U.S. patent application number 11/840567 was filed with the patent office on 2007-12-06 for calibrating measurements of analyte concentrations in solvents from an electromagnetic spectrum.
This patent application is currently assigned to C8 MEDISENSORS INC.. Invention is credited to Jan Lipson.
Application Number | 20070279628 11/840567 |
Document ID | / |
Family ID | 34221437 |
Filed Date | 2007-12-06 |
United States Patent
Application |
20070279628 |
Kind Code |
A1 |
Lipson; Jan |
December 6, 2007 |
CALIBRATING MEASUREMENTS OF ANALYTE CONCENTRATIONS IN SOLVENTS FROM
AN ELECTROMAGNETIC SPECTRUM
Abstract
Weak signals scattered from analytes at multiple wavelengths can
be summed to illuminate either a single detector or a multiplicity
of detectors, offering the possibility of concentrating the
spectral energy on a smaller total detector area. In addition, a
method is disclosed whereby a calibration of the resulting signal
for a given analyte can be obtained by means of measuring the
quantity of water in the sample volume and by means of measuring
the salinity of the fluid in the sample volume.
Inventors: |
Lipson; Jan; (Cupertino,
CA) |
Correspondence
Address: |
FENWICK & WEST LLP
SILICON VALLEY CENTER
801 CALIFORNIA STREET
MOUNTAIN VIEW
CA
94041
US
|
Assignee: |
C8 MEDISENSORS INC.
2242 Camden Avenue, Suite 204
San Jose
CA
95124
|
Family ID: |
34221437 |
Appl. No.: |
11/840567 |
Filed: |
August 17, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
10923264 |
Aug 20, 2004 |
7266401 |
|
|
11840567 |
Aug 17, 2007 |
|
|
|
60497072 |
Aug 22, 2003 |
|
|
|
Current U.S.
Class: |
356/317 ;
356/306 |
Current CPC
Class: |
G01J 3/44 20130101; G01J
3/1838 20130101; G01J 3/0229 20130101; G03H 1/0005 20130101; G01N
21/274 20130101; G01N 21/31 20130101; G01J 3/0232 20130101; G01J
3/02 20130101 |
Class at
Publication: |
356/317 ;
356/306 |
International
Class: |
G01J 3/30 20060101
G01J003/30 |
Claims
1. A method of calibrating a measurement of a concentration of an
analyte dissolved in a solvent within a sample, the method
comprising: detecting an amplitude of a signal from a spectral line
scattered from the solvent within the sample; detecting a
scattering signal of the analyte dissolved within the sample; and
normalizing the scattering signal of the analyte based on the
amplitude of the signal from the spectral line scattered from the
solvent.
2. The method of claim 1, further comprising: determining a
quantity of solvent within the sample from the amplitude of the
spectral line scattered from the solvent.
3. The method of claim 2, further comprising: determining a
quantity of analyte within the sample based on the normalized
scattering signal of the analyte and the quantity of solvent within
the sample, wherein the quantity of analyte within the sample is
proportional to the quantity of solvent within the sample.
4. The method of claim 1, wherein the step of detecting an
amplitude of a spectral line scattered from the solvent and the
step of detecting a scattering signal of the analyte are performed
by a single detector.
5. The method of claim 1, further comprising: detecting an
amplitude of a signal from a spectral line scattered from the
solvent within a reference cell containing a known quantity of
solvent; and determining a quantity of solvent within the sample
from the amplitude of the spectral line scattered from the solvent
within the sample in comparison to the amplitude of the signal from
the spectral line scattered from the solvent within the reference
cell having the known quantity of solvent.
6. The method of claim 1, wherein the normalized scattering signal
of the analyte is insensitive to changes in sample volume.
7. The method of claim 1, wherein the solvent is water.
8. The method of claim 1, wherein the sample comprises biological
material.
9. The method of claim 8, wherein the biological material is human
tissue.
10. The method of claim 9, wherein the human tissue comprises
blood.
11. The method of claim 9, wherein the human tissue comprises
interstitial fluid.
