using angle dependent light scattering for the detection and characterization of nucleic acids and proteins
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US5029475A (en) * 1989-05-22 1991-07-09 Agency Of Industrial Science And Technology Measuring spatial distribution of spacings between point scatterers
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7224769B2 (en) 2004-02-20 2007-05-29 Aribex, Inc. Digital x-ray camera
US7496178B2 (en) 2004-02-20 2009-02-24 Aribex, Inc. Portable x-ray device
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US9277866B2 (en) 2009-11-19 2016-03-08 Modulated Imaging, Inc. Method and apparatus for analysis of turbid media via single-element detection using structured illumination
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US9883803B2 (en) 2012-11-07 2018-02-06 Modulated Imaging, Inc. Efficient modulated imaging
US10342432B2 (en) 2012-11-07 2019-07-09 Modulated Imaging, Inc. Efficient modulated imaging

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