U.S. patent application number 15/540255 was filed with the patent office on 2020-01-16 for device and method for optical analysis using multiple integrated computational elements.
The applicant listed for this patent is HALLIBURTON ENERGY SERVICES, INC.. Invention is credited to Bin Dai, Christopher Michael Jones, James M. Price.
Application Number | 20200018162 15/540255 |
Document ID | / |
Family ID | 61760860 |
Filed Date | 2020-01-16 |
United States Patent
Application |
20200018162 |
Kind Code |
A1 |
Price; James M. ; et
al. |
January 16, 2020 |
DEVICE AND METHOD FOR OPTICAL ANALYSIS USING MULTIPLE INTEGRATED
COMPUTATIONAL ELEMENTS
Abstract
A method including generating integrated computational element
(ICE) models and determining a sensor response as the projection of
a convolved spectrum associated with a sample library with a
plurality of transmission profiles determined from the ICE models.
The method includes determining a regression vector based on a
multilinear regression that targets a sample characteristic with
the sensor response and the sample library and determine a
plurality of regression coefficients in a linear combination of ICE
transmission vectors that results in the regression vector. The
method further includes determining a difference between the
regression vector and an optimal regression vector. The method may
also include modifying the ICE models when the difference is
greater than a tolerance, and fabricating ICEs based on the ICE
models when the difference is within the tolerance. A device and a
system for optical analysis including multiple ICEs fabricated as
above, are also provided.
Inventors: |
Price; James M.; (Woodlands,
TX) ; Dai; Bin; (Spring, TX) ; Jones;
Christopher Michael; (Katy, TX) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
HALLIBURTON ENERGY SERVICES, INC. |
Housston |
TX |
US |
|
|
Family ID: |
61760860 |
Appl. No.: |
15/540255 |
Filed: |
September 29, 2016 |
PCT Filed: |
September 29, 2016 |
PCT NO: |
PCT/US2016/054386 |
371 Date: |
June 27, 2017 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01J 2003/1226 20130101;
G01N 21/31 20130101; G01N 2021/855 20130101; E21B 47/002 20200501;
G01J 3/513 20130101; G01N 2201/1293 20130101; E21B 47/10 20130101;
G01J 3/027 20130101; E21B 49/081 20130101; G01J 3/0227 20130101;
G01N 21/84 20130101; G01N 2201/129 20130101 |
International
Class: |
E21B 49/08 20060101
E21B049/08; G01N 21/31 20060101 G01N021/31; G01N 21/84 20060101
G01N021/84; E21B 47/00 20060101 E21B047/00 |
Claims
1. A method, comprising: generating a plurality of integrated
computational element (ICE) models; determining a sensor response
from a projection of a plurality of ICE transmission vectors
associated with the plurality of ICE models and a convolved
spectrum associated with a sample library; determining a regression
vector based on a multilinear regression that targets a sample
characteristic from the sample library and the sensor response;
determining a plurality of regression coefficients in a linear
combination of the plurality of ICE transmission vectors that
results in the regression vector; determining a difference between
the regression vector and an optimal regression vector associated
with the sample characteristic; modifying the plurality of ICE
models when the difference between the regression vector and the
optimal regression vector is greater than a selected tolerance; and
fabricating a plurality of ICEs based on the plurality of ICE
models when the difference between the regression vector and the
optimal regression vector is within the selected tolerance.
2. The method of claim 1, wherein generating the plurality of ICE
models comprises selecting a random number of layers and a random
thickness for each layer in each ICE model.
3. The method of claim 1, wherein modifying the plurality of ICE
models comprises: modifying a number of layers and a thickness for
each layer for at least one of the plurality of ICE models to
obtain a plurality of modified ICE models; determining a modified
sensor response from the plurality of modified ICE models and the
convolved spectrum associated with the sample library; determining
a modified regression vector from the plurality of modified ICE
models and the modified sensor response; determining a difference
between the modified regression vector and the optimal regression
vector; iteratively repeat the modifying the number of layers, the
determining a modified sensor response, the determining a modified
regression vector, and the determining a difference between the
modified regression vector and the optimal regression vector until
the difference between the modified regression vector and the
optimal regression vector is within the selected tolerance; and
fabricating the plurality of ICEs based on the plurality of
modified ICE models.
4. The method of claim 1, wherein determining a difference between
the regression vector and the optimal regression vector comprises
determining a mean square error between the regression vector and
the optimal regression vector.
5. The method of claim 1, further comprising determining the
optimal regression vector from a partial least squares model of the
convolved spectrum and the sample library, targeting the sample
characteristic.
6. The method of claim 1, wherein determining the regression vector
and the plurality of regression coefficients comprises calibrating
an optical computing device with the plurality of ICEs and with the
sample library.
7. The method of claim 1, further comprising determining an
accuracy and a sensitivity of an optical computing device that
includes the plurality of ICEs based on the regression vector and
the sample library.
8. The method of claim 1, further comprising storing in a memory
the plurality of regression coefficients for each ICE transmission
vector when the difference between the regression vector and the
optimal regression vector is within the selected tolerance.
9. The method of claim 1, further comprising: measuring a spectral
performance of each of the ICEs in a fabrication batch of the
plurality of ICEs; selecting a combination of ICEs from the
fabrication batch based on the spectral performance; and disposing
the combination of ICEs in an optical computing device that
measures the sample characteristic.
10. The method of claim 1, wherein fabricating the plurality of
ICEs comprises measuring a performance of a post-fabrication
combinatorial configuration between different ICEs from a
fabrication batch for each of the plurality of ICEs.
11. The method of claim 1, wherein fabricating the plurality of
ICEs comprises: fabricating one or more of the plurality of ICEs
sequentially; and re-modeling an ICE that has not been fabricated
based on a post-fabrication spectral performance of the one or more
of the plurality of ICEs.
12. A device, comprising: at least two integrated computational
elements (ICEs) positioned to optically interact with sample light
to generate a first modified light from a first ICE and a second
modified light from a second ICE; and a detector that separately
measures the first modified light to provide a first signal and the
second modified light to provide a second signal, wherein each one
of the at least two ICEs comprises a plurality of alternating
layers of material and each layer of material has a thickness
selected such that a linear combination of the first signal with
the second signal is proportional to a sample characteristic.
13. The device of claim 12, further comprising a multiplexer that
directs a first portion of sample light to the first ICE and a
second portion of sample light to the second ICE.
14. The device of claim 12, wherein the detector comprises a first
detector to measure the first modified light, and a second detector
to measure the second modified light, the first detector being
spatially separated from the second detector.
15. The device of claim 12, wherein the detector measures the first
modified light and the second modified light separated in time.
16. A system, comprising: a light source that generates an
illumination light to interact with a sample and form a sample
light; an optical computing device comprising: at least two
integrated computational elements (ICES) positioned to optically
interact with the sample light to generate a first modified light
from a first ICE and a second modified light from a second ICE; and
a detector that separately measures the first modified light to
provide a first signal and the second modified light to provide a
second signal, wherein each one of the at least two ICEs comprises
a plurality of alternating layers of material and each layer of
material has a thickness selected such that a linear combination of
the first signal with the second signal is proportional to a sample
characteristic; and a controller comprising a processor and a
memory, wherein the processor forms the linear combination of the
first signal and the second signal based on at least two regression
coefficients associated with the at least two integrated
computational elements (ICEs) stored in the memory.
17. The system of claim 16, wherein the optical computing device
further comprises a multiplexer that directs a first portion of the
sample light to the first ICE and a second portion of the sample
light to the second ICE.
18. The system of claim 16, wherein the detector in the optical
computing device comprises a first detector to measure the first
modified light, and a second detector to measure the second
modified light, the first detector being spatially separated from
the second detector.
19. The system of claim 16, wherein the detector in the optical
computing device measures the first modified light and the second
modified light separated in time.