12. The method of claim 1, wherein the analyte is glucose.
13. An apparatus for calibrating a measurement of a concentration
of an analyte dissolved in a solvent within a sample, the apparatus
comprising: one or more sources of optical radiation; a passive
optical system that transmits the optical radiation from at least
one of the sources to the sample, and collects at least one
spectral line from a scattering signal of the analyte dissolved
within the sample and collects at least one spectral line from a
scattering signal of the solvent within the sample; at least one
detector that detects the scattering signal from the analyte
dissolved within the sample and detects the scattering signal from
the solvent within the sample; and a processing device that
normalizes the scattering signal of the analyte based on an
amplitude of the scattering signal of the solvent within the
sample.
14. The apparatus of claim 13, further comprising: a reference cell
containing a known quantity of solvent, wherein the passive optical
system transmits the optical radiation from at least one of the
sources to the reference cell and collects at least one spectral
line from a scattering signal of the solvent within the reference
cell, wherein at least one detector detects the scattering signal
from the solvent within the reference cell, and wherein the
processing device determines a quantity of solvent within the
sample from the amplitude of the scattering signal from the solvent
within the sample in comparison to an amplitude of the scattering
signal from the solvent within the reference cell.
15. The apparatus of claim 13, wherein the normalized scattering
signal of the analyte is insensitive to changes in sample
volume.
16. The apparatus of claim 13, wherein the solvent is water.
17. The apparatus of claim 13, wherein the sample comprises
biological material.
18. The apparatus of claim 17, wherein the biological material is
human tissue.
19. The apparatus of claim 18, wherein the human tissue comprises
blood.
20. The apparatus of claim 18, wherein the human tissue comprises
interstitial fluid.
21. The apparatus of claim 13, wherein the analyte is glucose.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application is a continuation of U.S. patent
application Ser. No. 10/923,264, entitled "Measuring Analytes from
an Electromagnetic Spectrum Using a Wavelength Router", filed Aug.
20, 2004, which claims priority under 35 U.S.C. .sctn. 119(e) to
U.S. Provisional Patent Application Ser. No. 60/497,072, filed Aug.
22, 2003. Each of the foregoing is incorporated herein by reference
in its entirety.
BACKGROUND OF THE INVENTION
[0002] 1. The Field of the Invention
[0003] This invention relates generally to measuring analytes in
samples and, more specifically, to measuring analytes based on an
electromagnetic spectrum that is characteristic of the analyte, for
example as can be used to make non-invasive measurements of
analytes in biological organisms.
[0004] 2. Background and Relevant Art
[0005] Many attempts have been made to create appropriate apparatus
for the non-invasive measurement of significant substances within
biological organisms. The importance of such measurement capability
arises not only from the need to observe biochemical reactions in
such organisms without disturbance to the system but also in order
to help control chronic diseases such as diabetes, where it is
highly desirable to measure the patients blood glucose levels much
more frequently than is practical, when puncturing the skin is
required. Molecular spectroscopy has been proposed to make such
measurements. However, the blood and interstitial fluids contain a
very great number of compounds which must be distinguished.
Absorption spectroscopy in the visible or near infrared suffers
from the difficulty that the spectrum of many compounds that are
present in the blood and other tissues substantially overlap in
this region. Mid-IR spectroscopy produces spectra which are
considerably more unique to individual molecules but suffers from
two serious problems: (1) Detectors must be operated at cold
temperatures if they are to be sufficiently sensitive, and (2)
Water absorbs mid-IR radiation strongly and such radiation can only
penetrate a few tens of microns into an organism.
[0006] Raman spectroscopy has been proposed to obviate some of
these difficulties. In Raman spectroscopy, a scattering spectrum is
produced at frequencies which are at the difference or sums of the
frequencies of the illuminating radiation and the characteristic
spectral frequencies of the molecule. Difference frequency
generation is referred to as Stokes scattering, and sum frequency
generation is referred to as Anti-Stokes scattering. The resulting
spectral signatures are advantageously particular to the analytes
of interest. However, the cross-sections for Raman scattering are
small, and the resulting scattered signals are weak. Weak signals
can also arise from spectroscopies that use other non-linear
processes or where the available power from the light source is
small. Other representative examples would include four wave
mixing, frequency doubling, and multi-photon fluorescence.
[0007] U.S. Pat. No. 6,064,897, entitled "Sensor utilizing Raman
spectroscopy for non-invasive monitoring of analytes in biological
fluid and method of use," proposes the use of a multiplicity of
bandpass filters and detectors to monitor a multiplicity of
significant spectral lines emerging from the analyte of interest.
