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Design of a portable infrared spectrometer: application to the noninvasive measurement of glucose

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Design of a portable infrared spectrometer: application to the noninvasive measurement of glucose

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Content DESIGN OF A PORTABLE INFRARED SPECTROMETER:
APPLICATION TO THE NONINVASIVE MEASUREMENT OF GLUCOSE
by
Mark Anthony Sisson
A Thesis Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(Biomedical Engineering)
December 1994
Copyright 1994 Mark Anthony Sisson
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This thesis, written by
Mark Anthony Sisson
under the guidance of Faculty Committee and
approved by all its members, has been presented to
and accepted by the School of Engineering in partial
fulfillment of the requirements for the degree of
MASTER OF SCIENCE
BIOMEDICAL ENGINEERING
Date 4 -r^ V j
Faculty Committee
X,
/ l A ' U ' c A v i u A Ottko
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Acknowledgments
I would like to thank my thesis committee for their guidance during my research.
I thank Professor Jean-Michel Maarek for his advice throughout the writing of this
thesis and Professor Michael Khoo for inspiration in his class to reach deeper to
understand not only how but why. Special thanks go to Dr. Vasilis Marmarelis,
the Department Head of the Biomedical Engineering Department at USC for his
faith in my abilities.
Thanks to Dr. Mark Arnold, Associate Professor of Chemistry at the University of
Iowa. Mark's dedication to his work and well thought out research plan is an
inspiration to the scientific community. Kevin Hazen, a bright young doctoral
student of Professor Arnold's was extremely helpful in not only his technical
capabilities but being someone to bounce ideas off of.
Special acknowledgment goes to my family, especially my wife Lee Ann. Thanks
for the many times watching the boys while I was studying and doing my
research. To my sons, Ryan and Reid, thanks for trying to understand why Dad
couldn't go to the park or play ball because he had studying to do, I hope
someday my hard work will rub off on you two.
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Contents
Introduction......................................................................................................1
1 Background...................................................................................................... 3
2 Theory of Measuring Glucose Using NIR Spectroscopy.......................... 5
2.1 Reflectance versus Transmittance Measurements................................. 6
2.2 Glucose Spectra..........................................................................................9
3 Michelson Interferometer - Theory of Operation...................................... 11
3.1 Resolution...................................................................................................12
3.2 Apodization.................................................................................................14
3.3 Phase Correction.......................................................................................14
3.4 Beam Divergence......................................................................................15
3.5 Mirror Misalignment.................................................................................. 16
3.6 Sampling..................................................................................................... 17
3.7 Dynamic Range......................................................................................... 17
4 Measurement of Glucose Noninvasively Using a Fourier
Transform Spectrometer..............................................................................19
4.1 Apparatus.................................................................................................. 23
4.2 Procedure...................................................................................................24
4.3 Instrument Parameters.............................................................................24
4.3.1 Source.........................................................................................25
4.3.2 Beamsplitter................................................................................ 25
4.3.3 Mirrors..........................................................................................26
4.3.4 Detector...................................................................................... 26
5 Instrument Design......................................................................................... 28
5.1 Infrared Radiation Source........................................................................28
5.2 Beamsplitter............................................................................................... 31
5.3 Mirrors.........................................................................................................33
5.4 Detector......................................................................................................34
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5.4.1 PbS Detector.............................................................................. 37
5.4.2 InGaAs Detector......................................................................... 38
5.4.3 Detector Summary......................................................................39
5.5 Interferometer.............................................................................................39
5.5.1 Optical Path Difference and Spectral Resolution...................41
5.5.2 Beam Diameter........................................................................... 42
5.5.3 Parameter Optimization.............................................................43
5.6 Instrument Design Summary.....................................................................45
6 Data Processing Techniques...................................................................... 47
6.1 PLS Regression................ 47
6.2 Digital Filtering............................................................................................48
6.3 Conclusion.................................................................................................. 51
7 Conclusions...................................................................................................52
Bibliography...................................................................................................54
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LIST OF FIGURES
2.1 D-Glucose, anhydrous (dextrose) molecule...................................................... 6
2.2 Typical NIR spectroscopic measurement techniques......................................7
2.3 Absorbance peak locations of major constituents in a possible
bioreactor solution..............................................................................................10
3.1 Schematic diagram of a Michelson interferometer......................................... 11
3.2 Simple spectra and its interferogram................................................................12
4.1 Concentration plot for the glucose calibration model in an aqueous
solution over the 4850 - 4250 cnr1 spectral range using Fourier
filtering and 6 PLS factors................................................................................ 20
4.2 Concentration plot for the glutamine calibration model in an
aqueous solution over the 4700 - 4320 cm-1 spectral range using
Fourier filtering and 7 PLS factors.................................................................. 20
4.3 Concentration plot for the glucose calibration model in a buffered
protein matrix over the 4600 - 4200 cm-1 spectral range using
Fourier filtering and 12 PLS factors................................................................ 21
4.4 Concentration plot for the glucose calibration model in a bovine
plasma matrix over the 5000 - 4002 cm*1 spectral range using
Fourier filtering and 10 PLS factors................................................................ 22
4.5 Estimated vs. measured glucose concentrations in a bovine plasma
matrix from a Beckman-Astra glucose analyzer over the 5000 -
4002 cm-1 spectral range using Fourier filtering and 18 PLS
factors..................................................................................................................22
4.6 Percent error of prediction variation for 3.09 to 17.98 mM glucose
concentrations over the spectral region 4850 - 4220 cnr1-........................ 23
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4.7 Theoretical calculations of beamsplitter efficiency vs. wavelength
for a CaF2 beamsplitter with a 2.5-pm air gap between the film and
compensator plate.............................................................................................26
4.8 Typical spectral response of an InSb detector................................................ 27
5.1 Infrared radiation source schematic..................................................................31
5.2 Effective indices as a function of the index of refraction for a BK7
glass cube...........................................................................................................32
5.3 Reflectivities of Aluminum, Silver, and Gold mirror surfaces at
various wavelengths..........................................................................................34
5.4 Spectral response of a PbS cell........................................................................ 38
5.5 Current and anticipated spectral response characteristics of an
InGaAs cell at 25°C...........................................................................................39
5.6 Interferometer utilizing one rotating retroreflector is shown in both
its extreme positions......................................................................................... 41
5.7 Ray tracing on the plane mirror. The dashed ellipse is the
projection on the retroreflector and the solid ellipse represents the
track of the exit ray. The point E is the entrance projection point............... 43
5.8 Geometrical parameters for an interferometer with a 5 inch
retroreflector....................................................................................................... 44
5.9 Proposed spectrometer utilizing one rotating retroreflector...........................45
6.1 Response surface for glucose. 4 PLS factors were used over the
spectral range from 4850 - 4250 cnrr1. The glutamine response
surfaces used 5 PLS factors over the spectral range from 4700 -
4320 cm*1........................................................................................................... 50
6.2 Response surface for glutamine. 5 PLS factors were used over the
spectral range from 4700 - 4320 cnrr1............................................................ 50
Table 5.1 Types and characteristics of infrared detectors................................. 36
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Glossary of Terms
Apodization
Suppression of the magnitude of the side-lobes of a sine function.
Absorbance
Logarithm of the reciprocal of the transmittance.
Beam Divergence
The beam angle created by an uncollimated source.
D* (D-Star)
The D* is the detectivity of a detector that indicates the S/N ratio when
radiant energy of 1W is incident on the detector. Since the D* is normalized
by an active area of 1cm2 and a noise bandwidth of 1 Hz, it is independent
of the size and shape of the active element. The higher the D* value, the
better the detector.
Diffuse Reflectance
Energy that escapes from the surface of a sample after having penetrating
the sample.
Dynamic Range
The degree of accuracy the amplitude of the interferogram is sampled at.
Internal Reflectance
Energy that passes through the sample, reflects from the substrate, and
passes back through the sample.
Mertz Phase Correction
The process of removing unwanted sine components from an interferogram.
The Mertz method uses an amplitude spectrum calculated with reference to
a point of stationary phase. The calculated amplitude spectrum is multiplied
at each frequency by the cosine of the difference between the measured
phase angle and the reference phase angle.
Michelson Interferometer
A device that can split a beam of radiation into two paths and then
recombine them so that the intensity variations of the exit beam can be
measured as a function of pathlength difference.
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Noise Equivalent Power (NEP)
The radiant power that produces a signal-to-noise ratio of 1 at the detector
output.
Partial Least Squares (PLS) Regression
A statistical technique involving least squares regression used for
processing spectral data.
Photoconductlve Detector
A semiconductor detector whose resistance decreases with an increase in
light intensity.
Photovoltaic Detector (Photodiode)
A semiconductor detector that converts radiant energy into current or
voltage when radiant flux enters its PN junction.
Retardation
Change in the optical pathlength caused by the mirror movement of an
interferometer.
Specular Reflectance
Energy reflected directly from the outside of a surface.
Spectral Resolution
Resolving ability of the spectrometer measured in wavenumber (cm'1).
Transmittance
The ratio of the radiant energy transmitted through a sample to the radiant
energy impinging on the sample.