20. The system of claim 16, wherein the at least two ICEs comprise
more than two ICEs but less than a number of principal components
in a partial least squares regression model used to determine an
optimal regression vector for the sample characteristic.
Description
BACKGROUND
[0001] In the field of oil and gas exploration and production,
sample characterization of reservoir or wellbore fluid compositions
is desirable to determine fluid quality, hydrocarbon composition,
or to adjust and modify a drilling parameter based on the above.
Some sample characterization measurement devices sacrifice
measurement quality in favor of the compactness and robustness
desirable in field applications. Thus, optimal measurement
protocols typically remain in the laboratory and away from
practical field applications.
BRIEF DESCRIPTION OF THE DRAWINGS
[0002] The following figures are included to illustrate certain
aspects of the present disclosure, and should not be viewed as
exclusive embodiments. The subject matter disclosed is capable of
considerable modifications, alterations, combinations, and
equivalents in form and function, as will occur to those skilled in
the art and having the benefit of this disclosure.
[0003] FIG. 1 illustrates a system for optical analysis of a
formation fluid from an optical computing device using multiple
Integrated Computational Elements (ICEs).
[0004] FIG. 2 illustrates a cross-sectional view of an exemplary
ICE for measuring a desired characteristic of a sample.
[0005] FIG. 3 illustrates a chart with spectra of a sample light
from reference fluids having varied methane concentrations.
[0006] FIG. 4 illustrates a chart with convolved spectra of a
sample light from a reference fluid having varied methane
concentrations.
[0007] FIG. 5 illustrates a chart with transmission spectra of a
first ICE and a second ICE, in an optical computing device for
methane measurement.
[0008] FIG. 6 illustrates a chart with a regression vector for an
optical computing device using dual ICE sensing elements and an
optimal regression vector for a methane measurement.
[0009] FIG. 7 illustrates a logging while drilling (LWD) system
configured to measure a characteristic of a sample during wellbore
drilling with an optical computing device.
[0010] FIG. 8 illustrates a wireline system configured to measure a
characteristic of a sample during formation testing and sampling
with an optical computing device.
[0011] FIG. 9 illustrates a flow chart including steps in a method
for fabricating an optical computing device.
[0012] In the figures, elements or steps having the same or similar
reference numerals have the same or similar description and
configuration, unless stated otherwise.
DETAILED DESCRIPTION
[0013] The present disclosure relates to systems, devices and
methods for measuring a selected characteristic of a sample in the
oil and gas exploration and extraction industry using an optical
computing device with multiple integrated computational sensing
elements. Embodiments disclosed herein include the design,
fabrication and post-fabrication qualification of optical computing
devices having multiple integrated computational elements that are
capable of reproducing similar measurement results as compared to
optimal measurement techniques.
[0014] An Integrated Computational Element (ICE) as disclosed
herein is a processing element that optically interacts with a
substance to determine quantitative and/or qualitative values of
one or more physical or chemical properties of the substance (or
sample characteristic). The ICE may include a multilayered
interference element designed to operate over a continuum of
wavelengths in the electromagnetic spectrum including the
ultraviolet (UV, about 290 nm to about 400 nm), the visible (VIS,
about 400 nm to about 750 nm), the near-infrared (NIR, about 750 nm
to about 2500 nm), the mid-infrared range (MIR, about 2500 nm to
about 10,000 nm), or any sub-set of those regions. Electromagnetic
radiation that optically interacts with the ICE is modified to be
readable by a detector such that an output of the detector can be
correlated to the physical or chemical property or "characteristic"
of the substance being analyzed.
[0015] As used herein, the term "characteristic" refers to a
chemical, mechanical, or physical property of a substance. The
sample characteristic may include a quantitative or qualitative
value of one or more chemical constituents or compounds present
therein, or any physical property associated therewith. Such
chemical constituents and compounds may be alternately referred to
as "analytes." Illustrative sample characteristics that can be
monitored with the optical computing devices described herein can
include chemical composition (e.g., identity and concentration in
total or of individual components), phase presence (e.g., gas, oil,
water, etc.), impurity content, ion content, pH, alkalinity,
viscosity, density, ionic strength, total dissolved solids, salt
content (e.g., salinity), porosity, opacity, bacteria content,
total hardness, combinations thereof, state of matter (solid,
liquid, gas, emulsion, mixtures, etc.), and the like.
[0016] As used herein, the term "electromagnetic radiation" refers
to radio waves, microwave radiation, mid-infrared (MIR) and
near-infrared radiation (NIR), visible light (WS), ultraviolet
light (UV), X-ray radiation and gamma ray radiation.
[0017] As used herein, the term "optical computing device" refers
to an optical device that is configured to receive an input of
electromagnetic radiation from an electromagnetic source, to
interact the electromagnetic radiation with a substance and to
produce an output of electromagnetic radiation from a processing
element arranged within the optical computing device. In some
embodiments, an optical computing device also includes a detector
to generate an electronic signal indicative of a sample
characteristic. The processing element may be, for example, an ICE,
or a multilinear optical element (MOE). The electromagnetic
radiation that optically interacts with the processing element is
modified so as to be readable by a detector, such that an output of
the detector can be correlated to a particular characteristic of
the substance. The output of electromagnetic radiation from the
processing element can be reflected, transmitted, and/or dispersed
electromagnetic radiation. Whether the detector analyzes reflected,
transmitted, or dispersed electromagnetic radiation may be dictated
by the structural parameters of the optical computing device as
well as other considerations known to those skilled in the art. In
addition, emission and/or scattering of the fluid, for example via
fluorescence, luminescence, Raman, Mie, and/or Raleigh scattering,
can also be monitored by optical computing devices.
[0018] As used herein, the term "optically interact" or variations
thereof refers to the reflection, transmission, scattering,
diffraction, or absorption of electromagnetic radiation either on,
through or from one or more processing elements (i.e., ICE or MOE
components) or a substance being analyzed by the processing
elements. Accordingly, optically interacted light refers to
electromagnetic radiation that has been reflected, transmitted,
scattered, diffracted, or absorbed, emitted, or re-radiated, for
example, using a processing element, but may also apply to
interaction with a substance.
[0019] Embodiments as disclosed herein include optical computing
devices that use multiple ICEs in parallel. The multiple ICEs are
modeled using multilinear regression techniques to match an optimal
regression vector and measure a desired sample characteristic.
Conventional sensors include a single optical element, such as a
broadband filter, in conjunction with a neutral density filter to
reproduce a regression vector that may provide a less than optimal
solution for measuring the desired sample characteristic. Using a
single ICE approach may result in solutions far from a theoretical
limit for sensor performance in the laboratory. An optimal
measurement of a sample characteristic may be obtained by
performing a partial least squares (PLS) regression over a sample
library including a plurality of calibrated spectra.
[0020] This disclosure provides a method to fabricate multiple ICEs
for an optical computing device such that an optimal regression
vector is closely matched. An optimal regression vector, for a
given sample library, is a vector spanning the given wavelength
region of interest and whose dot product with each of the spectra
in the sample library is proportional to the sample characteristic
(e.g., analyte concentration of interest, and the like). In some
embodiments, an optimal regression vector may also be orthogonal to
interfering compounds or factors, meaning that the dot product of
the optimal regression vector with a spectrum from any of the
interfering compounds or factors is zero, nearly zero, or
negligible for measurement purposes. An optimal regression vector
can be obtained by performing an independent partial least squares
(PLS) multilinear regression analysis on convolved spectra and
measured concentration values obtained from the sample library.
Therefore, by matching the optimal regression vector, an optical
computing device may realize optimal limits for measurement
accuracy and sensitivity of the sample characteristic.
