Method and system for measuring porosity of particles
A method for analyzing porosity of a particle and a medium disposed in the porosity of the particle. A video-holographic microscope is provided to analyze interference patterns produced by providing a laser source to output a collimated beam, scattering the collimated beam off a particle and interacting with an unscattered beam to generate the interference pattern for analyzation to determine the refractive index of the particle and a medium disposed in the porosity of the particle to measure porosity and the medium.
1. A method of analyzing a particle in suspension, comprising the steps of:
providing a video holographic microscope;
providing a laser source for producing a collimated output beam comprised of a plurality of different wavelengths of light;
scattering the collimated output beam off the particle by simultaneously using the plurality of different wavelengths of light to generate a plurality of scattered beams and a combination of the scattered beams and an unscattered portion of the output beam to generate a plurality of interference patterns;
recording intensity of the interference pattern;
analyzing the interference patterns to determine refractive index of the particle; and
determining a measure of at least one of porosity of the particle and a medium disposed in the porosity of the particle.
2. The method as defined in claim 1 wherein the step of analyzing the interference pattern comprises applying a Lorenz-Mie formalism to determine at least one of the refractive index of the particle and the medium disposed in the porosity of the particle.
3. The method as defined in claim 1 further including the step of analyzing the interference pattern during growth of the particle, thereby enabling characterization of development of the porosity in the particle and the medium disposed in the porosity of the particle.
4. The method as defined in claim 2 wherein the Lorenz-Mie formalism comprises,
I ( r )=| E 0 ( r )+ E 0 ( r p ) f s ( k ( r−r p ))| 2 ,
where I(r) is intensity of the interference pattern recorded at position r, E 0 (r) is the electric field of the output laser at position r, r p is the position of the particle, k is the wavenumber of the light, and f s (kr) is the Lorenz-Mie scattering function that describes scattering of light by the particle, wherein the Lorenz-Mie scattering function depends on radius of the particle, a p , and on effective refractive index n p of the particle.
5. The method as defined in claim 1 further including a computer system for executing computer software to carry out the steps of analyzing the interference pattern and comparing the refractive index of the bulk to the refractive index of the particle.
6. The method as defined in claim 4 wherein n 2 is selected from the group consisting of n m , refractive index of the suspension fluid wetting the particle, and n 2 =1 wherein the porosity of the particle is a void.
7. A method of analyzing a particle in suspension, comprising the steps of:
providing a video holographic microscope;
providing a laser source for producing a collimated output beam comprised of a plurality of different wavelengths of light;
scattering the collimated output beam off the particle by simultaneously using the plurality of different wavelengths of light to generate a plurality of scattered beams and a combination of the scattered beams and an unscattered portion of the output beam to generate a plurality of interference patterns;
recording intensity of the interference pattern;
analyzing the interference patterns through application of a Lorenz-Mie formalism to determine at least one of the refractive index of the particle and the medium disposed in the porosity of the particle wherein the Lorenz-Mie formalism comprises,
I ( r )=| E 0 ( r )+ E 0 ( r p ) f s ( k ( r−r p ))| 2 ,
where I(r) is intensity of the interference pattern recorded at position r, E 0 (r) is the electric field of the output laser at position r, r p is the position of the particle, k is the wavenumber of the light, and f s (kr) is the Lorenz-Mie scattering function that describes scattering of light by the particle, wherein the Lorenz-Mie scattering function depends on radius of the particle, a p , and on effective refractive index n p of the particle; and
determining a measure of at least one of porosity of the particle and a medium disposed in the porosity of the particle.
8. The method as defined in claim 7 further including the step of analyzing the interference pattern during growth of the particle, thereby enabling characterization of development of the porosity in the particle and the medium disposed in the porosity of the particle.
9. The method as defined in claim 7 further including a computer system for executing computer software to carry out the steps of analyzing the interference pattern and comparing the refractive index of the bulk to the refractive index of the particle.
10. The method as defined in claim 7 wherein n 2 is selected from the group consisting of n m , refractive index of the suspension fluid wetting the particle, and n 2 =1 wherein the porosity of the particle is a void.