The premise of the method is that a multiplicity of spectral lines
is better correlated to any particular analyte than a single line,
in the presence of other substances that may have confounding
spectra. In addition, the patent presents a system using discrete
transmission filters, which can have small attenuation. Such
systems, however, may be limited in sensitivity by detector noise.
The dark current of detectors scales adversely with increasing
detector area. A multiplicity of detectors will therefore, in
aggregate have approximately N.sub.d times the total dark current
of an individual detector, where N.sub.d is the number of
detectors. Because the dark current can be algebraically subtracted
from the signal, the noise contribution arises from its variance,
rather than from the mean value. The variance will be proportional
to (N.sub.d).sup.1/2. The approach, described in U.S. Pat. No.
6,064,897, therefore suffers from the difficulty that the aggregate
noise scales with the number of detectors.
[0008] Raman scattering has also been proposed in the aqueous humor
of the eye to measure glucose concentrations, as in U.S. Pat. No.
6,181,957. The aqueous humor has desirable optical properties such
as high transparency. However, it is highly desirable to perform
such monitoring through the skin so as to be able to continuously
measure the relevant analytes. Also, serious issues of eye safety
are entailed with the proposed method. Irrespective of the choice
of measurement location, U.S. Pat. No. 6,181,957 also does not
propose a method to resolve the problem of measuring weak scattered
signals with practical detectors.
[0009] Raman scattering to measure multiple analytes in blood was
reported in thesis work by T. W. Koo in a dissertation entitled,
"Measurement of blood analytes in turbid biological tissue using
near infrared Raman spectroscopy," published by MIT, in August
2001. Weak Raman signals are reported with as little as 6 counts
per every 10 seconds for glucose. Long measurement times and high
laser power is required (300 seconds, and 280 mW). These parameters
are not practical for many applications.
[0010] In other work, glucose measurements were made, in vivo,
using Raman scattering where light was introduced through the
finger tip {"Noninvasive blood analysis by tissue modulated NIR
Raman spectroscopy," J. Chaiken et al., in Proceedings of SPIE Vol.
4368, p. 134 (2001)}. The method improves the signal size but still
uses cooled detectors, high laser power, and a low f number
spectrometer that is expensive. The basic problem of weak signals
remains unresolved.
[0011] Another difficulty, which has been of great importance in
noninvasive measurements is the establishment of a reliable
calibration for a wide variety of patients, that will remain valid
over varying conditions and over time. Variations arise from many
sources including the following: (1) Temperature, (2) Presence of
varying concentrations of confounding substances with overlapping
spectra, (3) Presence of other substances which affect the spectrum
of the analyte either in regard to the amplitude, shape, or
position of the spectral lines, (4) Variations in the location of
the sampling, and in particular the fraction of blood, and
interstitial fluid that may be therein, and (5) Drifts in the
instrument including the wavelength of sources or of spectroscopic
optical components.
[0012] Calibration has been sought through regression techniques,
based on the spectra of multiple substances, obtained by measuring
the individual amplitudes of many spectral lines. Such techniques
remain sensitive to variations in the size and constituency of the
sample volumes, and also result in much more complex spectrometers.
The work of Chaiken et al. adds thereto a method based on
subtracting signals using spectra obtained from a finger without
pressure, with respect to a pressed finger. Referring to FIG. 11 of
the aforementioned reference, there is still much scatter in the
correlation between the Raman measurement and laboratory
measurements of glucose, rendering the technique disadvantageously
inaccurate.
BRIEF SUMMARY OF THE INVENTION
[0013] These and other limitations are addressed by an apparatus
whereby weak signals at multiple wavelengths can be summed to
illuminate either a single detector or a multiplicity of detectors,
offering the possibility of concentrating the spectral energy on a
smaller total detector area. In addition, a method is disclosed
whereby a calibration of the resulting signal for a given analyte
can be obtained by means of measuring the quantity of water in the
sample volume and by means of measuring the salinity of the fluid
in the sample volume.
[0014] In one aspect of the invention, a multiplicity of holograms
is used to route the scattering wavelengths emerging from the
sample to either a single detector or to more than one detector. In
particular, the spectral energy emerging from the analyte to be
measured generally appears in multiple spectral lines. Using the
wavelength router, the energy in most or all of these spectral
lines can be directed to a single detector, thus greatly increasing
the signal to noise ratio for the measurement.
