Method for characterizing particles in suspension from frequency domain photon migration measurements
Abstract
Methods are provided for measuring isotropic scattering coefficients of suspensions using multiply scattered radiation that is modulated in amplitude at selected modulation frequencies. The radiation may be light. Quantities describing diffusion of the multiply scattered radiation are preferably measured at a plurality of distances between source and receiver and a plurality of frequencies. Linear regression techniques are provided for maximizing accuracy of the scattering data at a selected wavelength of a radiation. Methods are provided for inversing an integral equation so as to determine a calculated value of scattering coefficient. Parameters are varied to minimize the difference between the calculated and measured scattering coefficients and thereby to determine volume fraction, particle size distribution and interparticle force between the particles in a suspension. By incorporating a first principles model to account for interparticle force, the measurements can be used to determine a parameter governing interparticle forces in a suspension. The suspension may be in a liquid or a gas.
Claims
exact text as granted — not AI-modified1 . A method for measuring an isotropic scattering coefficient for radiation having a selected wavelength and being multiply scattered in a suspension of particles, comprising:
(a) placing the suspension between a source and a detector of the radiation, the source and the detector being disposed at a first selected distance apart, the radiation having an intensity, the intensity being modulated at a first selected frequency of modulation; (b) measuring at least two characteristics of the radiation at the source and the detector, the two characteristics being selected from among AC attenuation of the radiation, DC attenuation of the radiation, and phase shift of the radiation; (c) changing the selected distance apart of the source and the detector to a different selected distance apart and repeating step (b); and (d) from the selected two characteristics and a mathematical solution of the diffusion equation for propagation of light through a multiple scattering medium expressed as a linear function of the selected distance, calculating the scattering coefficient.
2 . The method of claim 1 further comprising, after step (d), repeating step (c) so as to change the selected distance apart to a plurality of selected distances apart and repeating step (d) for each selected distance apart.
3 . The method of claim 1 further comprising, after step (a), changing the selected frequency of modulation at least once and repeating steps (b) through (d).
4 . The method of claim 1 further comprising, after step (c), calculating a criteria parameter, Q, from the results of step (b), where
ln
2
(
rAC
rel
/
r
0
)
-
ln
2
(
rPS
rel
/
r
0
)
ln
2
(
rDC
rel
/
r
0
)
=
Q
,
where AC rel is the ratio of AC measured at r to that measured at r o , PS rel , is the difference in measured phase at r and r o , and DC rel is the ratio of DC measured at r to that measured at r o .
5 . The method of claim 1 wherein in step (c) the selected distance is changed by moving the source or the detector so as to change the selected distance apart.
6 . The method of claim 1 wherein in step (c) the selected distance is changed by substituting an alternate source or detector.
7 . The method of claim 2 wherein the plurality of selected distances is at least three selected distances.
8 . The method of claim 3 wherein the step of changing the selected frequency of modulation is repeated at least twice.
9 . The method of claim 7 further comprising the step of performing a linear regression of a logarithm of calculated products of a ratio of the selected distance to an initial distance and a relative selected characteristic, at a plurality of selected distances.
10 . The method of claim 3 further comprising repeating steps (b), (c) and (d) for a plurality of selected distances and frequencies and simultaneously regressing combinations of the characteristics of the radiation selected in step (b) of claim 1 .
11 . The method of claim 1 wherein the suspension of particles is an aerosol.
12 . The method of claim 1 wherein the radiation is light.
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29 . Apparatus for measuring volume fraction, particle size distribution or interaction of particles in a suspension, comprising:
a source and a detector of a radiation adapted for location in a sample of the suspension at a selected distance apart; electronic apparatus for supplying a modulated radiation to the source at a selected modulated frequency; and a system for receiving signals from the modulated radiation, executing a computer program and displaying results of the execution.
30 . The system of claim 29 further comprising a plurality of sources disposed at a plurality of distances from the detector.
31 . The system of claim 29 further comprising a plurality of detectors disposed at a plurality of distances from the source.
32 . The system of claim 29 further comprising a mechanical device for changing the selected distance apart of the source and the detector.
33 . The system of claim 29 wherein the suspension is an aerosol.
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