[0021] Typically, `optimal` regression vectors may include positive
and negative lobes. The negative lobes may correspond to portions
of the spectral response from the sample that are subtracted from
the signal to obtain a response calibrated according to the desired
sample characteristic. Furthermore, in cases where the sample
characteristic involves a complex combination of factors (e.g.,
`principal components`), the spectral signature of an optimal
regression vector may have a high frequency of features (i.e., a
rapid sequence of narrow cusps and troughs along a wavelength
dimension). The presence of negative lobes and high frequency
spectral features in optimal regression vectors reduces the
parameter space availability of single ICE models to measure the
desired sample characteristic according to specification.
[0022] Embodiments of the present disclosure provide multiple ICEs
that enable a better reproduction of an optimal solution for a
problem involving a larger number of principal components. For
example, single ICE approaches may be able to solve a measurement
task when the PLS regression is satisfied with up to two or three
principal components. Making use of two or more ICEs, however, as
described herein, may perform measurement tasks when the PLS
regression is satisfied with up to four, five, six or even more
principal components. Typically, measurement tasks where the PLS
solution includes a higher number of principal components involve
more complex samples for handling (e.g., samples having more
interfering compounds, multiple phases, and the like).
[0023] Embodiments as disclosed herein provide optical computing
devices that include multiple ICEs to yield high frequency features
of an optimal regression vector. By using multiple ICEs to match an
optimal regression vector, the optical computing devices disclosed
herein may realize superior sensitivity and accuracy, and offer a
wider range of designs that perform within desired operating
specifications.
[0024] The multiple ICEs for optical computing devices as disclosed
herein are obtained from an initial random layer stack (i.e.,
arbitrary number of layers having arbitrary thicknesses) that
yields an initial transmission spectrum. The layer stack may be
constrained to alternate between high- (e.g., silicon) and low-
(e.g., silicon dioxide) index materials on a BK7 substrate,
respectively. The dot product is obtained by projecting the
transmission spectrum of the initial layer stack against a sample
library, which may include an optical Pressure-Volume-Temperature
(PVT) calibration spectral database. The predictive performance
(i.e., accuracy and sensitivity) of the initial layer stack is
evaluated from the obtained projection, and a regression analysis
based on minimization of a merit-function follows. The regression
analysis includes modifying (altering) initial layer stacks of the
ICEs (e.g., modifying the number of layers and their thicknesses
for each of the multiple ICEs). New transmission spectra are
calculated for the modified ICE models, and a new value for the
merit-function is calculated. The multiple ICE models are modified
iteratively until a global minimum of the merit function is
achieved. Embodiments consistent with the present disclosure
provide multiple ICEs to improve the measurement of the sample
characteristics with an optical computing device.
[0025] In some embodiments, the merit-function in the iteration
cycle is a measure of a match between the regression vector of the
multiple ICE model and the optimal regression vector. Thus, the
sensitivity and accuracy of an optical computing device that
employs multiple ICEs closely resembling an optimal regression
vector may approach the theoretical limit.
[0026] In a first embodiment, a method includes generating a
plurality of integrated computational element (ICE) models and
determining a sensor response from a projection of a plurality of
ICE transmission vectors associated with the ICE models and a
convolved spectrum associated with a sample library. The method may
also include determining a regression vector based on a multilinear
regression that targets a sample characteristic from the sample
library and the sensor response, and determining a regression
coefficient for each of the plurality of ICE transmission vectors
in a linear combination that results in the regression vector. In
some embodiments, the method includes determining a difference
between the regression vector and an optimal regression vector
associated with the sample characteristic and modifying the
plurality of ICE models when the difference between the regression
vector and the optimal regression vector is greater than a selected
tolerance. Further, the method may include fabricating a plurality
of ICEs based on the plurality of ICE models when the difference
between the regression vector and the optimal regression vector is
within the selected tolerance.
[0027] In a second embodiment, an optical computing device includes
at least two integrated computational elements (ICEs) positioned to
optically interact with sample light to generate a first modified
light from a first ICE and a second modified light from a second
ICE. The optical computing device may also include a detector that
separately measures the first modified light to provide a first
signal and the second modified light to provide a second signal. In
some embodiments, each one of the at least two ICEs includes a
plurality of alternating layers of material and each layer of
material has a thickness selected such that a linear combination of
the first signal with the second signal is proportional to a sample
characteristic.
[0028] In yet another embodiment, a system includes a light source
that generates an illumination light to interact with a sample and
form a sample light, an optical computing device, and a controller.
The optical computing device includes at least two integrated
computational elements (ICEs) positioned to optically interact with
the sample light to generate a first modified light from a first
ICE and a second modified light from a second ICE, and a detector
that separately measures the first modified light to provide a
first signal and the second modified light to provide a second
signal. Each one of the at least two ICEs includes a plurality of
alternating layers of material and each layer of material has a
thickness selected such that a linear combination of the first
signal with the second signal is proportional to a sample
characteristic. The controller includes a processor and a memory,
wherein the processor forms the linear combination of the first
signal and the second signal based on at least two regression
coefficients associated with the at least two integrated
computational elements (ICEs) stored in the memory.
[0029] FIG. 1 illustrates a system 10 for measuring a sample
characteristic of a formation fluid 150 from an optical computing
device 101. Optical computing device 101 includes multiple ICEs
100-1 through 100-m (hereinafter collectively referred to as ICEs
100). System 10 includes a light source 140 and an optical
computing device 101. Light source 140 generates an illumination
light 141 conveyed to optically interact with formation fluid 150
(i.e., the `sample`), thus generating a sample light 142. Light
source 140 may be a broadband lamp with a tungsten light bulb, a
laser, a light-emitting diode, or any other source of
electromagnetic radiation. In some embodiments, sample light 142
may include fluorescence emitted photons or Raman shifted photons
derived from formation fluid 150.
[0030] In some embodiments, optical computing device 101 includes
an optical multiplexer 110, ICEs 100, and at least one detector
130, shown as detectors 130-1 through 130-m. Optical multiplexer
110 separates sample light 142 into a plurality of beams of
modified light 143-1 through 143-m (hereinafter collectively
referred to as modified lights 143). Optical multiplexer 110 may
include a free-space, waveguide, or a fiber-optic based
multiplexer, without limitation. In some embodiments, optical
multiplexer 110 may include a beamsplitter, a lens, an arrayed
waveguide grating, or any combination of the above. Upon receipt of
modified lights 143, each detector 130 generates a sensing signal,
shown as signals 135-1 through 135-m (hereinafter collectively
referred to as sensing signals 135).
[0031] Sensing signals 135 reach a controller 160 through a
transmission line 170 that communicably couples the detectors 130
to the controller 160. Transmission line 170 may be an electrical
wire, an optical fiber, a radio-frequency wireless communication
line or another type of wireless communication device for
transmitting electromagnetic signals. In some embodiments,
transmission line 170 may be an acoustic line configured to
propagate sound pulses through a wellbore fluid. In some
embodiments, multiplexer 110 separates each of modified lights 143
in time, so that sensing signals 135 form a trace of pulses along
the transmission line 170 to the controller 160.
[0032] ICEs 100 optically interact with portions of sample light
142 to provide modified lights 143. A resulting property of
modified lights 143 may include an intensity indicative of a
spectral density distribution of sample light 142. The spectral
density distribution of sample light 142 may, in turn, be
associated with chemical and physical properties of formation fluid
150. In some embodiments, an additional resulting property of
modified lights 143 indicative of chemical or physical properties
of formation fluid 150 may comprise an intensity, a polarization
state, a phase, a wavelength, or any combination of the above. The
transmission spectra of ICEs 100 is pre-selected according to a
model that transforms sensing signals 135 into a data value
associated with the optimal regression vector, which is determined
based on a desired characteristic of substance 150. In some
embodiments, the model that transforms sensing signals 135 into a
data value associated with the optimal regression vector may
include a linear regression algorithm (e.g., principal component
analysis), or a multilinear regression (MLR).