[0015] Further, the functionality of the router can be extended to
combine the input energies of sources at multiple wavelengths, thus
advantageously increasing the input optical power from a
multiplicity of relatively inexpensive sources. Moreover, a portion
of the power can be diverted to a reference cell, which is used to
calibrate the measurement. The functionality of the router can be
made general in that all or part of any input or output wavelength
can be diverted to any of the appropriate locations or to multiple
locations.
[0016] Another aspect of the invention concerns calibration
techniques. As the analytes of interest are often dissolved in
water, the quantity of a given analyte in the sample volume should
scale as the quantity of water in the volume. The quantity of water
is independently determined by measuring the amplitude of
scattering signals at an appropriate Raman excited spectral line of
water. By using a reference cell which contains water, the signal
size can be calibrated absolutely to a specific quantity of water.
In addition, it has been found that the absolute spectral location
of a line of water will vary as a function of the quantity of free
ions in the water. In particular, the line will shift in proportion
to the concentration of sodium chloride, which is the dominant
source of ions in most biological samples. The concentration of
sodium chloride in human blood is held in a narrow range. Hence,
the measurement can be assumed to be from a known fixed quantity,
and an additional precise calibration is thereby obtained. The
spectral shift, however, is quite small. Using the reference cell,
which contains water without salt, and taking the difference signal
at two advantageously chosen spectral positions, a precise
determination is still possible. The reference cell can contain
other materials, such as known concentration of analytes, to
provide other types of calibration.
[0017] Additional features and advantages of the invention will be
set forth in the description which follows, and in part will be
obvious from the description, or may be learned by the practice of
the invention. The features and advantages of the invention may be
realized and obtained by means of the instruments and combinations
particularly pointed out in the appended claims. These and other
features of the present invention will become more fully apparent
from the following description and appended claims, or may be
learned by the practice of the invention as set forth
hereinafter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] In order to describe the manner in which the above-recited
and other advantages and features of the invention can be obtained,
a more particular description of the invention briefly described
above will be rendered by reference to specific embodiments thereof
which are illustrated in the appended drawings. Understanding that
these drawings depict only typical embodiments of the invention and
are not therefore to be considered to be limiting of its scope, the
invention will be described and explained with additional
specificity and detail through the use of the accompanying drawings
in which:
[0019] FIG. 1 is a block diagram of a device according to the
invention.
[0020] FIGS. 2a and 2b are diagrams illustrating wavelength routing
by the wavelength router of FIG. 1.
[0021] FIGS. 3a and 3b are diagrams showing the basic operation of
reflection holographic optical elements (HOEs).
[0022] FIG. 4 is a diagram showing an HOE that splits incident
light.
[0023] FIG. 5 is a drawing of one embodiment of a device according
to the invention.
[0024] FIGS. 6a and 6b are spectral diagrams illustrating an
example of the disposition of source wavelengths, spectral lines of
an analyte, and wavelengths of holograms, for the device in FIG.
5.
[0025] FIGS. 6c and 6d are spectral diagrams illustrating a
calibration method for the device in FIG. 5 based on salinity
measurements.
[0026] FIG. 7 is a drawing of a compact embodiment of a device
according to the invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0027] FIG. 1 is a high-level block diagram of a device according
to the invention, primarily showing the optical functionality of
the major components within the device. In this particular example,
the device includes four sources S1-S4, two detectors 140A-B, a
reference cell 125 and shutter 120, a sample 135 and shutter 130,
and a wavelength router 110.
[0028] Generally speaking, the device operates as follows. The
sources S1-S4 produce light that is routed by the wavelength router
110 to the reference cell 125 and/or sample 135 via the respective
shutter 120,130. The shutters 120,130 allow time gating of the
illumination. Light scattered from the reference cell 125 and/or
sample 135 is routed by the wavelength router 110 to the detectors
140.
