NEW TECHNIQUE FOR PERFORMING DIELECTRIC PROPERTY MEASUREMENTS AT MICROWAVE FREQUENCIES

• US 20110057653A1
• Filed: 09/02/2010
• Published: 03/10/2011
• Est. Priority Date: 09/08/2009
• Status: Active Grant

• Current Assignee: California Institute of Technology
• Original Assignee: California Institute of Technology
• Inventors: Jackson, Henry W., Barmatz, Martin B.
• Granted Patent: US 8,653,819 B2
• Time in Patent Office: Days
• US Class Current: 324/316
• CPC Class Codes: G01R 33/1223 Measuring permeability, i.e. permeameters G01R33/14 takes precedence

Abstract

A method, system, apparatus, and computer readable medium has been provided with the ability to obtain a complex permittivity ∈ or a complex permeability μ of a sample in a cavity. One or more complex-valued resonance frequencies (f_m) of the cavity, wherein each f_m is a measurement, are obtained. Maxwell'"'"'s equations are solved exactly for ∈, and/or μ, using the f_m as known quantities, thereby obtaining the ∈ and/or μ of the sample.

Claims

1. A method of obtaining at least one property selected from a complex-valued dielectric permittivity (∈

) and a complex valued magnetic permeability (μ

) of at least one sample, comprising;

(a) obtaining a measured complex-valued resonance frequency f_cavity of a cavity when empty;

(b) obtaining a measured complex-valued resonance frequency f_sample the cavity containing the sample, wherein f_cavity and f_sample are measurements by exciting the cavity with one or more cavity resonant modes; and

(c) solving Maxwell'"'"'s equations exactly for the property, using the f_cavity and the f_sample.

2. The method of claim 1, wherein the cavity and the sample are annular or cylindrical regions.

3. The method of claim 2, wherein the solving step (c) further comprises solving the Maxwell'"'"'s equations for a complex-valued resonance frequency f of the cavity including the sample, wherein the f is a function of the property, the method further comprising:

(d) obtaining an experimentally determined electrical conductivity σ

_w of the cavity'"'"'s walls using the f_cavity;

(e) using the σ

_w to modify the f to account for a power absorbed by the cavity'"'"'s walls, thereby obtaining a resultant complex valued resonant frequency F that is a function of the property; and

(f) obtaining the property by solving F=f_sample.

4. The method of claim 3, further comprising:

obtaining a range of values for the property; and

selecting the value in the range that satisfies F=f_sample to any desired precision.

5. The method of claim 3, wherein the sample is non-magnetic, has any size, and is positioned along the cavity'"'"'s axis.

6. The method of claim 3, wherein to obtain the μ

of the sample that is magnetic, the cavity resonant modes comprise at least one Transverse Magnetic (TM_0n0) mode, and a magnetic field and an electric field associated with the TM_0n0 mode, where n is an integer, the method further comprising;

(g) performing the steps (a)-(f) for the sample that is a first cylindrical sample positioned along the cavity'"'"'s axis, the first cylindrical sample having a first radius that is sufficiently small so that the magnetic field'"'"'s strength at the first radius'"'"'s end is negligible, thereby allowing the Maxwell'"'"'s equations and the F to be solved for only one unknown, the ∈

=∈

_sample; and

(h) performing the steps (a)-(f) for the sample that is a second cylinder comprising a same material as the first cylinder, and having a larger radius than the first radius, such that the second cylinder positioned along the axis experiences both the magnetic field and the electric field, thereby allowing the Maxwell'"'"'s equations and the F to be solved for only one unknown, the μ

, using the ∈

=∈

_sample obtained in step (g).

7. The method of claim 3, wherein to obtain the μ

of the sample that is magnetic, the cavity resonant modes comprise;

a first frequency, a first magnetic field, and a first electric field associated with a first TM_0n0 mode, where n is an integer,

a second frequency, a second magnetic field and a second electric field associated with a second TM_0n0 mode,

the first frequency and the second frequency such that the ∈ and

the μ

at the first frequency are negligibly different from the ∈ and

the μ

at the second frequency; and

the method further comprising;

(g) exciting the cavity with the first TM_0n0 mode where the sample is an annulus positioned at a radius of the cavity associated with a maximum of the first electric field and a zero of the first magnetic field;

(h) performing the steps (a)-(f) using the first TM_0n0 mode, thereby allowing the Maxwell'"'"'s equations and the F to be solved for only one unknown, the ∈

_sample; and

(i) performing steps (a)-(f) using the second TM_0n0 mode so that the sample experiences both the second electric field and the second magnetic field, thereby allowing the Maxwell'"'"'s equations and the F to be solved for only one unknown, the μ

, using the ∈

=∈

_sample obtained in step (h).