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Abstract
This thesis describes the design of a portable spectrometer capable of operating
in the near-infrared (NIR) spectral region. A potential use for this device is the
noninvasive measurement of glucose and glutamine for use in fed-batch
bioreactors. The instrument accuracy and resolution is based on research that
has been conducted by the Chemistry Department at the University of Iowa using
NIR for glucose measurements. The instrument is based on a Michelson type
interferometer utilizing a rotating retroreflector with a PbS detector yielding
spectral resolutions down to 0.1 cm*1 and specific detectivities (D*) of 4 x 1011.
These components allow for a rugged, compact, inexpensive device.
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INTRODUCTION
The purpose of this thesis is to present a possible design for a portable infrared
spectrometer that can be used for the noninvasive measurement of glucose and
glutamine. The instrument parameters are based upon successful results from a
laboratory bench-top infrared spectrometer used by researchers at the University
of Iowa's Chemistry Department.
Chapter 1 presents background information as well as, previous and future uses
of infrared spectroscopy and in particular near-infrared spectroscopy.
Chapter 2 presents the theoretical principles utilized when applying near-infrared
spectroscopic techniques to the measurement of glucose.
Chapter 3 describes the operational theory of a Michelson interferometer. The
capabilities and limitations of this type of instrument such as maximum resolution,
methods to correct for apodization, phase correction, allowable beam divergence,
effects of mirror misalignment, maximum sampling rates and dynamic range are
discussed.
Chapter 4 discuses the research carried out at the University of Iowa and
establishes the minimum instrument criteria required for noninvasive glucose and
glutamine measuring. Instrument characteristics such as the radiation source,
beamsplitter, mirrors, and detector are presented.
Chapter 5 presents the design of the portable spectrometer. The requirements
for the infrared radiation source and a possible candidate are discussed. The
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beamsplitter requirements are given and a method for optimizing performance is
shown. A comparison of mirror coatings is examined for optimal performance.
Several detector types are discussed and a current off-the-shelf model is chosen
as a possible candidate. An interferometer using a rotating retroreflector is
examined and maximum resolutions are presented.
Chapter 6 discusses the data processing techniques required for constructing a
calibration model. The technique uses digital filtering of the raw spectral data
and partial least squares regression to establish the calibration model.
Chapter 7 presents the thesis conclusions. A comprehensive list of the reference
materials used to prepare the thesis is presented in the bibliography.
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CHAPTER 1
Background
During the beginning of the 19th century, the English astronomer Sir William
Herschel was attempting to determine which color within the visible spectrum
was responsible for the heat in sunlight. Using a prism to separate the sun's
colors, he moved a thermometer from one color to the next. It was not until he
placed the thermometer below the red end of the spectrum did the temperature
begin to rise. Because he couldn't see this light he named it infrared (IR), using
the Latin prefix meaning below.
It wasn't until about 1900 that Coblentz built an IR spectrometer with a rock salt
prism. He measured the spectra of several hundred compounds in the 1-15
micrometer (pm) range. He discovered that no two compounds have the same
spectra. He also found certain spectral patterns existed and compounds that
have similar chemical groupings have similar absorption bands. This observation
paved the way for chemists to identify the structure of a compound by its spectra.
Prior to World War II, the near-infrared (NIR) region of the spectrum was
considered to be of little use for compositional spectroscopy. Since the NIR
region consisted of frequency overtones and combination bands in a narrow
region (750 - 3000 nm) the difficulties associated with overlapping and resolution
were enormous.
In the late 1960s, Karl Norris, considered to be the "father" of NIR, began working
on quantitative measurements of agricultural products using NIR spectroscopy.
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Norris' work lead to the design of instruments to measure protein, oil, and
moisture in soybeans.
The first commercial NIR spectrometer was produced by Dickey-John in 1971.
Their instrument incorporated a tungsten-halogen source, six research grade
interference filters, and uncooled lead sulfide detectors at 0° and 45°.
Today NIR spectroscopy finds it way into not only the agriculture and food
industries, but the petro-chemical, pharmaceutical, and most recently the medical
industries.
A recent goal of medical researchers is the noninvasive measurement of blood
constituents such as glucose, cholesterol, alcohol, among others. The use of
NIR spectroscopy has recently been accelerated for use in diabetic monitoring.
The ability to measure glucose levels through an appendage would result in ease
of usage for millions of individuals who suffer from diabetes mellitus.
Recently another use for noninvasive monitoring of glucose and glutamine has
surfaced, as a control sensor in fed-batch bioreactors. The manufacture of
products from microorganisms and animal cell cultures grown in a bioreactor has
shown many benefits. Bioreactors operating in the batch mode are limited by
nutrient exhaustion or by-product accumulation. A method to measure and
control the amount of fuel required for the production of bacteria, yeast, insect
cells, and mammalian cells is required. Invasive sensors based on enzymatic
reactions are currently used but require sample withdrawal and exhibit limited
stability. The use of a noninvasive sensor would greatly enhance the scientists
ability to study how cells are grown.
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CHAPTER 2
Theory of Measuring Glucose Using NIR Spectroscopy
Infrared radiation absorbed by an organic molecule is converted into energy of
molecular vibration. The molecules vibrate at frequencies corresponding to
wavelengths in the infrared region of the electromagnetic spectrum. Only
vibrations that result in rhythmic changes in the dipole moment of a molecule can
cause absorbances in the infrared. The vibrational spectra appear as bands
because each single vibrational energy change is accompanied by several
rotational energy changes. These vibrational-rotational bands result in
signatures for particular molecules and molecular bonds. The exact frequency or
wavelength of absorption depends on the relative masses of the molecules, the
force constants of the bonds, and the molecular geometry. Fundamental
absorptions usually occur in the mid-infrared region, 4000 - 400 cnr1 (cm’1 =
104/|im). Changes in the vibrational and rotational energies at higher levels are
known as overtones. As the overtones increase there are dramatic decreases in
the intensities. First and second overtones occur at approximately one half and
one third of the wavelength of the fundamental.
The D-Glucose molecule is shown in Figure 2.1. There are several
characteristics of this molecule that exhibit vibrational tendencies, such as C-H
stretching and vibrational transitions of the O-H bond. When two or more
vibrations occur simultaneously the result is a combination band. Some of the
strongest of the combination bands are found between the wavelengths of the C-
H stretching vibration and its first overtone (between 6600 and 3500 cm'1). The
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carbon-hydrogen stretching vibrations likely correspond to the equatorial C-H
bonds in the pyranose ring and/or the CH2 plane deformation at C-6 in
nonglycosidic glucose.
OH H
OH OH
H OH
Figure 2.1 - D-Glucose, anhydrous (dextrose) molecule.
2.1 Reflectance versus Transmittance Measurements
The intensity of absorption can be described in terms of transmittance:
T = / / / 0 (2.1)
where I is the intensity of the incoming radiation and l0 the energy incident on the
sample. Using the Beer/Lambert Law the intensity I can be expressed by the
following:
I0910 Oo/l) = logw ( 1 / T ) = kcp=A (2.2)
or:
A = logw (1 /T ). (2.3)
A is the absorbance, k is the molecular absorption coefficient that is a
characteristic of each molecular species, c is the concentration of the absorbing
molecules and p is the path length of the radiation through the sample. Thus, if
Beer's law is upheld and no association occurs between absorbing molecules,
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there exists a linear relationship between absorbance and concentration.
Similarly for reflectance (R) equation (2.2) can be expressed as:
or more familiarly:
logw (1 / R) = kcp=A
A = logw (1 /R ).
(2.4)
(2.5)
Figure 2.2 shows the transmittance and reflectance measurement techniques
used in near-infrared spectroscopy. Although, the differences look minimal, the
results can be quite dramatic. Reflectance measurements, for example,
generally can penetrate only 1-4 mm of the front surface of solid samples. This
small energy penetration can lead to large variations when measuring
nonhomogeneous samples as compared to using a transmittance technique.
O '
source monochromator sample detector
Transmittance Configuration
a
O
sample
source monochrcmator [IT
detectors
Reflectance Configuration
Figure 2.2 - Typical NIR spectroscopic measurement techniques.
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Transmittance measurements are more frequently used when the sample
contains large particles. Smaller particles create surface scatter resulting in a
loss of energy transmitted through a sample. An instrument operating in
transmittance mode therefore must output sufficient radiation to allow for
transmission through the sample. Due to larger pathlengths, longer wavelengths
are generally used when collecting transmittance data. Caution must be
exercised as the longer wavelengths cause more scattering and can cause the
sample temperature to increase.
In reflectance measurements all incident light flux is either absorbed or reflected.
Both the specular and the diffuse reflection components are superimposed
causing the pathlength to be indeterminable. Thus, the pathlength as well as the
concentration become unknowns in the Beer/Lambert Law. Most reflectance
measurements require information from several regions in the infrared spectrum.
A matrix solution is set up as part of a calibration process. The calibration
generally involves a regression modeling procedure that identifies the minimum
number of terms that can define a chemical property. The particle size or
scattering becomes the first principal component in a reflectance calibration
model.