[0033] Transmission line 170 transmits sensing signals 135 to
controller 160 for data processing. Controller 160 may include a
processor 161 and a memory 162. Memory 162 stores data and commands
which, when executed by processor 161, cause controller 160 to
direct system 10 to perform steps in methods consistent with the
present disclosure. For example, upon execution by processor 161 of
commands in memory 162, controller 160 may process sensing signals
135 to determine a desired sample characteristic from sample light
142. Controller 160 may also communicate with light source 140 to
control or modify illumination light 141.
[0034] FIG. 2 illustrates a schematic cross-sectional view of an
exemplary integrated computational element (ICE) 200 for measuring
a concentration in sample fluid 150. ICE 200 may be similar to or
the same as any of ICEs 100 and, therefore, may be used in optical
computing device 101 in conjunction with one or more additional
ICEs. As illustrated, ICE 200 includes a plurality of alternating
layers of material 203 and 204, such as silicon (Si) and SiO.sub.2
(quartz), respectively. In general, layers 203, and 204 include
materials whose index of refraction is high and low, respectively
(e.g., different, in general). Other examples of materials for use
in layers 203 and 204 might include niobia and niobium, germanium
and germania, MgF, SiO, and other high and low index materials
known in the art. Layers 203, 204 may be strategically deposited on
an optical substrate 206. In some embodiments, optical substrate
206 is BK-7 optical glass. In other embodiments, optical substrate
206 may be another type of optical substrate, such as quartz,
sapphire, silicon, germanium, zinc selenide, zinc sulfide, or
various plastics such as polycarbonate, polymethylmethacrylate
(PMMA), polyvinylchloride (PVC), diamond, ceramics, combinations
thereof, and the like.
[0035] At the opposite end (e.g., opposite optical substrate 206 in
FIG. 2), ICE 200 may include a layer 208 that is generally exposed
to the environment of the device or installation, and may be able
to detect a sample substance. The number of layers 203, 204 and the
thickness of each layer 203, 204 for the plurality of ICES 200 are
determined from the spectral attributes acquired from an optimal
regression vector solving for measuring a sample characteristic.
The spectrum of interest of a sample characteristic includes any
number of different wavelengths. It should be understood that ICE
200 does not in fact represent any particular sample
characteristic, but is provided for purposes of illustration only.
Consequently, the number of layers 203, 204 and their relative
thicknesses bear no correlation to any particular sample
characteristic. Nor are layers 203, 204 and their relative
thicknesses necessarily drawn to scale, and therefore should not be
considered limiting of the present disclosure. Moreover, those
skilled in the art will readily recognize that the materials that
make up each layer 203, 204 (i.e., Si and SiO.sub.2) may vary,
depending on the application, cost of materials, and/or
applicability of the material to the given substance being
analyzed.
[0036] In some embodiments, the material of each layer 203, 204 can
be doped or two or more materials can be combined, together with
those of the other ICEs in the optical computing device, to achieve
a desired optical characteristic. In addition to solids, ICE 200
may also contain liquids and/or gases, optionally in combination
with solids, in order to produce a desired optical characteristic.
In the case of gases and liquids, ICE 200 can contain a
corresponding vessel (not shown), which houses the gases or
liquids. Exemplary variations of ICE 200 may also include
holographic optical elements, gratings, piezoelectric, light pipe,
and/or acousto-optic elements, for example, that can create
transmission, reflection, and/or absorptive properties of
interest.
[0037] Layers 203 and 204 exhibit different refractive indices. By
properly selecting the materials of layers 203, 204 and their
relative thickness and spacing, ICE 200 may be configured to
selectively pass/reflect/refract predetermined fractions of
electromagnetic radiation at different wavelengths. Each wavelength
is given a predetermined weighting or loading factor. The thickness
and spacing of layers 203, 204 may be determined using a variety of
approximation methods from the spectrum of the characteristic or
analyte of interest. These methods may include inverse Fourier
transform (IFT) of the optical transmission spectrum and
structuring ICE 200 as the physical representation of the IFT. The
approximations convert the IFT into a structure based on known
materials with constant refractive indices.
[0038] The weightings that layers 203, 204 of ICE 200 apply at each
wavelength are set to a known equation, or data, or spectral
signature, in combination with the rest of the multiple ICEs 200 in
the optical computing device. When electromagnetic radiation
interacts with a substance, unique physical and chemical
information about the substance may be encoded in the
electromagnetic radiation that is reflected from, transmitted
through, or radiated from the substance. This information is often
referred to as the spectral "fingerprint" of the substance. ICE 200
performs the dot product of the electromagnetic radiation received
(e.g., any one of sample lights 142, cf. FIG. 1) and the wavelength
dependent transmission function of ICE 200. The wavelength
dependent transmission function of ICE 200 is determined by the
layer material refractive index, the number of layers 203, 204 and
the layer thicknesses. The transmission function of ICE 200 is
designed to mimic, in conjunction with at least one other ICE, a
desired regression vector derived from the solution to a linear
multilinear problem targeting a desired sample characteristic. As a
result, a suitable combination of the output light intensities of
at least two ICEs 200 (e.g., the intensity of modified lights 143,
cf. FIG. 1) is proportional to a dot product of a transmission
spectrum of the sample with an optimal regression vector associated
with the characteristic of interest. Accordingly, the weighed
output light intensities of at least two ICEs 200 is a direct
indicator of a value (e.g., analyte concentration) of the desired
sample characteristic. Note that the weighting coefficients for the
light intensities a first and a second modified lights 143 may have
a different sign.
[0039] Optical computing devices 101 (cf. FIG. 1) that employ
multiple ICEs 200 may be capable of extracting the information of
the spectral fingerprint of multiple characteristics or analytes
within a substance and converting that information into a
detectable output regarding the overall properties of the
substance. That is, through suitable configurations of the two or
more ICEs 200 in an optical computing device as disclosed herein,
electromagnetic radiation associated with a selected characteristic
of a sample can be separated from electromagnetic radiation
associated with all other components of the sample. Thus, the
selected sample characteristic may be estimated in real-time or
near real-time. Accordingly, the combination of two or more ICEs
200 is able to distinguish and process electromagnetic radiation
related to a sample characteristic.
[0040] FIG. 3 illustrates a chart 300 with spectra 301-1, . . . ,
301-k, (collectively referred to hereinafter as spectra 301) of a
sample light from a reference fluid having varied methane
concentrations. Spectra 301 may be selected from a sample library
wherein the varied methane concentration of multiple samples have
been carefully calibrated in advance of an ICE modeling step. Chart
300 spans a minimum to a maximum transmitted intensity (I.sub.0 to
I.sub.m) in the ordinate axis (arbitrary units) and covers a
wavelength range from .lamda..sub.0 at about 1500 nm to about
.lamda..sub.m 2500 nm (i.e., NIR), in the abscissae. The ordinates
of chart 300 indicate the spectral intensity of sample light 142
impinging on ICEs 100 (cf. FIG. 1).
[0041] Spectra 301 were collected using a high-resolution
spectrometer with oil samples under known pressure and temperature,
such as through the use of a Fourier transform infrared
spectrometer (FUR). Consequently, the spectra 301 may be
characterized as the `optimal` against which subsequent spectra
will be measured (compared). As depicted, spectra 301 include over
four hundred light and medium oil transmission spectra obtained
from an existing Pressure-Volume-Temperature (PVT) database with
varied methane concentrations (i.e., the sample library). Spectra
301 in the PVT database span a methane concentration range from
0-0.1786 grams per cubic centimeter (glee) of methane dissolved in
the oil samples. Spectra 301 are collected over a range of
pressures, temperatures, and methane concentrations such that a
multilinear model of significant rank can be developed and used to
build predictive ICEs. The rank is a measure of how well defined
the experimental design is. It is associated with a number of
independent concentrations for a given analyte and the number of
truly independent fluids in a data set. When a multilinear model
has sufficient rank, then fewer calibration spectra are needed to
be included in a solution satisfying specifications.