8. The method of claim 3, wherein the sample in the cavity is in a sample holder, and the sample holder has a complex-valued dielectric permittivity (∈

_holder), the method further comprising;

obtaining a measured complex-valued resonance frequency f_holder of the cavity comprising the sample holder without the sample;

solving the Maxwell'"'"'s equations for a complex-valued resonance frequency g of the cavity including the sample holder without the sample, wherein the g is a function of the ∈

_holder;

modifying the g to account for the σ

_w, thereby obtaining a resultant complex-valued resonant frequency G that is a function of the ∈

_holder;

obtaining the ∈

_holder by solving G=f_holder; and

performing the steps (a)-(f) for the sample inserted in the sample holder in the cavity, wherein the solving of F=f_sample uses the ∈

_holder obtained by the solving of G=f_holder.

9. The method of claim 3, wherein the cavity comprises one or more additional materials having known material dielectric permittivity and known material magnetic permeability, such that the property is an only unknown during the solving step (f).

10. The method of claim 3, wherein the solving of F=f_sample further comprises finding roots of F−

f_sample=0, by;

(i) specifying a range of values for z within a first rectangle in a complex plane, wherein the z are complex numbers in a complex plane;

(ii) introducing a mesh into the first rectangle, thereby forming the mesh comprising mesh points at corners of second rectangles, wherein the second rectangles are smaller than the first rectangles;

(iii) evaluating Re F(z) at each of the mesh points;

(iv) determining one or more first sides of the second rectangles where the Re (F(z)) changes sign;

(v) evaluating Im F(z) at each of the mesh points;

(vi) determining one or more second sides of the second rectangles where the Im (F(∈

)) changes sign;

(vii) selecting the second rectangles having both the first sides and second sides, where both the Re F(z) and the Im F(z) change sign, to obtain selected second rectangles;

(viii) interpolating the Re F(z) in the selected second rectangles to define a Re F(z) null line;

(ix) interpolating the Im F(z) in the selected second rectangles to define an Im F(z) null line;

(x) finding a first intersection point between the Re F(z) null line and the Im F(z) null line;

(xi) setting the second rectangle as the first rectangle and repeating steps (i)-(x) using the second rectangle as the first rectangle, thereby finding a second intersection point;

(xii) obtaining a difference between the first intersection point and the second intersection point, and comparing the difference with a precision parameter that is equal to a desired precision;

(xiii) repeating the method until the difference is at least as small as the precision parameter, thereby obtaining a final intersection point; and

(xiv) setting the final intersection point equal to the property.

11. The method of claim 1, further comprising:

using the property to interpret remote sensing data obtained from earth or extra-terrestrial material, thereby identifying one or more compositions, optical properties, or dimensions of the material; and

transmitting, storing, or displaying the remote sensing data, compositions, optical properties, or dimensions of the material.

12. A computer readable storage medium encoded with computer program instructions which when accessed by a computer cause the computer to load the program instructions to a memory therein creating a special purpose data structure causing the computer to operate as a specially programmed computer, executing a method of obtaining at least one property selected from a complex-valued dielectric permittivity (∈

) and a complex valued magnetic permeability (μ

) of at least one sample, comprising;

(a) receiving, in the specially programmed computer, a measured complex-valued resonance frequency f_cavity of a cavity when empty;

(b) receiving, in the specially programmed computer, a measured complex-valued resonance frequency f_sample of the cavity containing the sample, wherein f_cavity and f_sample are measurements obtained by exciting the cavity with one or more TM_0n0 cavity resonant modes; and

(c) solving, in the specially programmed computer, Maxwell'"'"'s equations exactly for the property, using the f_cavity and the f_sample.

13. The computer readable storage medium of claim 12, wherein the cavity and the sample are annular or cylindrical regions.

14. The computer readable storage medium of claim 13, wherein the solving step (c) further comprises solving, in the specially programmed computer, the Maxwell'"'"'s equations for a complex-valued resonance frequency f of the cavity including the sample, wherein the f is a function of the property, the method further comprising:

(d) receiving, in the specially programmed computer, an experimentally determined electrical conductivity σ

_w of the cavity'"'"'s walls using the f_cavity;

(e) using, in the specially programmed computer, the σ

_w to modify the f to account for a power absorbed by the cavity'"'"'s walls, thereby obtaining a resultant complex valued resonant frequency F that is a function of the property; and

(f) obtaining, in the specially programmed computer, the property by solving F=f_sample.

15. The computer readable storage medium of claim 14, further comprising:

receiving, in the specially programmed computer, a range of values for the property; and

selecting, in the specially programmed computer, the value in the range that satisfies F=f_sample to any degree of precision.

16. The computer readable storage medium of claim 14, wherein the sample is non-magnetic, has any size, and is positioned along an axis of the cavity.

17. The computer readable storage medium of claim 14, wherein to obtain the μ

of the sample that is magnetic, the cavity resonant modes comprise at least one Transverse Magnetic (TM_0n0) mode, and a magnetic field and an electric field associated with the TM_0n0 mode, where n is an integer, the method further comprising;

(g) performing the steps (a)-(f) for the sample that is a first cylindrical sample positioned along an axis of the cavity, the first cylindrical sample having a first radius that is sufficiently small so that the magnetic field'"'"'s strength at the first radius'"'"'s end is negligible, thereby allowing the Maxwell'"'"'s equations and the F to be solved for only one unknown, the ∈

; and

(h) performing the steps (a)-(f) for the sample that is a second cylinder comprising a same material as the first cylinder, and having a larger radius than the first radius, such that the second cylinder positioned along the axis experiences both the magnetic field and the electric field, thereby allowing the Maxwell'"'"'s equations and the F to be solved for only one unknown, the μ

, using the ∈

obtained in step (g).