There are several techniques that can be applied when performing spectroscopy
in the reflectance mode. Specular reflectance techniques require the reflected
radiation from the surface of the sample be at an angle equivalent to the incident
angle. This procedure requires a flat, smooth sample surface and results in low
amounts of reflected radiation. A second reflectance technique is diffuse
reflectance. In this technique the direction of reflected light is random with
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respect to the incoming beam. The use of FTIR spectrometers is mandated with
this procedure due to the low amounts of reflectivity. The spectra resemble
transmission spectra with different relative intensities. The use of Kubelka-Munk
theory [1] on diffuse reflectance spectra results in a similar spectra to that of an
absorbance spectra. A third type of reflectance measurement involves internal
reflectance. The sample under study is placed in close contact with an internal
reflectance element such as a crystal with a high refractive index or more
recently a planar waveguide. Complete internal reflection occurs a short distance
into the sample. The resulting spectra resembles transmission spectra. This
method is dependent on several parameters such as, the incident angle, sample
size, wavelength, number of reflections, and the refractive indices of the sample
and the reflectance element.
2.2 Glucose Spectra
The measurement of glucose spectra using near-infrared spectroscopy presents
many difficulties. The interference effects from water and other constituents in
the sample can overshadow the glucose bands. Figure 2.3 shows the
absorbance peaks of some major constituents in a bioreactor sample in the
wavelength region from 1000 to 2600 pm. This figure is intended to identify
absorbance peaks, therefore the curves are based on pure samples.
The selection of a wavelength region must include not only the glucose bands,
but also allow for measurements to be made without imparting large amounts of
power (and therefore heat) into the sample. To distinguish glucose bands an
attempt should be made to choose a wavelength region in which the fundamental
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frequencies or at worst the first overtones are present. This results in a
wavelength region from approximately 1.3 to 10 pm for glucose. Because water
is such an abundant constituent in the normal glucose sample, the region chosen
should try to be at a minimum water absorption band. Additionally, the higher
wavelength regions require larger amounts of power which in turn cause heating
of the water, therefore these regions should be avoided. The spectral region
from 2.0 to 2.5 pm contains first overtone glucose bands and is in a "valley" of
water absorbance. Additionally, this region does not require large amounts of
power to illuminate the sample.
----------------- Glucose
---------------------Glutamine
Water
Lactate
Relative
Absorbance
1000 1200 1400 1600 1800 2000 2200 2400 2600
Wavelength ( pm)
Figure 2.3 - Absorbance peak locations of major constituents in a possible
bioreactor solution.
REFERENCES
1. P. Kubelka, F. Munk, Journal of the Optical Society of America, 38, 448,
1948.
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CHAPTER 3
Michelson Interferometer - Theory of Operation
A Michelson interferometer is an instrument that splits a beam of radiation into
two paths and then recombines them so the variations of the exit beam can be
measured. Figure 3.1 shows a schematic diagram of a simple Michelson
interferometer. This device consists of two mutually perpendicular plane mirrors,
one of which moves at a constant velocity. Between the fixed mirror and the
movable mirror is a beamsplitter, where the beam from an external source can be
partially reflected to the fixed mirror and partially transmitted to the movable
mirror. Once each beam has been reflected back to the beamsplitter, they are
again partially reflected and partially transmitted. Therefore, a portion of the
beams have traveled in the path to both the fixed and the movable mirrors to
reach the detector. The superimposed beams create both constructive and
destructive interference patterns referred to as interferograms.
Fixed m irror
! N
r ;
> < 1
....T
' I
: / r
i /
Source .
1 /
-------------------_ ,|---------
Beamsplitter | \
1
1
> i <.
i
' i
i
i
i
Movable
m irro r
Direction of
motion
Detector
Figure 3.1 - Schematic diagram of a Michelson interferometer.
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Figure 3.2 shows a simple interferogram. A Michelson interferometer is often
referred to as a Fourier transform interferometer because of the methods used to
extract meaningful data from the interferogram. An interferogram obtained from
a Michelson interferometer contains all the wavelengths (spectral elements)
incident onto the interferometer in the total time the interferometer produces the
interferogram. This interferogram cannot be used directly because the spectral
data is not in an interpretable sequence. A Fourier transformation of the
interferogram is used to order the spectral data.
Spectrum Interferogram
freq retardation
Figure 3.2 - Simple spectra and its interferogram.
3.1 Resolution
The resolution of a spectrum measured interferometrically depends on the
maximum retardation of the scan (retardation is the change in path length caused
by the movement of the mirror). For example, a spectrum composed of a doublet
with both components having equal intensity, would result in an interferogram
that is a superposition of two cosine waves. If the doublet has a separation of
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Av cm'1, then a retardation of 1/2 Av*1 cm results in an out-of-phase condition.
Once the retardation reaches Av-1 cm the cosine waves are back in-phase.
Therefore, to complete one beat frequency, a retardation of A v'1 cm is required.
Increasing the retardation of the scan to a point where the two lines are just in-
phase would result in
A=Av"1 cm, (3.1)
where A is the end of scan retardation. If the maximum retardation by an
instrument is given by Amax, the best spectral resolution, Av, would be given by
Av = (Amax)'^ cm'1. (3.2)
Mathematically, what this implies is restriction of the maximum retardation
essentially multiplies the interferogram by a truncation function. The resulting
spectrum is then the convolution of the Fourier transform of the complete
interferogram with the Fourier transform of the truncation function. The spectrum
of an infinitely long cosine wave interferogram is a delta function of frequency v,
while the spectrum of the truncation function is a sine function. When these two
results are convolved the resultant curve is a sine function with a single spectral
line at v.
One method used to define the resolution of a spectrometer is the full-width at
half-height (FWHH) method. This method states that two triangularly shaped
lines of equal intensity and half-width are not resolved until the spacing between
the lines is greater than the full-width at half-height of either line. It can be shown
that two lines with sine shapes are not resolved until the dip in the spectral lines
are on the order of 22% of the frequency. This shows that the sine function is not
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a particularly useful shape for infrared spectroscopy. A method of circumventing
this problem is through a process known as apodization.
3.2 Apodization
Apodization is the process in which the magnitude of the side-lobes of the sine
function are suppressed. This process is carried out by replacing the truncation
function with a weighting function. The most common of the apodization
functions is the triangular apodization function. Application of the triangular
apodization function results in fully resolved spectral lines with a 1% dip instead
of the 22% dip when using a truncation function.
3.3 Phase Correction
Corrections to the phase angle of a measured interferogram may arise due to
optical, electronic, or sampling effects. Two common examples which cause
phase angle deviations are sampling the interferogram on just one side. This
sampling method requires the first data point to be precisely at zero retardation.
A second problem results from electronic filtering of high frequency components,
these filters tend to induce a phase lag into the interferogram. In essence the
addition of phase angle has the effect of adding sine components to the cosine
wave interferogram. Removing these sine components or their effects is known
as phase correction.
The use of double-sided measuring corrects the first phase angle problem. This
method requires no precise knowledge of the zero retardation point. There are
several disadvantages though. First it requires the moving mirror to be translated
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twice as far as the single-sided method. This then means twice the
measurement time is required which in turn results in computational time of
nearly four times. Another disadvantage is all real spectral information and the
noise is computed to have positive values because of the squaring function used.
Therefore, a true representation of the noise, which is randomly positive and
negative, is not realized.
The Mertz phase correction method is most commonly used. This method
calculates the amplitude spectrum with reference to a point of stationary phase.
The original interferogram is multiplied by a weighting function. The calculated
amplitude spectrum is then multiplied at each frequency by the cosine of the
difference between the measured phase angle and the reference phase angle to
yield the true phase corrected spectrum.
3.4 Beam Divergence
The use of a finite source in the interferometer results in a beam of radiation that
is not perfectly collimated. The largest throughput of radiation is desired without
degrading the spectrum. If a noncollimated beam of light is passing through an
interferometer with a divergence half-angle a, at zero retardation, the path
difference between the central ray passing to the fixed and movable mirrors is
zero, there is also no difference for the extreme rays. If the movable mirror is
moved an amount d, the increase in retardation for the central ray is 2d, while for
the extreme ray it is 2d/cos a. Thus, a path difference has been generated
between the central and extreme ray. It is desirable to determine the maximum
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beam half-angle that can be used given a maximum frequency ( v,^) for a
predetermined spectral resolution (Av). Equation 3.3 shows this relationship:
f a - ^ /2
Av
V . ^ m a x /
(3.3)
Additionally, beam divergence also shifts the frequency of a computed spectral
line from its true value. The actual frequency calculated from an interferogram,
v", can be related to the true frequency, v, by the equation 3.4:
'\
J
(3.4)
3.5 Mirror Misalignment
There are two effects dependent on the alignment of the mirrors in a Michelson
interferometer. The first is the alignment of the fixed mirror relative to the
movable mirror. The second depends on how accurately the plane of the moving
mirror is held during the scan.
If the moving mirror and the fixed mirror are at different angles in relationship to
the plane of the beamsplitter, then the beam from the moving mirror will hit the
detector at a different position than the beam of the fixed mirror. This
misalignment will cause a reduction in the amplitude of the interferogram.
In the case of misalignment of the mirror drive, an optical path difference will be
generated between the two extreme rays rather than a path difference between
the extreme rays and the central ray. When this situation occurs, the area of the
beam is reduced thus reducing the radiation reaching the detector.