[0042] FIG. 4 is another chart 400 depicting convolved spectra
401-1 through 401-k (hereinafter collectively referred to as
spectra 401) of sample light 142 from a reference fluid 150 having
varied methane concentrations. The abscissae in chart 400 are the
same as in chart 300 (i.e., spanning a wavelength range from
.lamda..sub.0 to .lamda..sub.m). The ordinates of chart 400
indicate a convolved spectral intensity of sample light 142
impinging on optical elements 102 (FIG. 1), spanning a range from
-Cm to +Cm, where Cm is a maximum absolute value of the convolved
spectra.
[0043] Convolved spectra 401 are derived from spectra 301 convolved
with the transmission function of the optical train coupling light
source 140 with detector 130. Convolved spectra 401 may include
transmission functions for sapphire windows in a sample cell, a
CaF.sub.2 rod, band pass filters, the emission profile of light
source 140 and the transmission/reflection profile of optical
components in multiplexer 110 (FIG. 1). Convolved spectra 401 are
normalized (i.e., Cm=1) and mean-centered (i.e., spanning a
negative and positive range -Cm to +Cm). Accordingly, spectra 401
may first be convolved with the optical train, and then normalized
and mean-centered.
[0044] FIG. 5 illustrates a chart 500 with a transmission spectrum
501 (T.sub.1) generated from a first ICE and a transmission
spectrum 502 (T.sub.2) generated from a second ICE in an optical
computing device (e.g., ICE 100-1, ICE 100-2, and optical computing
device 101, cf. FIG. 1), for methane measurement. The ordinates in
chart 500 indicate a transmittance value in arbitrary units (To,
Tm). The abscissae (.lamda..sub.0, .lamda..sub.m) in chart 500 may
be as described above (cf. charts 300 and 400, cf. FIGS. 3 and 4).
Accordingly, transmission spectra 501 and 502 may be obtained to
cooperatively produce a regression vector that is similar to the
optimal regression vector in a methane concentration measurement
configuration. The number of layers and their thickness (in
nanometers, nm) in the first ICE may be different from those of the
second ICE. In fact, each of the first and second ICEs may be
completely different from one another, and yet both ICEs 100-1 and
100-2 may be cooperatively or independently configured to measure
the sample characteristic (e.g., methane concentration).
[0045] FIG. 6 illustrates a chart 600 with a regression vector 601
for a methane concentration optical computing device and an optimal
regression vector 602. The abscissae (.lamda..sub.0, .lamda..sub.m)
in chart 600 may be as described above (e.g., charts 300 through
500, cf. FIGS. 3-5). The ordinates in chart 600 may be positive and
negative, covering a range (-R.sub.m, R.sub.m), where
|R.sub.m|.ltoreq.1.
[0046] In some embodiments, regression vector 601 (V.sub.r601) may
be computed as a solution to a multilinear regression (MLR)
targeting the sample characteristic using the convolved spectra
401, the sample library, and the ICE transmission spectra (e.g.,
transmission spectra 501 and 502, cf. FIG. 5). As a result, vector
V.sub.r601 may be expressed as follows:
{right arrow over (V)}r.sub.601=.beta..sub.1{right arrow over
(T)}.sub.1+.beta..sub.2{right arrow over (T)}.sub.2 (1)
[0047] where .beta..sub.1 and .beta..sub.2 are regression
coefficients obtained through the MLR solution. Regression vector
601 may have positive and negative components when the values of
.beta..sub.1 and .beta..sub.2 have opposite sign (i.e.,
.beta..sub.1=6.3, and .beta..sub.2=-8.9). The result of the MLR
solution using regression vector 601 may be expressed as a linear
expression for the methane concentration value, y, of a sample
having a transmission spectrum, S, as:
y=.gamma..sub.r({right arrow over (V)}.sub.r601{right arrow over
(S)})+.alpha..sub.r (2)
[0048] where slope (.gamma..sub.r) indicates the sensitivity of the
methane measuring optical computing device, and .alpha..sub.r is a
constant indicative of a neutral calibration adjustment. A
measurement accuracy of the optical computing device may be the
standard error of correction (SEC) obtained when all or nearly all
of spectra 401 (cf. FIG. 4) are considered as vector S, in Eq.
2.
[0049] Having obtained linear regression coefficients .gamma..sub.r
and .alpha..sub.r (cf. Eq. 2) and regression vector 601 (V.sub.r).
Processor 161 in optical computing device 101 may be configured to
perform the following operation with sensing signals 135-1
(s.sub.1) and 135-2 (s.sub.2):
y=.gamma..sub.r(.beta..sub.1s.sub.1+.beta..sub.2s.sub.2)+.alpha..sub.r
(3)
[0050] wherein s.sub.1={right arrow over (T)}.sub.1{right arrow
over (S)}, and s.sub.2={right arrow over (T)}.sub.2{right arrow
over (S)} (cf Eqs. 1 and 2). Optimal regression vector 602
(V.sub.optimal) is obtained with a partial least squares (PLS)
solution to the methane library (e.g., using spectra 301, cf. FIG.
3). Accordingly, the PLS solution renders a linear expression for
the methane concentration, y, as follows:
y=.gamma..sub.opt({right arrow over (V)}.sub.optimal{right arrow
over (S)})+.alpha..sub.opt (4)
[0051] vector S is as described above (cf. Eq. 2), slope
(.gamma..sub.opt) indicates an optimal sensitivity of the methane
measuring optical computing device, and .alpha..sub.opt is a
constant indicative of a neutral calibration adjustment specific to
the optimal solution expressed by Eq. 3. An optimal measurement
accuracy may be the standard error of correction (SEC) obtained
when all or nearly all of spectra 401 are considered in Eq. 4. In
some embodiments, a PLS accuracy and sensitivity may be considered
the optimal performance for an optical computing device.
Accordingly, optimal regression vector 602 (V.sub.optimal) is a
target shape to which regression 601 (V.sub.r) is desirably
similar, if not exactly identical. In some embodiments, the number
of layers and layer thicknesses of ICE 100-1 and ICE 100-2, are
selected to provide transmission spectra 501 (T.sub.1) and 502
(T.sub.2) such that the difference between regression vector 601
(V.sub.r, cf. Eq. 1) and optimal regression vector 602
(V.sub.optimal, cf. Eq. 4) is less than a pre-selected tolerance.
Accordingly, regression vector 601 may approximate the positive and
negative lobes, and the high frequency features of optimal
regression vector 602 (cf, ripples in optimal regression vector
602). It is noted that, in the above method, the particular number
of ICE devices to be used in Eq. 1 (i.e., two) is selected at an
early modeling stage of the optical computing device. In general,
and consistent with embodiments disclosed herein, the number of
ICEs used in the optical computing device may be any number greater
than 2.
[0052] The values of .gamma..sub.r and .alpha..sub.r may be
similar, but not necessarily equal, to .gamma..sub.opt and
.alpha..sub.opt, respectively. In some embodiments, memory 162
stores coefficients .gamma..sub.opt, .gamma..sub.r,
.alpha..sub.opt, and .alpha..sub.r. An optical computing device for
methane measurement using ICEs 100-1 and 100-2 as disclosed herein
(i.e., .beta..sub.1=6.3, and .beta..sub.2=-8.9) provides an
accuracy and sensitivity of 6.3% and 0.0347, which is close to the
PLS limits of 6.3% and 0.0349, respectively. Thus, a dual-ICE
optical computing device as disclosed herein may closely reproduce
the performance of a high fidelity PLS solution to a methane
measurement task.