[0029] The sources S1-S4 are shown as having a diversity of
wavelengths (wavelengths 1-4 in FIG. 1). The wavelength router 110
directs a linear combination of the incident light from the sources
S1-S4 via the shutters 120,130 to the sample 135 and/or to the
reference cell 125. If I.sub.k is the intensity of the kth source,
where each source is assumed to have a distinct wavelength, then
the intensity I.sub.r that illuminates the reference cell 125 and
the intensity I.sub.s that illuminates the sample 135 are given by:
I r = k = 1 W .times. .times. B k .times. I k ( 1 ) I s = k = 1 W
.times. .times. A k .times. I k ( 2 ) ##EQU1## respectively, where
0.ltoreq.A.sub.k.ltoreq.1, 0.ltoreq.B.sub.k.ltoreq.1, and
A.sub.k+B.sub.k.ltoreq.1, and W is the total number of sources. The
wavelength router 110 performs passive power splitting of the
incoming light to the different outputs. The coefficients A.sub.k
and B.sub.k describe the power splitting that occurs at wavelength
k. In this example, there is a one to one correspondence between
wavelengths and sources (i.e., source Sk produces light at
wavelength k), but this is not required. The specific functionality
can be chosen to route substantially all of a given wavelength to
either the reference cell 125 or sample 135 by designing the
wavelength router 110 so that the appropriate coefficient is
nominally equal to 1 or 0.
[0030] FIG. 2a is a diagram that shows the wavelength routing in a
pictorial diagram. The four arrows on the lefthand side represent
illuminating light produced by the four sources S1-S4. Each arrow
represents a different wavelength. Each path from a source to a
destination (either reference cell 125 or sample 135) represents a
predetermined fraction of each input wavelength diverted to the
appropriate destination. Light from sources S1, S2 and S4 is routed
by the wavelength router 110 to the reference cell 125. Light from
sources S2 and S3 is routed by the wavelength router 110 to the
sample 135. In this diagram, each destination is also represented
by arrows; the number of arrows is not meant to have a particular
meaning for the destinations. The number of arrows also is not
meant to imply characteristics about the physical location or
direction of the optical beams. For example, a single arrow does
not necessarily correspond to a single physical location or a
single incident angle. The corresponding light could be contained
in a single optical beam illuminating a single location, or a
number of separate optical beams illuminating different locations
and/or incident at different angles. In addition, light coming from
a source may also be contained in multiple optical beams.
[0031] When light from the router 110 illuminates either the
reference cell 125 or the sample 135, a scattering signal is
generated. The signal typically consists of a multiplicity of
spectral lines from the various substances within the reference
cell 125 or the sample 135. Processes which generate these spectral
lines include but are not limited to Raman scattering, second
harmonic generation, third harmonic generation, four wave mixing
and fluorescence. Any of these processes may produce a spectrum
which is characteristic of the analyte to be measured. Each
incident wavelength from a source can produce a multiplicity of
scattered wavelengths by one or several of the above processes.
[0032] Taking Raman scattering as a particularly useful example,
each incident wavelength will generate scattered wavelengths at
frequencies which are given by the difference of the incident
frequency and the characteristic Raman frequencies of the
substance. This process is referred to as Stokes Raman scattering.
Sum frequency generation also occurs and is referred to as
Anti-Stokes Raman scattering.
[0033] In the following, the Stokes process is used to illustrate
the function of this device but it is not limited to the Stokes
process. If there are N incident wavelengths on the sample 135 and
L characteristic Raman frequencies, then the scattered signal will
contain N.times.L=P Raman scattered wavelengths. Each such
wavelength may be routed to any of M detectors. As with the routing
from source to reference cell/sample, the routing from reference
cell/sample to detector is general and can be represented by the
equation: I d = k = 1 P .times. .times. C dk .times. P k ( 3 )
##EQU2## where I.sub.d is the total power incident on the dth
detector, P.sub.k is the scattered power at the kth scattered
wavelength, and C.sub.dk is the fraction of the power at the kth
wavelength diverted to the dth detector by the router 110. In the
absence of optical amplification, conservation of energy requires
that the coefficients C.sub.dk obey the following inequality for
any of the individual scattered wavelengths d = 1 M .times. .times.
C dk .ltoreq. 1 ( 4 ) ##EQU3## and where C.sub.dk.gtoreq.0 for all
values of d and k.
[0034] The function of the wavelength router 110 with respect to
the scattered wavelengths from the sample 135 is shown in FIG. 2b,
where each path represents the fraction of a given scattered
wavelength diverted to a given detector. It is assumed in this
example that there are five Raman lines of interest in the sample
and the illuminating light is at two different wavelengths. Hence,
there are a total of 2.times.5=10 scattered wavelengths from the
sample. Each arrow on the righthand side represents one of the
scattered wavelengths. It is assumed that there is one Raman line
of interest in the reference cell. Hence, there are two scattered
wavelengths from the reference cell.