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3.6 Sampling
Any wave form that is a sinusoidal function of time or distance can be digitized
unambiguously using a sampling frequency equal to twice the bandwidth of the
system [1]. The interferogram may then be completely reconstructed without any
loss of information or signal-to-noise ratio. For a Michelson type interferometer
this is equivalent to digitizing the signal at retardation intervals of (2 v ^ ) ' 1 cm. It
is better to design a system where the signal is sampled at equal intervals of
retardation rather than equal intervals of time, since if the mirror velocity varies
slightly during the scan, the signal is still sampled at the correct intervals of
retardation. If the wave of highest frequency is not sampled at least twice per
wavelength, the information from the high frequency portion of the spectrum will
be computed to occur at another lower frequency as well as its true frequency.
This phenomenon is known as "folding" or “aliasing".
By limiting the bandwidth of the spectrum with an optical filter, a lower sampling
frequency can be used. This will reduce the number of data points and therefore
will reduce computational time. If the spectral range is restricted between a
minimum frequency, v ^ , and a maximum frequency, v ^ , the number of points
required is
N3 = Ym l°) . (3.5)
3.7 Dynamic Range
The degree of accuracy the amplitude of the interferogram should be sampled is
referred to as the dynamic range of the instrument. The dynamic range can be
17
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described as the ratio of the intensity of the signal at zero retardation to the root-
mean-square noise level. An important point for the sampling of interferograms,
is that at least two or three digits of the analog-to-digital converter (A/D) should
be sampling detector noise.
For a spectrum measured between and at a resolution of Av, there are
N resolution elements, where
The dynamic range of the interferogram is given to a good approximation by the
dynamic range of the spectrum multiplied by 4 n . For an average spectral
dynamic range of 300:1 at a resolution of 2 crrr1 for a bandwidth of 4000 cm-1,
the dynamic range of the interferogram is (2000)1/2 x 300 or 13,500:1. Thus at
least a 14-bit A/D would be needed.
REFERENCES
1. M. Woodward, Probability and Information Theory, Pergamon Press, New
York, 1955.
18
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CHAPTER 4
Measurement of Glucose Noninvasively Using a Fourier
Transform Spectrometer
Research has been carried out by the Chemistry Department at the University of
Iowa assessing the adequacy of using near-infrared (NIR) spectroscopy to
measure glucose and glutamine noninvasively. The goal of the research is the
accurate measurement of glucose and glutamine entirely from spectral
information in the presence of changing mediums and complex biological
matrices. The methods engaged by the Iowa researchers involve increasing the
matrix complexity while evaluating the soundness of the measurement at each
step. They hope to identify the critical chemical and physical parameters that
affect the measurements and develop schemes to overcome them. Their
protocol includes the generation of an independent data set used to evaluate the
glucose predicting calibration model. All testing was conducted in the 5000 to
4000 cm-1 (2.0 to 2.5 pm) spectral region. The results of the Iowa testing are
presented and then the detailed spectrometer parameters are established.
The research initiated with the determination of glucose in an aqueous matrix [1]
over a glucose range of 1 to 20 mM (1 mM = 18 mg/dL). (The normal glucose
range for humans is 80 - 120 mg/dL). The resulting partial least squares (PLS)
calibration model demonstrated the ability to predict glucose concentrations with
a standard error of prediction (SEP) of 0.3 mM and a mean percent error of 2.5%.
Further studies using glucose and glutamine in aqueous solutions [2] resulted in
determination of glucose concentrations from 1.66 to 59.91 mM with a SEP of
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0.32 mM and a mean percent error of 1.84% and glutamine concentrations of
1.10 to 30.65 mM with a SEP of 0.75 mM and a mean percent error of 6.67%.
Figures 4.1 and 4.2 show the calibration and prediction data points of glucose
concentration and glutamine concentration respectively.
Glucose
O
a
o
8
a
o
*u
< D
n
a
Calibration
60
50
40
30
20
10
0
0 10 20 30 40 50 60
Predction
d
< § 40
0 )
1 3
J 30
o
U 20
0 10 20 30 40 50 60
Actual Glucose Cone. (mM) Actual Gluoose Cone (mM)
Figure 4.1 - Concentration plot for the glucose calibration model in an aqueous
solution over the 4850 - 4250 cm'1 spectral range using Fourier filtering and 6
PLS factors.
Glutamine
2
E
d
c
o
0
4 >
c
E
CO
s
<3
"U
0 1
e g
U
Calibration
30
25
20
15
10
5
0
0 5 10 15 20 25 30
Actual Glutamine Cona (mM)
o
a
0 )
c
E
( D
s
o
■ o
V
m
U
Predction
30
25
20
15
10
5
0
0 5 10 15 20 25 30
Actual Glutamine Cone. (m M )
Figure 4.2 - Concentration plot for the glutamine calibration model in an aqueous
solution over the 4700 - 4320 cm'1 spectral range using Fourier filtering and 7
PLS factors.
20
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The complexity of the matrix was increased to a buffered-protein matrix with a
glucose range of 1.2 to 20 mM [3]. The resulting calibration model prediction
capability showed a SEP of 0.24 mM and mean percent error of 1.26%. Figure
4.3 shows the glucose concentration data. This testing demonstrated the
usefulness NIR spectroscopy in the glucose determination of a complex matrix.
The next step was to examine the effects of a changing matrix.
s
E
u
c
o
U
0 )
V>
o
o
.2
c o
~ o
0 )
■ s
O calibration set
~ a, prediction set A
«r prediction set B
20
15
10
5
o
o 5 10 15 20
Actual Glucose Cone. (mM)
Figure 4.3 - Concentration plot for the glucose calibration model in a buffered
protein matrix over the 4600 - 4200 cm-1 spectral range using Fourier filtering
and 12 PLS factors.
The use of an actual biological matrix was deemed appropriate to study the
affects of variations in the background spectra [4]. This testing protocol involved
the use of bovine plasma samples with glucose concentrations in the 2.5 to 25.5
mM range. The optimal calibration model resulted in a SEP of 0.37 mM with a
mean percent error of 4.28%, Figure 4.4 shows these results. The mean relative
standard deviation over 14 samples in the test set was 3.18%. Considering the
relative standard deviation of current commercially available glucose analyzers,
21
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such as the Beckman Astra, are quoted as 3 to 6%, these results are quite
promising. Figure 4.5 shows the glucose concentrations measured by the
Beckman Astra versus the concentrations predicted by the calibration model.
• calibration set
« prediction set
24
S
E
20
o
c
o
o
0 )
( f t
o
o
3
ID
* U
v
•M
re
E
0 4 8 12 16 20 24
Measured Glucose Cone. (mM)
Figure 4.4 - Concentration plot for the glucose calibration model in a bovine
plasma matrix over the 5000 - 4002 cm"1 spectral range using Fourier filtering
and 10 PLS factors.
Z
E
o
c
0 )
( f t
o
-2
" O
re
E
+ 3
C O
• calibration set
* prediction set
24
20
16
12
8
4
0
0 4 8 12 16 20 24
Measured Glucose Cone. (mM)
Figure 4.5 - Estimated vs measured glucose concentrations in a bovine plasma
matrix from a Beckman-Astra glucose analyzer over the 5000 - 4002 cm'1
spectral range using 18 PLS factors.
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Concerns exist about temperature variations during long term use of Fourier
transform spectrometers configured for use in the NIR region [5]. Further studies
conducted at Iowa have attempted to address this issue. Glucose
measurements in aqueous solution of concentrations from 1.25 to 19.66 mM
were examined over the temperature range of 32 to 41 °C [6]. The best
calibration model exhibited a SEP of 0.14 mM with a mean percent error of
2.64%. Figure 4.6 shows the variation in percent error of prediction for varying
glucose concentrations at different temperatures.
10
8
Prediction 6
Error (%) 4
2
1
Figure 4.6 - Percent error of prediction variation for 3.09 to 17.98 mM glucose
concentrations over the spectral region 4850 - 4220 cm’1
4.1 Apparatus
A Nicolet Model 740 Fourier transform spectrometer (Nicolet Instruments,
Madison, Wl), was used to collect the spectra. For the majority of the
experiments, the spectrometer configuration consisted of a tungsten-halogen
Temp (°C)
Glucose
Concentration (mM)
23
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lamp (75 to 250 W) as the source. A calcium fluoride beamsplitter and a
cryogenically cooled indium antimonide (InSb) detector were used. A multilayer
optical interference filter (Barr Associates, Westford, MA) was used to restrict the
incident beam from 5000 to 4000 cm"1 with 72% transmittance at 4400 c n r‘l .
Samples were placed in a 1-mm-pathlength rectangular cell composed of Infrasil
quartz (Wilmad Glass Co., Buena, NJ). Temperature control of ±0.1 °C was
achieved using a VWR Model 1140 refrigerated temperature bath (VWR
Scientific, Chicago, IL) in combination with the sample cell in an aluminum-
jacketed cell holder. A copper-constantan thermocouple probe (Omega Inc.,
Stamford CT) was placed in the sample and an Omega Model 670 digital meter
was used to monitor the temperature.
4.2 Procedure
Spectra were collected as double-sided interferograms with 16,384 points based
on 256 coadded scans. Triangular apodization and Fourier transformation were
used to produce a single-beam spectrum with a resolution of 1.9 cm-1. The
phase array used was based on 200 points on each side of the interferogram
centerburst. The Mertz phase correction method was used to yield the true
phase.