[0053] For the PLS regression leading to optimal regression vector
602, some embodiments select an appropriate number of principal
components according to the sample library and the desired sample
characteristic. The complexity of the measurement solution is
determined by the nature and quality of the sample library, and is
reflected in the number of principal components used by the PLS
regression to attain the optimal performance. In general, the
performance of the PLS regression is improved by increasing the
number of principal components, up to a point where further
addition of principal components results in negligible performance
improvement. In some embodiments, a larger number of principal
components in the PLS regression leads to optimal regression vector
602 having multiple positive and negative lobes, and multiple
ripple features. In such situations, it may be desirable to select
a larger number of ICE devices in Eq. 1 to match optimal regression
vector 602, as compared to situations in which optimal regression
vector 602 is smoother, or in which the PLS regression includes
fewer principal components.
[0054] FIG. 7 illustrates a logging while drilling (LWD) system 700
including a sensor that uses an optical computing device with
multiple ICEs. A downhole tool 730 includes optical computing
device 101 for measuring a selected characteristic of a formation
fluid. Drilling system 700 may be configured to drive a bottom hole
assembly (BHA) 704 positioned or otherwise arranged at the bottom
of a drill string 706 extended into the earth 702 from a derrick
708 arranged at the surface 710. The derrick 708 includes a kelly
712 and a traveling block 713 used to lower and raise the kelly 712
and the drill string 706. The BHA 704 may include a drill bit 714
operatively coupled to a tool string 716 which may be moved axially
within a drilled wellbore 718 as attached to drill string 706.
During operation, drill bit 714 penetrates earth 702 and thereby
creates wellbore 718. BHA 704 provides directional control of drill
bit 714 as it advances into earth 702. Tool string 716 can be
semi-permanently mounted with various measurement tools such as,
but not limited to, measurement-while-drilling (MWD) and
logging-while-drilling (LWD) tools, and a downhole tool 730.
Downhole tool 730 may be configured to take downhole measurements
of drilling conditions using an optical computing device having
multiple ICEs, as disclosed herein (e.g., optical computing device
101, cf. FIG. 1). In some embodiments, downhole tool 730 may be
self-contained within tool string 716, as shown.
[0055] Fluid or "mud" from a mud tank 720 may be pumped downhole
using a mud pump 722 powered by an adjacent power source, such as a
prime mover or motor 724. The mud may be pumped from mud tank 720,
through a stand pipe 726, which feeds the mud into the drill string
706 and conveys the same to the drill bit 714. The mud exits one or
more nozzles arranged in the drill bit 714 and in the process cools
drill bit 714. After exiting drill bit 714, the mud circulates back
to surface 710 via the annulus defined between wellbore 718 and
drill string 706, and in the process, returns drill cuttings and
debris to the surface. The cuttings and mud mixture are passed
through a flow line 728 and are processed such that a clean mud is
returned down hole through stand pipe 726 once again.
[0056] Downhole tool 730 may be controlled from the surface 710 by
a controller 760 having a processor 761 and a memory 762.
Controller 760, processor 761, and memory 762 may be as those in
any optical computing device as disclosed herein (e.g., controller
160, processor 161, and memory 162, cf. FIG. 1). Accordingly,
memory 762 may store commands that, when executed by processor 761,
cause controller 760 to perform at least some steps in methods
consistent with the present disclosure. For example, as a result of
a value measured for the selected characteristic of a formation
fluid by optical computing device 101, controller 760 may adjust or
modify a drilling parameter in drilling system 700. Modifying a
drilling parameter in drilling system 700 may include adjusting a
drill speed, adjusting a flow rate of the drilling mud or modifying
a drilling direction for drill bit 714 (e.g., from horizontal to
vertical or vice versa). In some embodiments, modifying a drilling
parameter may include injecting an additive to the drilling mud to
regulate the temperature of drill bit 714, or to improve the
quality of the mud or the extracted hydrocarbon, or to prevent the
extracted fluid from foaming or forming solid condensates along
wellbore 718.
[0057] FIG. 8 illustrates a wireline system 800 configured to
measure a characteristic of a sample during formation testing and
sampling with an optical computing device 101. Wireline system 800
may be configured to use a formation tester and calibrated optical
tool in determining types of formation fluids and the associated
characteristics through sampling after drilling of wellbore 718 is
complete. System 800 may include a downhole tool 802 that forms
part of a wireline logging operation that can include one or more
dual-ICE optical computing devices 101, as described herein, as
part of a downhole measurement tool. System 800 may include derrick
708 supporting traveling block 713. Wireline logging tool 802, such
as a probe or sonde, may be lowered by wireline or logging cable
806 into wellbore 718. Tool 802 may be lowered to the potential
production zone or the region of interest in the wellbore, and used
in conjunction with other components of the formation tester such
as packers and pumps to perform well testing and sampling.
[0058] Optical computing device 101 measures a selected
characteristic of the formation fluids. Measurement data generated
by optical computing device 101 may be real-time processed for
decision-making in the downhole. In some embodiments, measurements
from optical computing device 101 are communicated to a surface
logging facility 808 for storage, processing, and/or analysis.
Logging facility 808 may be provided with controller 860, including
a processor 861 and a memory 862 (e.g., controllers 160 and 760,
processors 161 and 761, and memories 162 and 762, cf. FIGS. 1 and
7). Memory 862 stores data and commands which, when executed by
processor 861, cause controller 860 to direct wireline system 800
to perform steps in methods consistent with the present
disclosure.
[0059] FIG. 9 illustrates a flow chart including steps in a method
900 for fabricating an optical computing device. The optical
computing device may include optical components, a plurality of
ICEs, one or more detectors, and a controller having a processor
and a memory (e.g., multiplexer 110, ICEs 100, detectors 130,
controller 160, processor 161, and memory 162, in optical computing
device 101, cf. FIG. 1). The memory in the controller may include
commands which, when executed by the controller, cause the optical
computing device to measure a selected sample characteristic.
Furthermore, in some embodiments the optical computing device may
be part of a system for measuring the selected sample
characteristic using a light source to interact an illumination
light with the sample and generate a sample light (e.g., system 10,
light source 140, illumination light 141, sample 150, and sample
light 142, cf. FIG. 1). Method 900 may be performed using a
plurality of spectra and convolved spectra from calibrated data
samples of a plurality of reference fluids in a sample library
(e.g., spectra 301, convolved spectra 401, cf. FIGS. 3 and 4).
Methods consistent with the present disclosure may include at least
some, but not all of the steps illustrated in method 900, performed
in a different sequence. Furthermore, methods consistent with the
present disclosure may include at least two or more steps as in
method 900 performed overlapping in time, or almost
simultaneously.
[0060] Step 902 includes generating at least one initial ICE model.
In some embodiments, step 902 includes generating an initial ICE
model having a random number of layers where each layer has a
random thickness. In other embodiments, however, step 902 includes
generating multiple initial ICE models. Accordingly, step 902 may
include generating a number of initial ICE models as low as two and
as large as practically feasible in an optical computing device
(e.g., twenty or more). Note that generating more initial ICE
models in step 902 may be desirable to allow greater flexibility in
finding a suitable combination of optical computing devices.
[0061] Step 904 includes determining a sensor response from the
convolved spectra from the sample library with respect to a desired
sample characteristic (e.g., an analyte concentration, and the
like), and from the initial ICE models. In some embodiments, step
904 includes projecting an ICE transmission vector from each
initial ICE model against the convolved spectra. For example, step
904 includes obtaining the dot product between the ICE transmission
profile and the convolved spectra. In some embodiments, step 904
may include forming the convolved spectra by convolving a fluid
transmission data in the plurality, of spectra from the sample
library with radiometric contributions involved in the optical path
of the optical computing device. Some of the radiometric
contributions considered in the convolved spectra may include,
without limitation a spectral emission of the lamp, the spectral
profile of a band pass filter, of the windows or other optical
elements in the optical computing device, a spectral profile of the
detector efficiency, and the like.
