# US 9,519,129 B2 · Method and system for measuring porosity of particles

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- Number: US 9,519,129 B2
- Document ID: US9519129B2
- Status: Granted
- Kind: B2
- Application number: 13/883,260
- Filed: 2011-11-04
- Published: 2013-10-24
- Granted: 2016-12-13
- Earliest claimed: 2010-11-05
- Assignees: New York University
- Applicants: Fook Chiong Cheong; Ke Xiao; David Pine; David G. Grier
- Inventors: Fook Chiong Cheong; Ke Xiao; David Pine; David G. Grier
- Web page: https://patentgrep.com/patent/US9519129B2

## CPC

- G01N 15/088: {Investigating volume, surface area, size or distribution of pores; Porosimetry}
- G01N 15/08: Investigating permeability, pore-volume, or surface area of porous materials
- G01N 15/1433: using image recognition
- G01N 21/453: {Holographic interferometry (for dimensional measurements G01B9/021 - G01B9/029)}
- G02B 21/367: {providing an output produced by processing a plurality of individual source images, e.g. image tiling, montage, composite images, depth sectioning, image comparison}
- G01N 21/4133: {Refractometers, e.g. differential}
- G01N 21/47: Scattering, i.e. diffuse reflection (G01N21/25, G01N21/41 take precedence {G01N21/55 takes precedence})
- G01N 2015/0846: {by use of radiation, e.g. transmitted or reflected light}
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)
- G02B: OPTICAL ELEMENTS, SYSTEMS OR APPARATUS

## Abstract

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.

## Claims

### Claim 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.

### Claim 2 (depends on 1)

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.

### Claim 3 (depends on 1)

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.

### Claim 4 (depends on 2)

The method as defined in claim 2 wherein the Lorenz-Mie formalism comprises,
I(r)=|E0(r)+E0(rp)fs(k(r−rp))|2,
where I(r) is intensity of the interference pattern recorded at position r, E0(r) is the electric field of the output laser at position r, rp is the position of the particle, k is the wavenumber of the light, and fs(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, ap, and on effective refractive index np of the particle.

### Claim 5 (depends on 1)

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.

### Claim 6 (depends on 4)

The method as defined in claim 4 wherein n2 is selected from the group consisting of nm, refractive index of the suspension fluid wetting the particle, and n2=1 wherein the porosity of the particle is a void.

### Claim 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)=|E0(r)+E0(rp)fs(k(r−rp))|2,
where I(r) is intensity of the interference pattern recorded at position r, E0(r) is the electric field of the output laser at position r, rp is the position of the particle, k is the wavenumber of the light, and fs(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, ap, and on effective refractive index np 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.

### Claim 8 (depends on 7)

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.

### Claim 9 (depends on 7)

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.

### Claim 10 (depends on 7)

The method as defined in claim 7 wherein n2 is selected from the group consisting of nm, refractive index of the suspension fluid wetting the particle, and n2=1 wherein the porosity of the particle is a void.