4.3 Instrument Parameters
The Nicolet 740 spectrometer contained many modifications in order to measure
glucose and glutamine concentrations with the high degree of accuracy that was
obtained. Therefore, the manufacturer's specifications quoted for the 740 are no
longer valid. A description of the modifications to the 740 spectrometer will allow
24
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for the determination of the instrument parameters such as, source intensity,
beamsplitter characteristics, mirror coatings, and detector sensitivity. From this
data, minimum instrument accuracy required for noninvasive NIR glucose
measurements can be established.
4.3.1 Source
The Nicolet Model 740 Fourier transform spectrometer was equipped with a
tungsten-halogen lamp with a back reflector. The power of the lamp was
increased from 75 W to 400 W and a liquid cooling jacket was installed around
the lamp assembly. The Jacquinot aperture was maintained at full open and an
interference filter with a high pass at 1.97 pm was used. This filter restricted
transmittance to 72% at 4400 cm-1. A 50% increase in the instrument output
intensity at 4400 cm-1 was realized when the infrared source was increased from
250 W to 400 W.
4.3.2 Beamsplitter
A calcium fluoride beamsplitter was utilized in the 740. This beamsplitter was
designed to operate over the spectral range of 15,800 to 1200 cm'1 (0.6 - 8.3
pm). A typical CaF2 beamsplitter installed at a 45° angle will exhibit the
efficiency shown in Figure 4.7. Over the spectral region of 2 - 2.5 pm, the
theoretical efficiency of the beamsplitter is approximately 88%. Thus, the
reflectance and transmittance would be more of a 45% / 55% split rather than the
ideal 50% / 50% split.
25
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100
8 0 -•
6 0 -■
4 0
20 - •
W avelength (m icrons)
Figure 4.7 - Theoretical calculations of beamsplitter efficiency vs wavelength for
a CaF2 beamsplitter with a 2.5-pm air gap between the film and compensator
plate.
4.3.3 Mirrors
The upgrading of the mirror surfaces from an aluminum coating to a gold coating
increased the intensity of the Nicolet 740 by approximately 20%. The increase in
intensity was probably due to not only the higher reflectivities of the mirror
surface but also a precise alignment of the mirrors.
4.3.4 Detector
The Nicolet 740 used a InSb detector operating cryogenically. A typical response
for this type of detector is shown in Figure 4.8. In the spectral region of 2 - 2.5
pm, the specific detectivity, D* of the detector is approximately 5 x 1010.
26
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o 101 2
1 2 3 4 5 6
Wavelength (urn)
Figure 4.8 - Typical spectral response of an InSb detector.
REFERENCES
1. M. A. Arnold, G.W. Small, Analytical Chemistry, 62, 1457, 1990.
2. H. Chung, M.A. Arnold, Simultaneous Measurement of Glucose and
Glutamine in Aqueous Solutions by near Infrared Spectroscopy, submitted for
publication in Applied Spectroscopy, 1994.
3. L.A. Marquardt, M.A. Arnold, G.W. Small, Analytical Chemistry, 65, 3271,
1993.
4. G.W. Small, M.A. Arnold, L.A. Marquardt, Analytical Chemistry, 65, 3279,
1993.
5. C.A. Young, K. Knutson, J.D. Miller, Applied Spectroscopy, 47, 7,1993.
6. K.H. Hazen, M.A. Arnold, G. W. Small, Applied Spectroscopy, 48, 477, 1994.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 5
Instrument Design
Although laboratory instruments currently exist that are capable of measuring
glucose noninvasively by means of NIR spectroscopy, none currently exist that
are readily portable and easy to use. An instrument is required that has little or
no moving parts, is relatively immune to vibrations, and can be built compactly.
Three prototype devices that meet these specifications have been built, they are
a multichannel Fourier-transform infrared spectrometer, an instrument based on
a Hadamard-coded photodiode-array, and a Michelson-type interferometer using
rotating retroreflectors. While the multichannel spectrometer and the Hadamard-
coded device meet the requirements for a portable device, they have never been
used for noninvasive glucose measuring. The Michelson-type interferometer on
the other hand was the type of instrument used by the University of Iowa
researchers. The use of a rotating retroreflector instead of a translating mirror
will allow the instrument described below to meet the portability requirements.
5.1 Infrared Radiation Source
The requirements for the radiation source are; emittance of a continuum of
radiation from at least 5000 to 4000 cm-1, an intensity level high enough to allow
transmittance through the sample, small size with a compact filament capable of
handling vibration, minimal fluctuations over the sampling period, and low power
consumption. Additionally, the window in which the radiation emerges must be of
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a material compatible with the wavelength range and have an aperture that can
control stray radiation.
Conventional infrared sources will produce large amounts of infrared radiation.
The infrared typically radiates in all directions, thus much of the infrared radiation
does not go into a useful beam directed into the spectrometer, even when back
reflectors are used. This stray radiation heats up the spectrometer and can
interfere with the signal that reaches the detector. Even when the heat source is
insulated, the insulation tends to heat up and will eventually become a source of
radiation which is transmitted by conduction, convection or reemission to other
parts of the instrument. Thus, conventional sources of infrared radiation can
cause unwanted heat in the spectrometer and require large amounts of power to
operate.
Examples of current infrared sources are tungsten-halogen lamps, lasers, and
"glow-bars". The tungsten-halogen lamp suffers from the problems stated above
and the current laser sources are expensive. The glow-bar is a coil of silicon
carbide that is resistively heated to about 1200°C. The coil is relatively large thus
making it costly and inefficient. The glow-bar on average consumes about 150
watts of power requiring a large separate power supply. Often times the glow bar
requires external cooling due to the large amounts of radiant heat it produces.
Water cooling the source would add weight, cost and inconvenience to a portable
interferometer.
A source sold under the trademark "PRO-STAR" or "PRO-IR" (Nicolet Instrument
Corporation, Madison,Wl) will meet the requirements for a portable interferometer
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source. The source is highly efficient in energy consumption, provides an exit
beam of infrared radiation which is easily focused into a well defined beam,
produces little radiation in other than the beam direction, and is sealed to
minimize contact with ambient gases. The source is compact and lightweight,
since it requires no reflectors to focus the beam. The source provides an output
infrared beam having beam power equivalent to a conventional source while
consuming much less wattage.
The infrared source has a core with an outlet port formed by a narrow channel
and sealed with a window made from calcium fluoride, quartz, or similar infrared
transmissive material. An electrical resistive heating infrared element is
supported within a containment cavity and surrounded by an insulating core
material. The insulator core is a ceramic fiber material that has a high thermal
efficiency and very low thermal conductivity. The ceramic fiber material can be
formed so there is very little space between the cavity wall and the infrared
element. Therefore, the only significant outlet for the heat is the outlet port.
Because very little heat is lost by conduction through the insulator core, the
temperature of the heating element can be maintained for the desired infrared
wavelength resulting in high efficiency of electrical to thermal conversion.
Nicolet has shown that an infrared radiation source such as this requires as little
as 15 watts of power when compared to conventional sources requiring 150
watts. For a portable device used in measuring glucose and glutamine, an
infrared source that draws less than 30 watts of power should suffice. Thus,
there is no need for an additional power supply. Additionally, a filter can be
incorporated at the outlet port (either in the window or outside the window) to
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Window
w /optical aperture
restrict the spectral range from 5000 to 4000 cm'1. Figure 5.1 presents a
schematic of this type of infrared radiation source.
Heating Element
Insulator Core
Source Body
Figure 5.1 - Infrared radiation source schematic.
5.2 Beamsplitter
One of the key components controlling the performance of a Michelson-type
interferometer used for infrared spectroscopy is the beamsplitter. The
beamsplitter divides an incident beam of light into two components, a reflected
component and a transmitted component, whose relative intensities can be
specified and the design permits a prescribed reflectance/transmittance split.
Beamsplitters are generally thin films whose reflectance is determined by the
refractive index of the material, n, the film thickness, d, the beam incident angle,
6, and the radiation frequency under examination, v.
Using the method of Gilo [1], a nonpolarizing beamsplitter inside a BK7 glass
cube will be designed for use in the 5000 to 4000 cm'1 (2000 to 2500 nm) range.
Gilo's method utilizes the fact that in a quarter-wave stack at v two effective
indices that obey the Brewster condition affect only the spectral performance of
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the s state at v (s-polarization is perpendicular to the plane of incidence, p-
polarization is parallel to the incidence plane).
For p-polarization, the design index of refraction is given by:
np = n/cosQ. (5.1)
For s-polarization, the design index of refraction is given by:
ns = n cos 6. (5.2)
Using Snell's law, cos 9 = (1 - S2 / n2) 1/2, where S = no sin 6o (S is commonly
referred to as the numerical aperture in geomeirical optics and is constant in all
layers in a film system) and0o and no are the entrance material incidence angle
and index of refraction, respectively, np and ns are given by,
np = n/(1 -S 2 /n 2) 1/2, (5.3)
ns = n (1 -S 2 /n 2 )M (5.4)
Figure 5.2 shows equations 5.3 and 5.4 graphically for a BK7 glass cube (no =
1.52) and 9p = 45°.