[0062] Step 904 includes determining the detector response with the
dot product between each of the multiple initial ICE models and the
convolved spectra. Accordingly, the sensor response includes a
plurality of values associated with a signal from each of the
plurality of detectors in the optical computing device. In optical
computing devices using a reduced number of detectors (e.g., one
detector and multiple signals from each of multiple modified
lights), the sensor response may include the multiple signals
collected by the one or fewer detectors.
[0063] Step 906 includes determining a regression vector based on a
multilinear regression (e.g., an MLR) that targets a sample
characteristic (e.g., a measured concentration of an analyte of
interest) with the sensor response and the sample library. For
example, in some embodiments step 906 includes applying an MLR
solution to the sensor response obtained from calibrated spectra
and measured methane concentrations in a methane sample library
(cf. FIGS. 3-6).
[0064] Step 908 includes determining a plurality of regression
coefficients in a linear combination of the plurality of ICE
transmission vectors that results in the regression vector.
Specifically, step 908 may include obtaining a plurality, in, of
regression coefficients (.beta..sub.i, i=1, . . . , m) that can be
applied to the ICE transmission profiles of each one of the initial
ICE models (T.sub.ICE1, i=1, . . . , m) in a linear combination to
define the regression vector, V.sub.r, as follows:
V.sub.r.beta..sub.1T.sub.ICE1+.beta..sub.2T.sub.ICE2+ . . .
.beta..sub.mT.sub.ICEm. (5)
[0065] It is noted that Eq. 5 is a generalization of Eq. 1 for
m-ICES and with respect to any sample characteristic (i.e., not
only methane concentration).
[0066] Step 910 includes comparing the regression vector V.sub.r
obtained in step 906 (cf. Eq. 5), to an optimal regression vector
based on a difference between the regression vector and the optimal
regression vector. In some embodiments, step 910 may include
determining a difference between the regression vector, V.sub.r,
and the optimal regression vector V.sub.optimal. The optimal
regression vector, V.sub.optimal, may be obtained using a PLS
method applied to the convolved spectral data set and the
calibration library, and targeting the desired sample
characteristic. Accordingly, step 910 may include selecting a
merit-function as a mean squared error (MSE) between V.sub.r and
V.sub.optimal, as follows:
MSE = N ( V r i - V ideal i ) 2 ( 6 ) ##EQU00001##
[0067] Where N is the dimension of vectors V.sub.r and
V.sub.optimal, which is equal to the number of wavelength entries
in the spectra of FIGS. 3-6.
[0068] Step 912 includes modifying the ICE models to improve
regression vector, V.sub.r, based on the optimal regression vector.
In some embodiments, step 910 may include modifying the number and
thickness of the material layers in at least one or more of the
initial ICE models based on the MSE merit-function cf. Eq. 6).
Accordingly, the number and thickness of each of the material
layers in each of the initial ICE models is adjusted to reduce, or
minimize, the merit-function in Eq. 6.
[0069] In some embodiments, step 912 may include minimizing the
merit-function by iteratively modifying at least one of the number
of layers and thicknesses of the `in` initial ICE models. After
modifying the number and thickness of at least one the `m` initial
ICE models, methods consistent with the present disclosure may
iterate steps 906 through 912 to generate a new set of transmission
spectra and resulting regression vector, V.sub.r. Accordingly, in
some embodiments step 912 includes repeating iteration cycles of
steps 906 through 912, until the merit function is lower than, or
equal to, a pre-selected tolerance. In some embodiments, the
pre-selected tolerance may indicate that vectors V.sub.r and
V.sub.optimal are within a selected distance from one another,
where the selected distance is given in a pre-determined metric of
the N-dimensional space for vectors V.sub.r and V.sub.optimal (cf
Eq. 6).
[0070] In some embodiments, method 900 iterates the plurality of
`In` ICE models in view of the merit-function to yield a regression
vector V.sub.r that can be incorporated into the controller
processor, or memory. Accordingly, method 900 may further include
the step of storing a plurality of coefficients and of spectral
profiles for the m-ICE models (e.g., coefficients .beta..sub.1, . .
. , .beta..sub.m, and spectral profiles, T.sub.ICE1, . . . ,
T.sub.ICEm, cf. Eq. 5) in the controller processor, or the
controller memory, for data processing. The resulting SEC and
sensitivity of the optical computing device may be substantially
close to the optimal limit.
[0071] Step 914 includes fabricating a plurality of ICEs according
to the modified ICE models when the regression vector is within the
selected tolerance from the optimal regression vector. In some
embodiments, step 914 may include forming combinatorial
configurations between different ICEs from a fabrication batch for
each of the plurality of ICEs, and qualifying the measurement
performance of an optical computing device having each of the
multiple combinatorial configurations. Accordingly, step 914
includes assembling an optical computing device using the
combinatorial configuration of multiple post-fabrication ICEs that
shows the best performance. Step 914 includes measuring the
performance of a post-fabrication combinatorial configuration of
the multiple ICEs using a measured accuracy and sensitivity of the
post-fabrication optical computing device.
[0072] For example, in some embodiments step 914 includes measuring
at least some of the calibrated physical samples associated with
the sample library using the post-fabrication optical computing
device and finding the accuracy and sensitivity obtained from a
linear regression analysis as described herein (cf. Eq. 2).
[0073] In some embodiments, step 914 may include fabricating one or
more of the plurality of ICEs sequentially and re-modeling the ICEs
that have not yet been fabricated based on the performance of the
fabricated ICEs. For example, when the target is a multiple ICE
optical computing device having m-ICEs (cf FIG. 1), step 914 may
include fabricating a first ICE from the `m` models obtained
through step 912. Based on the post-fabrication spectral
performance of the first ICE in Eqs. 5 and 6, step 914 may include
slightly modifying the remaining `m-1` ICE models according to
steps 904 through 912 in order to further reduce the value of the
merit-function (cf Eq. 6). This sequence is repeated in step 914
for the second ICE, the third ICE, and so on until all `m` ICE
models have been fabricated and the post-fabrication analysis
renders satisfactory results.
[0074] Those skilled in the art will readily appreciate that the
methods described herein, or large portions thereof may be
automated at some point such that a computerized system may be
programmed to transmit data from an optical computing device using
an ICE element. Computer hardware used to implement the various
methods and algorithms described herein can include a processor
configured to execute one or more sequences of instructions,
programming stances, or code stored on a non-transitory,
computer-readable medium. The processor can be, for example, a
general purpose microprocessor, a microcontroller, a digital signal
processor, an application specific integrated circuit, a field
programmable gate array, a programmable logic device, a controller,
a state machine, a gated logic, discrete hardware components, an
artificial neural network, or any like suitable entity that can
perform calculations or other manipulations of data. In some
embodiments, computer hardware can further include elements such
as, for example, a memory (e.g., random access memory (RAM), flash
memory, read only memory (ROM), programmable read only memory
(PROM), electrically erasable programmable read only memory
(EEPROM)), registers, hard disks, removable disks, CD-ROMS. DVDs,
or any other like suitable storage device or medium.
[0075] Executable sequences described herein can be implemented
with one or more sequences of code contained in a memory. In some
embodiments, such code can be read into the memory from another
machine-readable medium. Execution of the sequences of instructions
contained in the memory can cause a processor to perform the
process steps described herein. One or more processors in a
multi-processing arrangement can also be employed to execute
instruction sequences in the memory. In addition, hard-wired
circuitry can be used in place of or in combination with software
instructions to implement various embodiments described herein.
Thus, the present embodiments are not limited to any specific
combination of hardware and/or software.