18. The computer readable storage medium of claim 14, wherein to obtain the μ

of the sample that is magnetic, the cavity resonant modes comprise;

a first frequency, a first magnetic field, and a first electric field associated with a first TM_0n0 mode, where n is an integer,

a second frequency, a second magnetic field and a second electric field associated with a second TM_0n0 mode,

the first frequency and the second frequency such that the ∈ and

the μ

at the first frequency are negligibly different from the ∈ and

the μ

at the second frequency; and

the method further comprising;

(g) exciting the cavity with the first TM_0n0 mode where the sample is an annulus positioned at a radius of the cavity associated with a maximum of the first electric field and a zero of the first magnetic field;

(h) performing the steps (a)-(f) using the first TM_0n0 mode, thereby allowing the Maxwell'"'"'s equations and the F to be solved for only one unknown, the ∈

; and

(i) performing steps (a)-(f) using the second TM_0n0 mode so that the sample experiences both the second electric field and the second magnetic field, thereby allowing the Maxwell'"'"'s equations and the F to be solved for only one unknown, the μ

, using the ∈

obtained in step (h).

20. The computer readable storage medium of claim 14, wherein the cavity comprises one or more additional materials having known material dielectric permittivity and known material magnetic permeability, such that the property is an only unknown during the solving step (f).

22. The computer readable storage medium of claim 12, further comprising:

using, in the specially programmed computer, the property to interpret remote sensing data obtained from earth or extra-terrestrial material, thereby identifying one or more compositions, optical properties, or dimensions of the material; and

transmitting, storing, or displaying the remote sensing data, compositions, optical properties, or dimensions of the material using the specially programmed computer.

19. The computer readable storage medium 14, wherein the sample in the cavity is in a sample holder, and the sample holder has a complex-valued dielectric permittivity (∈

_holder), the method further comprising;

receiving, in the specially programmed computer, a measured complex-valued resonance frequency f_holder of the cavity using a TM_0n0 mode, the cavity comprising the sample holder without the sample;

solving, in the specially programmed computer, the Maxwell'"'"'s equations for a complex-valued resonance frequency g of the cavity including the sample holder without the sample, wherein the g is a function of the ∈

_holder;

modifying, in the specially programmed computer, the g to account for the σ

_w, thereby obtaining a resultant complex-valued resonant frequency G that is a function of the ∈

_holder;

obtaining, in the specially programmed computer, the ∈

_holder by solving G=f_holder; and

performing the steps (a)-(f) for the sample inserted in the sample holder in the cavity, wherein the solving of F=f_sample uses the ∈

_holder obtained by the solving of G=f_holder.

21. The computer readable storage medium 14, wherein the solving of F=f_sample further comprises finding roots of F−

f_sample=0, by;

(i) specifying, in the specially programmed computer, a range of values for z within a first rectangle in a complex plane, wherein the z are complex numbers in a complex plane;

(ii) introducing, in the specially programmed computer, a mesh into the first rectangle, thereby forming the mesh comprising mesh points at corners of second rectangles, wherein the second rectangles are smaller than the first rectangles;

(iii) evaluating, in the specially programmed computer, Re F(z) at each of the mesh points;

(iv) determining, in the specially programmed computer, one or more first sides of the second rectangles where the Re F(z) changes sign;

(v) evaluating, in the specially programmed computer, Im F(z) at each of the mesh points;

(vi) determining, in the specially programmed computer, one or more second sides of the second rectangles where the Im F(∈

) changes sign;

(vii) selecting, in the specially programmed computer, the second rectangles having both the first sides and second sides, where both the Re F(z) and the Im F(z) change sign, to obtain selected second rectangles;

(viii) interpolating, in the specially programmed computer, the Re F(z) in the selected second rectangles to define a Re F(z) null line;

(ix) interpolating, in the specially programmed computer, the Im F(z) in the selected second rectangles to define an Im F(z) null line;

(x) finding, in the specially programmed computer, a first intersection point between the Re F(z) null line and the Im F(z) null line;

(xi) setting, in the specially programmed computer, the second rectangle as the first rectangle and repeating steps (i)-(x) using the second rectangle as the first rectangle, thereby finding a second intersection point;

(xii) obtaining, in the specially programmed computer, a difference between the first intersection point and the second intersection point, and comparing the difference with a precision parameter that is equal to a desired precision;

(xiii) repeating, in the specially programmed computer, the method until the difference is at least as small as the precision parameter, thereby obtaining a final intersection point; and

(xiv) setting, in the specially programmed computer, the final intersection point equal to the property.