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0.8
1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2 .2 2.32.4
Index of Refraction
Figure 5.2 - Effective indices as a function of the index of refraction for a BK7
glass cube.
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The design methodology Gilo uses consists of 6 steps, they are as follows:
1) Choose a pair of layer materials with a large difference between their np
values, using equation 5.3 or Figure 5.2.
2) Using a pair of layers, design an effective quarter-wave stack that obtains the
desired transmittance for the p-polarization at v .
3) Choose a different pair of layer materials having almost the same np.
4) Add an effective quarter-vvave stack of this pair of layers to the previous stack,
until the s-polarization transmittance at v rises to a value close to that of the p-
polarization.
5) Distribute the pairs of layers of the second stack in the multilayer to obtain the
desired performance outside of v. This is done by keeping odd-numbered
quarter-wave layers at odd positions and even-numbered layers at even
positions. This method has been demonstrated by Thelen [2].
6) Finish the design by computer optimization, using a standard thin-film design
program such as Film*calc from FTG Software Associates, Princeton NJ.
Using a design approach such as this will result in an optimal beamsplitter with
as practically possible a 50% reflectance, 50% transmittance split over the
desired wavelength.
5.3 Mirrors
Directing the infrared radiation from the source to the interferometer and then
onto the detector requires mirrored surfaces that reflect 100% of the radiation.
To accomplish this goal the mirror first surface must be coated with a metal and
the reflectance calculated. Calculation of the reflectance requires the refractive
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index, n, and the attenuation index K, to be known of the metal. Figure 5.3
shows the calculated reflectivity for Ag, Au, and Al. The equation used to
determine the reflectivity, r2, is,
r2 = [(1 - n)2 + K?]/[(1 + n)2 + K2]. (5.5)
From Figure 5.3, a first surface coating of Au or Ag will be used to maximize
reflectivity in the 2 to 2.5 |im region.
0.7
0.5
C O o>
W avelength (m icrons)
Figure 5.3 - Reflectivities of Aluminum, Silver, and Gold mirror surfaces at
various wavelengths.
5.4 Detector
There are two key parameters to optimize when choosing a detector for infrared
spectroscopy, the spectral response and the temperature characteristics of the
detector. The spectral response or sensitivity of a detector is commonly
expressed in terms of the noise equivalent power (NEP). The NEP of a detector
is the ratio of the detector noise voltage to the voltage responsivity. While NEP is
34
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dependent on the area of the detector, a function referred to as specific
detectivity, D*, is used which is independent of the detector area for most
materials. For most detectors the change in ambient temperature results in
changes in the spectral response, the dark resistance, and the time constant.
An optimal detector for use in noninvasive glucose sensing will have a D *> 4 x
101 1 and be operable at temperatures £ -20°C.
There are two main types of infrared detectors: the thermal type and the quantum
type. The thermal type detectors allow for responsivity with no dependence on
wavelength and room temperature operation. Their drawbacks include slower
response speed and lower detectivity than the quantum type. A few of the
specific thermal type detectors include: the thermopile, this device utilizes the
thermo-electromotive force generated between two different types of conductors,
bolometers, these are resistors than change resistance with incident infrared
radiation, pyroelectric detectors, these devices generate an electric charge on the
surface of a crystal with the variation of temperature.
Quantum type detectors feature high detectivity and fast response times. They
are wavelength dependent and the majority require some type of cooling. These
detectors can be subclassed into intrinsic and extrinsic types. Intrinsic type
detectors are highly wavelength dependent due to their inherent energy gap and
their responsivity decreases dramatically outside their wavelength range.
Intrinsic photoconductive type detectors change their conductivity when infrared
radiation is incident and have high responsivity. These type of devices include
detectors fabricated from PbS, PbSe, and HgCdTe. Intrinsic type detectors that
35
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are photovoltaic detectors generate an electric current when infrared radiation is
incident and have high responsivity and fast response speed. This class includes
Ge, InGaAs, InAs, InSb, and HgCdTe detectors. Extrinsic type detectors are
photoconductive devices whose wavelength range is determined by the levels of
impurities doped in the Ge or Si semiconductors. Extrinsic detectors require
cooling to liquid helium temperature. Table 5.1 show types and characteristics of
certain infrared detectors.
Types of Detectors Detectors Spectral
Response (mm)
Operating
Temperature (K)
D*
(cm • Hz1/2 /W)
Photoconductive PbS 1 to 3.6 77 - 300 1 x 1 0 9
type PbSe 1.5 to 5.8 77 - 300 1 x 108
HgCdTe 2 to 16 77 2 x 1 0 10
Photovoltaic Ge 0.8 to 1.8 300 1 x 1 0 11
type InGaAs 0.7 to 1.7 300 5 x 1 0 12
InAs 1 to 3.1 77-196 1 x1010
InSb 1 to 5.5 77 2 x 1 0 1°
HgCdTe 2 to 16 77 1 X 1010
Extrinsic Ge:Au 1 to 10 77 1 X 1011
type Ge:Hg 2 to 14 4.2 8 X 109
Ge:Cu 2 to 30 4.2 5 X 109
Ge:Zn 2 to 40 4.2 5 x 109
Si:Ga 1 to 17 4.2 5 x 109
Si.As 1 to 23 4.2 5 x 109
Table 5.1 - Types and characteristics of infrared detectors.
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5.4.1 PbS Detector
Lead Sulfide (PbS) detectors utilize the principle of decreased resistance with
application of increasing incident radiation. They exhibit high detectivities
compared to other photoconductive semiconductor type infrared detectors and
can operate at room temperature.
PbS cells are made by using a chemical deposition process in which a granular
thin film is formed onto a glass substrate. The detector can be packaged in a
hermetically sealed metal case, sealed inside a dewar and cooled by liquid
nitrogen, or thermo-electrically cooled inside a metal case. When thermo-
electrically cooling the detector a thermistor and thermoelectric device sealed in a
vacuum or nitrogen environment provide the cooling.
PbS detectors exhibit peak spectral response at 2.2 pm. Decreasing the
temperature of the detector results in these peak responses to be shifted in the
direction of longer wavelengths. Figure 5.4 shows typical spectral response of
PbS detectors at room temperature (25°C), thermoelectrically cooled (-20°C),
and cryogenically cooled (-77°C). The detectivity of the PbS detector is
increased by an order of magnitude when cooled with dry ice (-77°C).
Associated with this cooling is an increase in the dark resistance and an increase
in the time constant of the cell. These increases allow for higher detectivity and
better frequency response of the detector.
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1012
5 f"-
IQ”
I
o
lO
o
Q
109
1 2 3 4
Wavelength ( pm)
Figure 5.4 - Spectral response of a PbS cell.
5.4.2 InGaAs Detector
The InGaAs detector is a semiconductor device which uses a photovoltaic effect
in which a voltage is generated upon the application of infrared radiation. This
device currently exhibits the highest detectivity of all commercially available
infrared detectors operating at room temperature. InGaAs detectors are currently
limited to 1.7 pm although new doping techniques are pushing this upper limit out
to the theoretical limit for photovoltaic detectors of 2.6 pm at a D* of 2 x 1012 (see
Figure 5.5). Data processing techniques are available that will take into account
the nonlinearity in the 2 - 2.5 pm region.
-77° C -20°C
25°C
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----------------IDEAL LIMIT
ANTICIPATED RESPONSE
13
0
12
10
11
0
10
1 2 3 4
Wavelength (pm)
Figure 5.5 - Current and anticipated spectral response characteristics of an
InGaAs cell at 25°C.
5.4.3 Detector Summary
The portable interferometer described herein will use a thermo-electrically cooled
PbS detector operating at -20°C yielding a D* of 4 x 1011. A future upgrade may
be the InGaAs detector operating at 25°C with a D* of approximately 2 x 1012.
5.5 Interferometer
A Michelson type interferometer with a rotating retroreflector will be used for this
device. The retroreflector has been used in Fourier transform spectrometers in
the past [3]. The retroreflector takes advantage of the feature that the reflected
39
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radiation is parallel to the incoming radiation beam and is independent of the
reflector's orientation. The interferometer can thus be aligned under operation
and allows for tilt and shear compensation. The path length changes result from
the rotation of an excentrical and tilted retroreflector with respect to the optical
axis of the interferometer. This continuous rotation results in a sinusoidal
alteration of the path difference. Another advantage of the rotating retroreflector
is the spectral and time resolution are independent of each other. Two
interferograms per revolution can be acquired regardless of the spectral
resolution. However, the signal frequency and data rate increases with
increasing spectral resolution, thus the analog to digital conversion and the data
transfer rate to the computer determine the time resolution. Therefore the limiting
parameters are that of the analog to digital converter for the time resolution and
the maximum path length for the spectral resolution. A device similar to that of
Haschberger et al. will be used and is shown in Figure 5.6 [4]. This design
employs one retroreflector, is driven by a vibration-free dc motor, and can be
constructed very compactly. The maximum optical path difference, which yields
spectral resolution, and the beam diameter, which determines the radiation
throughput and consequently the signal to noise ratio, are two key optical
parameters of this device.