[0076] As used herein, a machine-readable medium will refer to any
medium that directly or indirectly provides instructions to a
processor for execution. A machine-readable medium can take on many
forms including, for example, non-volatile media, volatile media,
and transmission media. Non-volatile media can include, for
example, optical and magnetic disks. Volatile media can include,
for example, dynamic memory. Transmission media can include, for
example, coaxial cables, wire, fiber optics, and wires that form a
bus. Common forms of machine-readable media can include, for
example, floppy disks, flexible disks, hard disks, magnetic tapes,
other like magnetic media, CD-ROMs, DVDs, other like optical media,
punch cards, paper tapes and like physical media with patterned
holes, RAM, ROM, PROM, EPROM and flash EPROM.
[0077] Embodiments disclosed herein include:
[0078] A. A method, including generating a plurality of integrated
computational element (ICE) models and determining a sensor
response from a projection of a plurality of ICE transmission
vectors associated with the ICE models and a convolved spectrum
associated with a sample library. The method may also include
determining a regression vector based on a multilinear regression
that targets a sample characteristic from the sample library and
the sensor response, and determining a regression coefficient for
each of the plurality of ICE transmission vectors in a linear
combination that results in the regression vector. In some
embodiments, the method includes determining a difference between
the regression vector and an optimal regression vector associated
with the sample characteristic and modifying the plurality of ICE
models when the difference between the regression vector and the
optimal regression vector is greater than a selected tolerance.
Further, the method may include fabricating a plurality of ICEs
based on the plurality of ICE models when the difference between
the regression vector and the optimal regression vector is within
the selected tolerance.
[0079] B. An optical computing device, including at least two
integrated computational elements (ICEs) positioned to optically
interact with sample light to generate a first modified light from
a first ICE and a second modified light from a second ICE. The
optical computing device may also include a detector that
separately measures the first modified light to provide a first
signal and the second modified light to provide a second signal. In
some embodiments, each one of the at least two ICEs includes a
plurality of alternating layers of material and each layer of
material has a thickness selected such that a linear combination of
the first signal with the second signal is proportional to a sample
characteristic.
[0080] C. A system, including a light source that generates an
illumination light to interact with a sample and form a sample
light, an optical computing device, and a controller. The optical
computing device includes at least two integrated computational
elements (ICEs) positioned to optically interact with the sample
light to generate a first modified light from a first ICE and a
second modified light from a second ICE, and a detector that
separately measures the first modified light to provide a first
signal and the second modified light to provide a second signal.
Each one of the at least two ICEs includes a plurality of
alternating layers of material and each layer of material has a
thickness selected such that a linear combination of the first
signal with the second signal is proportional to a sample
characteristic. The controller includes a processor and a memory,
wherein the processor forms the linear combination of the first
signal and the second signal based on at least two regression
coefficients associated with the at least two integrated
computational elements (ICEs) stored in the memory.
[0081] Each of embodiments A, B, and C may have one or more of the
following additional elements in any combination:
[0082] Element 1, wherein generating the plurality of ICE models
includes selecting a random number of layers and a random thickness
for each layer in each ICE model. Element 2, wherein modifying the
plurality of ICE models includes: modifying a number of layers and
a thickness for each layer for at least one of the plurality of ICE
models to obtain a plurality of modified ICE models, determining a
modified sensor response from the plurality of modified ICE models
and the convolved spectrum associated with the sample library,
determining a modified regression vector from the plurality of
modified ICE models and the modified sensor response, determining a
difference between the modified regression vector and the optimal
regression vector, iteratively repeat the modifying the number of
layers, the determining a modified sensor response, the determining
a modified regression vector, and the determining a difference
between the modified regression vector and the optimal regression
vector until the difference between the modified regression vector
and the optimal regression vector is within the selected tolerance,
and fabricating the plurality of ICEs based on the plurality of
modified ICE models. Element 3, wherein determining a difference
between the regression vector and the optimal regression vector
includes determining a mean square error between the regression
vector and the optimal regression vector. Element 4, further
including determining the optimal regression vector from a partial
least squares model of the convolved spectrum and the sample
library, targeting the sample characteristic. Element 5, wherein
determining the regression vector and the plurality of regression
coefficients comprises calibrating an optical computing device with
the plurality of ICEs and with the sample library. Element 6,
further including determining an accuracy and a sensitivity of an
optical computing device that includes the plurality of ICEs based
on the regression vector and the sample library. Element 7, further
including storing in a memory the plurality of regression
coefficients for each ICE transmission vector when the difference
between the regression vector and the optimal regression vector is
within the selected tolerance. Element 8, further including
measuring a spectral performance of each of the ICEs in a
fabrication batch of the plurality of ICEs, selecting a combination
of ICEs from the fabrication batch based on the spectral
performance, and disposing the combination of ICEs in an optical
computing device that measures the sample characteristic. Element
9, wherein fabricating the plurality of ICEs includes measuring a
performance of a post-fabrication combinatorial configuration
between different ICEs from a fabrication batch for each of the
plurality of ICEs. Element 10, wherein fabricating the plurality of
ICEs includes fabricating one or more of the plurality of ICEs
sequentially, and re-modeling an ICE that has not been fabricated
based on a post-fabrication spectral performance of the one or more
of the plurality of ICEs.
[0083] Element 11, further including a multiplexer that directs a
first portion of sample light to the first ICE and a second portion
of sample light to the second ICE. Element 12, wherein the detector
includes a first detector to measure the first modified light, and
a second detector to measure the second modified light, the first
detector being spatially separated from the second detector.
Element 13, wherein the detector measures the first modified light
and the second modified light separated in time.
[0084] Element 14, wherein the optical computing device further
comprises a multiplexer that directs a first portion of the sample
light to the first ICE and a second portion of the sample light to
the second ICE. Element 15, wherein the detector in the optical
computing device comprises a first detector to measure the first
modified light, and a second detector to measure the second
modified light, the first detector being spatially separated from
the second detector. Element 16, wherein the detector in the
optical computing device measures the first modified light and the
second modified light separated in time. Element 17, wherein the at
least two ICEs comprise more than two ICEs but less than a number
of principal components in a partial least squares regression model
used to determine an optimal regression vector for the sample
characteristic.
[0085] Therefore, the present disclosure is well adapted to attain
the ends and advantages mentioned as well as those that are
inherent therein. The particular embodiments disclosed above are
illustrative only, as the present disclosure may be modified and
practiced in different but equivalent manners apparent to those
skilled in the art having the benefit of the teachings herein.
Furthermore, no limitations are intended to the details of
construction or design herein shown, other than as described in the
claims below. It is therefore evident that the particular
illustrative embodiments disclosed above may be altered, combined,
or modified and all such variations are considered within the scope
and spirit of the present disclosure. The disclosure illustratively
disclosed herein suitably may be practiced in the absence of any
element that is not specifically disclosed herein and/or any
optional element disclosed herein. While compositions and methods
are described in terms of "comprising," "containing," or
"including" various components or steps, the compositions and
methods can also "consist essentially of" or "consist of" the
various components and steps. All numbers and ranges disclosed
above may vary by some amount. Whenever a numerical range with a
lower limit and an upper limit is disclosed, any number and any
included range falling within the range is specifically disclosed.
In particular, every range of values (of the form, "from about a to
about b," or, equivalently, "from approximately a to b," or,
equivalently, "from approximately a-b") disclosed herein is to be
understood to set forth every number and range encompassed within
the broader range of values. Also, the terms in the claims have
their plain, ordinary meaning unless otherwise explicitly and
clearly defined by the patentee. Moreover, the indefinite articles
"a" or "an," as used in the claims, are defined herein to mean one
or more than one of the element that it introduces. If there is any
conflict in the usages of a word or term in this specification and
one or more patent or other documents that may be incorporated
herein by reference, the definitions that are consistent with this
specification should be adopted.
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