40
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PLANE BORE
MIRROR
ROTATING
RETROREFLECTOR
MIRROR
SOURCE
BEAMSPLITTER
AXIS OF
ROTATION
DETECTOR
Figure 5.6 - Interferometer utilizing one rotating retroreflector is shown in both its
extreme positions.
5.5.1 Optical Path Difference and Spectral Resolution
As mentioned previously, the rotating motion of the retroreflector results in a
sinusoidally modulated alteration of the path difference, according to:
where s(t) is the optical path length change, A is the amplitude of the change in
optical path length, and cot is the phase angle. For the device of Figure 5.6, the
maximum optical path difference Smax is given by:
This is because the path difference varies constantly by the same amount in both
arms and are 180° out of phase. For example, at c o t =90°, the path length in one
arm is at a minimum (shortest distance to beamsplitter) while the other arm is at
a maximum distance to the beamsplitter. Therefore, a device such as this allows
for twice the amount of path length variation as a single retroreflector device.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
s(t) = A sin c o t, (5.6)
S m a x ~ 4A — 16 Iq sin Ipl. (5.7)
41
In general the maximum spectral resolution for an instrument of this design is
determined by the effective aperture of the retroreflector. The incoming and
outgoing radiation beams must under all angles of rotation impinge upon the
retroreflector, therefore all other components are sized based upon the
retroreflector sizing. The spectral resolution depends on the diameter of the
incident beam and the maximum retardation of the interferometer. For this
device, the spectral resolution is approximately inverse to the maximum optical
path difference of the instrument with reference to the zero path difference. The
maximum spectral resolution will always be slightly less than the inverse of the
maximum path difference due to corrections in phase using slightly smaller path
differences than the maximum.
5.5.2 Beam Diameter
The allowable diameter of the beam traveling to the retroreflector is determined
by the rays that traverse the rotating retroreflector. The exit ray from the
retroreflector follows an elliptical track that is twice as wide as the projection track
of the reflector's center. The size of the ellipse depends on the parameters (5 and
l0 as shown in Figure 5.7. A set of inequalities have been deduced by
Haschberger et al. [5] and assembled in a simulation routine that determine
whether the ray meets one of the three reflecting planes of the retroreflector. An
iterative approach is required to determine the path of the rays for each angle of
rotation and every entrance vector. Because the optical throughput of the
interferometer is dependent on the beam diameter, maximization of the
transmitted beam will result in a higher efficiency instrument.
42
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A(90°)
Z(27df)
A(270°)
4 l0 COS p
Figure 5.7 - Ray tracing on the plane mirror. The dashed ellipse is the projection
on the retroreflector and the solid ellipse represents the track of the exit ray. The
point E is the entrance projection point.
5.5.3 Parameter Optimization
For the interferometer arrangement shown in Figure 5.6 with a retroreflector
having an aperture diameter of 5 inches, the maximum path difference smaxand
maximum beam diameter dwax are shown as functions of the angle p and the
lateral displacement l0 in Figure 5.8. The smax curves are calculated according
to equation (5.7), and dmax is approximated using Haschberger's simulation
routine mentioned previously. From Figure 5.8, the dmax curve contains two
distinct branches: the first shows for a given lateral displacement /0 the maximum
beam diameter remains nearly constant for increasing p. For small P's, the
impact point of the incoming beam is near the retroreflector's center, and moves
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
away from center with increasing p. With an increasing (5 the probability of an
incorrect pass increases due to the limited size of the plane mirrors. Therefore,
to maintain the diameter of the traversing ray constant, the angle p must
decrease with increasing lQ (sloped branch of the curve). The lateral
displacement is bounded by the radius of the retroreflector's aperture, ( lQ = /
2 cosfi). The shaded area in Figure 5.8 shows the combination of p and l0 that
should be chosen when using a retroreflector with an aperture of 5 inches.
\ \ N
max
1.0
_____C .Q ........ ................
2.4
................\ 8.0
7 n
1 fi
- o-O
. ‘■ V n a x [cml
____ 4.0
2.0
5 10 15 20
PC0]
Figure 5.8 - Geometrical parameters for an interferometer with a 5 inch
retroreflector.
To optimize the optical throughput, an elliptical transmitted beam should be used.
This is because the limiting aperture of the rotating retroreflector has an elliptical
shape. If the diameter of the circular incoming beam is dimensioned according to
the larger diameter of the ellipse, then the area of the transmitted beam will
increase by nearly twice. The detector can than be equipped with an elliptical
44
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cold stop which results in a slight reduction of luminosity. This slight reduction
should be offset by the added throughput. Instruments of this type have been
shown to have spectral resolutions on the order of 0.1 cm’1.
5.6 Instrument Design Summary
Figure 5.9 shows a pictorial of the proposed instrument. The spectrometer
consists of a light source of 40 W or less in which the output can be focused to a
certain beam diameter. The radiation then enters the beamsplitter made from a
multilayer dielectric stack. Mirrors with gold or silver plated first surfaces direct
both radiation beams through gold or silver plated plane bore mirrors onto the
retroreflector surfaces. The retroreflector is laterally displaced by an amount l0
and tilted at an angle p. The retroreflector is driven by a vibration free dc stepper
motor. The transverse radiation beam is directed back through the beamsplitter
onto a lead sulfide detector that is thermally cooled. Triangular apodization and
the Mertz phase correction method will be applied to the output of the detector.
The data processing scheme will be discussed in Chapter 6.
PLANE BORE
MIRROR
MIRROR SOURCE
BEAMSPLrrrER
AXIS OF
ROTATION
MOTOR
RETROREFLECTOR
SAMPLE CELL
DETECTOR
Figure 5.9 - Proposed spectrometer utilizing one rotating retroreflector.
45
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REFERENCES
1. M. Gilo, Applied Optics, 31, 5345, 1992.
2. A. Thelen, Applied Optics, 15, 2983, 1976.
3. M. Murty, Journal of the Optical Society of America, 50, 83,1960.
4. P. Haschberger, V. Tank, Journal of the Optical Society of America A, 10,
2344, 1993.
5. P. Haschberger, V. Tank, Journal of the Optical Society of America A, 10,
2342, 1993.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER 6
Data Processing Techniques
The prediction of glucose concentration directly from a collected spectra requires
the information present in the glucose bands be extracted. A data processing
scheme that is capable of duplicating the accuracies and repeatablities of current
glucose analyzers is required for the noninvasive device. Several methods have
been used to process glucose spectral information in the near, mid and far
infrared regions. These methods include linear regression techniques by
researchers at Worcester Polytechnic Institute [1], neural networks were used by
Mendelson and his colleagues [2], and chemometric methods such as partial
least squares and principal component regression were used by Ries Robinson
and Sandia National Laboratory and their work with noninvasive glucose sensing
[3]. A particular promising method uses the strategies for coupling digital filtering
with partial least-squares (PLS) regression and constructing multivariate
calibration models from Fourier transform near-infrared absorbance spectra [4],
6.1 PLS Regression
One of the most widely used methods for processing spectral data and
constructing a calibration model for predicting analyte concentrations is PLS
regression. When using PLS for near-infrared glucose determination, the input is
an n x p matrix of absorbance spectra, where n is the number of spectra and p is
the number of absorbance values, and a n x 1 vector of measured glucose
concentrations. Generally, the absorbance matrix is centered by subtracting the
47
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mean absorbance from each absorbance element. This results in an h + 1 term
calibration model of the form
d = bo + bixi\ 1 +... + bhxih (6.1)
where c/ is the predicted glucose concentration of spectrum /, the x/ terms are
PLS factor scores. The b terms are coefficients determined from multiple linear
regression analysis of the measured glucose concentrations of the calibration
data and the h sets of PLS scores computed of the calibration samples.
The PLS processing scheme provides a means to extract data components from
a set of input spectra using variance in the concentration vector. There are two
disadvantages of using PLS for glucose measuring though. First, if there are
noise components that correspond with the glucose concentration they can
influence the PLS factor scores. Second, if there are large baseline or other
variations, the early factors will extract components of the variation that correlate
with concentration. Therefore, often times the PLS regression techniques are
unable to model glucose concentrations adequately due to the significant spectral
variation that exists. An alternate data processing approach using near-infrared
spectroscopy for glucose determination must be developed.
6.2 Digital Filtering
Using digital filtering as a preprocessing tool coupled with the PLS regression
has been shown to yield acceptable glucose prediction results in a variety of
solutions. Digital filtering techniques remove certain frequency components from
the measured data. This method is based on the fact that very low frequency
information is dominated by slowly varying components (baseline variation) and
48
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high frequency information is dominated by rapidly varying noise components of
the spectrum. Giucose concentration information is present in a middle range of
frequencies.
The digital filter used by the University of Iowa researchers is a Fourier filter
which selectively passes spectral features according the spectral band shape.
The process initially performs a Fourier transform of the raw absorbance spectra.
The Fourier transform separates the high, low, and mid sine waves according to
their frequencies (digital frequencies) and the transformed spectrum is multiplied
by as Gaussian function, therefore the data under the Gaussian is weighted. The
Gaussian response function contains two key components, the mean position of
the Gaussian along the digital frequency axis and the standard deviation of the
Gaussian which defines the width of the filter. The ideal mean position and
standard deviation for the Gaussian response function are important. The mean
position must allow the filter to weight the molecular absorption features within
the spectrum. The analyte dependent information that passes through the filter is
maximized by the standard deviation width. An inverse transformation is
performed to return the data back to its original domain. The method used to
determine the mean and standard deviation of the Gaussian response function
involves using PLS regression models for many combinations of mean positions
and standard deviation widths for the response function. The PLS calibration
model generated from the filtered spectra are evaluated using an independent
data set. The response function is then the reciprocal sum of the mean square
calibration error (MSE) and the mean square prediction error (MSPE). A
response surface is generated by plotting the mesh corresponding to the
49
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response function versus the mean position and standard deviation widths of the
Gaussian shaped filter. The optimum Gaussian function corresponds to the
lowest sum of mean square errors of calibration and prediction.
Figures 6.1 and 6.2 present the response surfaces for glucose and glutamine in
aqueous solutions [5], respectively.
Figure 6.1 - Response surface for glucose. 4 PLS factors were used over the
spectral range from 4850 - 4250 cm-1.
Figure 6.2 - Response surface for glutamine. 5 PLS factors were used over the
spectral range from 4700 - 4320 cm'1.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1/(MSE
Glucose
Mean Position
Standard Deviation
1/(MSE+MSPE)
Standard Deviduun u.uuu v.uu ^ oh Position
G lu tam in e
50
6.3 Conclusion
Preprocessing of the glucose and glutamine spectral data with Fourier filtering
prior to implementing PLS regression techniques have been shown to improve
the performance of calibration models. Additionally, the filtering decreases the
importance of the spectral range and reduces the number of PLS factors
required. The implementation of a data processing scheme such as this along
with the hardware described in Chapter 5 will result in a device that exhibits the
required accuracy for noninvasive measuring of glucose and glutamine.
REFERENCES
1. Y. Mendelson, A.C. Clermont, R.A. Peura, IEEE Trans Biomed Engr, 37,
458, 1990.
2. Y. Mendelson, A.C. Clermont, IEEE Trans Biomed Engr, 37, 492, 1990.
3. M. R. Robinson, R. P. Eaton, D. M. Haaland, D. M. Koepp, E. V. Thomas, B.
R. Stallard, P. L. Robinson, Clinical Chemistry, 38,1618, 1992.
4. G. W. Small, M. A. Arnold, L. A. Marquardt, Analytical Chemistry, 65, 3279,
1993.
5. H. Chung, M.A. Arnold, Simultaneous Measurement of Glucose and
Glutamine in Aqueous Solutions by near Infrared Spectroscopy, submitted
for pub in Applied Spectroscopy, 1994.
51
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CHAPTER 7
Conclusions
A portable Fourier transform infrared (FT1R) spectrometer can be constructed
that has accuracies and resolution that are equal or better to the modified Nicolet
Model 740 spectrometer used by the University of Iowa researchers.
Translational movements of the mirror surface have been replaced by a single
rotational motion allowing for a device that is rugged and can be built compactly.
Additionally, all the components in the spectrometer are readily available from a
variety of sources.
The interferometer exhibits spectral resolutions of 0.1 cm’1 as compared to the
Nicolet spectrometer used at Iowa of 1.9 cm'1. The infrared source will output
equivalent power at lower input wattage and removes the need for source
cooling. The beamsplitter will exhibit improved performance because it will be
optimized to operate over the 2.0 - 2.5 pm region. The radiation through the
portable spectrometer will be equal to that of the 740 due to similar optical
properties of the mirrors. The portable instrument will use a thermoelectrically
cooled PbS detector which has detectivities that are on the same order of the
modified liquid nitrogen cooled Iowa instrument. The post-processing schemes
will be similar to Iowa research in that triangular apodization and Mertz phase
correction will be applied. The data processing scheme will be identical to that of
the Iowa researchers, partial least squares regression with digital filtering as a
preprocessor.
52
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Construction of this FTIR spectrometer will allow for researchers to accurately
control glucose and glutamine in a fed-batch bioreactor. This will result in
accurate growth rates and patterns of cell cultures. Extensions of this device
may allow for use as a diabetic monitoring tool thus reducing the risks associated
with the invasive glucose monitoring techniques currently used by diabetics.
53
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Bibliography
J.T. Kuenster, K.H. Norris, W.F. McCarthy, Measurement of Hemoglobin
in Unlysed Blood by Near-Infrared Spectroscopy, Appl Spec, 48, 4, pp
484-488, 1994.
C.J. Pouchert, The Aldrich Library of Infrared Spectra, 3rd ed., Milwaukee,
WlrAldrich Chemical Co., Inc, 1981.
Y. Mendelson, Y. Wang, B.D. Gross, Noninvasive measurement of
hematocrit and hemoglobin content using differential optical analysis, US
Patent 05277181, 1994.
J.R. Braig, D.S. Goldberger, Noninvasive pulsed infrared
spectrophotometer, US Patent 05313941, 1994.
C.A. Young, K. Knutson, J.D. Miller, Significance of Temperature Control
in FT-NIR Spectrometers, Appl Spec, 47,1, pp 7-11,1993.
Y. Mendelson, A.C. Clermont, R.A. Peura, B-C Lin, Blood Glucose
Measurement by Multiple Attenuated Total Reflection and Infrared
Absorption Spectroscopy, IEEE Trans Biomed Engr, 37, 5, pp 458-465,
1990.
G. M. Hale, M. R. Querry, Optical Constants of Water in the 200-nm to
200-mm Wavelength Region, Appl Opt, 12, 3, pp 555-563, 1973.
P. Haschberger, V. Tank, Optimization of a Michelson interferometer with
a rotating retroreflector in optical design, spectral resolution, and optical
throughput, J Opt Soc Am A, 10, 11, pp 2338-2345,1993.
P. Haschberger, V. Tank, F. Lanzl, Michelson interferometer with a
rotating retroreflector: investigations on special features, Infrared Phys, 31,
pp351-360,1991.
P. Haschberger, O. Mayer, V. Tank, H. Dietl, Ray tracing through an
eccentrically rotating retroreflector used for path-length alteration in a new
Michelson interferometer, J Opt Soc Am A, 8, pp 1991-2000, 1991.
V. Tank, H. Dietl, P. Haschberger, E. Lindermeir, O. Mayer, Method and
apparatus for determining a path difference in a Michelson interferometer,
US Patent 05291268, 1994.
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A. Minato, N. Sugimoto, Y. Sasano, Optical design of cube-corner
retroreflectors having curved mirror surfaces, Appl Opt, 31, 28, pp 6015-
6020, 1992.
J. Kauppinen, P. Saarinen, Line-shape distortions in misaligned cube
corner interferometers, Appl Opt, 31,1, pp 69-74,1992.
D. M. Drake, C. D. Woodward, J.M. Coffin, High efficiency infrared source,
US Patent 05291022,1994.
J.C. Zwinkels, D.S. Gignac, Design and testing of a new high-accuracy
ultraviolet-visible-near-infrared spectrophotometer, Appl Opt, 31, 10, pp
1557-1567, 1993.
R.H. Barnes, J.W. Brasch, Non-invasive determination of glucose
concentration in body of patients, US Patent 0570874,1991.
J.L. Robichaud, W.K. Wong, R.A. VanTassel, Evaluation of a Hadamard-
coded photodiode-array spectrometer under low illumination, Appl Opt, 33,
1, pp 75-81, 1994.
M. Hashimoto, S. Kawata, Multichannel Fourier-transform infrared
spectrometer, Appl Opt, 1, 28, pp 6096-6101, 1992.
P.R. Solomon, A Vibration Immune Fourier Transform-Infrared
Spectrometer for Process Monitoring, DOE SBIR Phase II Award, 1994.
D.B. Fenner, On-Chip Infrared-Spectral Sensors by Superconducting
Detector Arrays, DOE SBIR Phase I Awards, 1993.
A.D. Hibbs, New Type of Infrared and Far Infrared Focal Plane Detector
with very Low NEP, NSF SBIR Phase I Awards, 1993.
K.H. Hazen, M.A. Arnold, G. W. Small, Temperature-Insensitive Near-
Infrared Spectroscopic Measurement of Glucose in Aqueous Solutions,
Appl Spec, 48, 4, pp 477-483,1994.
H. Chung, M.A. Arnold, Simultaneous Measurement of Glucose and
Glutamine in Aqueous Solutions by near Infrared Spectroscopy, submitted
for pub in Appl Spec, 1994.
L.A. Marquardt, M.A. Arnold, G.W. Small, Near-Infrared Spectroscopic
Measurement of Glucose in a Protein Matrix, Anal Chem, 65, pp 3271-
3278, 1993.
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G.W. Small, M.A. Arnold, L.A. Marquardt, Strategies for Coupling Digital
Filtering with partial Least-Squares Regression: Application to the
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Applied Optics, 31, pp 5345-5349, 1992.
56
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Asset Metadata

Creator Sisson, Mark Anthony (author)

Core Title Design of a portable infrared spectrometer: application to the noninvasive measurement of glucose

School Graduate School

Degree Master of Science

Degree Program Biomedical Engineering

Degree Conferral Date 1994-12

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, biomedical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Maarek, Jean-Michel (committee chair), Khoo, Michael C.K. (committee member), Marmarelis, Vasilis (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-1339

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