[0035] In many applications, it is preferable that the routing
scheme be a non-blocking architecture. The fraction of light that
is diverted to a particular destination at a given wavelength is
substantially independent of the fraction of light that is diverted
at any other wavelength or to any other destination (subject to
conservation of energy, of course). Mathematically, this means that
the coefficients C.sub.dk need not be correlated for different
values of k. Similarly, the coefficients A.sub.k need not be
correlated and the coefficients B.sub.k need not be correlated. In
many applications, it is also preferable that the architecture also
permits broadcasting, which can be defined as the diversion of a
fraction of a given wavelength to more than one destination. The
resulting architecture therefore preferably can be a completely
general linear non-blocking passive network with broadcast
capability.
[0036] FIGS. 3-7 give further detail on preferred embodiments for
the routing of source and signal wavelengths. Considerable progress
has been made recently in the storage of data in holographic media.
The purpose of such work was to maximize the number of independent
holograms that could be stored in a given archival film. It is also
possible to use such holograms as diffractive optical elements with
narrow-band spectral properties. Because these media are stable and
relatively thick (1 mm), it is possible to produce reflection
holograms, which have substantial diffraction efficiency over<1
nm of wavelength in the near infrared. It is therefore possible to
match the bandwidth of the hologram to that of the spectral line in
question, thus efficiently diffracting only the desired signal.
Narrow band holograms of this type are more readily obtained in
reflection as opposed to transmission. Such holograms are not
dichroic filters, which operate in transmission. In addition, these
holograms operate independently. The aggregate filter function of
two passband filters in series is the product of the individual
filter functions. In contrast, the diffractive output of a
multiplicity of holograms is essentially the sum of the diffraction
from the individual holograms. This property makes it possible to
construct complex, general routers, as the diffractive properties
of each hologram may be considered to be substantially independent
of the presence of other holograms.
[0037] Such holograms can be written by exposure to interfering
writing beams of appropriate wavelength and angle of incidence.
Upon exposure, the refractive index of the photosensitive material
changes in proportion to the local intensity, maxima and minima
corresponding to the constructive and destructive interference of
the incident writing beams. Optimally engineered materials can
respond with substantial index changes, and a large number of
independent holograms can be written in the same volume. A
multiplicity of such holograms can be used to construct a
wavelength router, which deflects wavelengths according to the
linear operations previously described.
[0038] Each hologram in general can be designed to divert a fixed
fraction of the light within a predetermined bandwidth in the
desired direction. Very high diffraction efficiency holograms can
be written to divert>95% of the light, if substantially all of a
particular wavelength is desired at a particular destination.
Alternatively, it is possible to write several holograms of lower
diffraction efficiency, each of which holograms is designed to
divert substantially the same wavelength, but where each hologram
is disposed at a different angle to divert some of the energy at
any wavelength to several destinations.
[0039] While the routing scheme described is general, it is
particularly advantageous when most of the spectral energy that is
emitted from the analyte to be measured is focused onto a single
detector. This is accomplished by diverting the preponderance of
the P different scattered wavelengths onto a single detector. A
large improvement in signal to noise ratio for the measurement of
the desired analyte can thereby be obtained. Multiple analytes can
be similarly treated, creating a spectrometer with very sensitive
detection properties for several substances.
[0040] The number of high diffraction efficiency holograms that can
be written in a given medium scales as follows:
N.sub.H.varies.n.sup.1T (4) where N.sub.H is the number of
holograms, n.sub.1 is the maximum change in the index of refraction
induced by photo-exposure, and T is the thickness of the
medium.
[0041] For a reflection hologram to have>96% diffraction
efficiency, the parameters must satisfy the following inequality:
V.sub.r.ident..pi.n.sub.1T/.lamda..sub.a cos
.psi..sub.o.gtoreq.3.pi./4 (5) where .lamda..sub.a is the
wavelength of the incident radiation and .psi..sub.o is the
complement of the angle of incidence of the radiation with respect
to holographic fringes (.pi./2-.theta..sub.0), where .theta..sub.0
is the angle of incidence. For small .psi..sub.o, .lamda..sub.a=0.9
.mu.m, and n.sub.1=0.02, Eqn. 5 yields T>34 .mu.m. In
consequence, every high diffraction efficiency hologram that is
written requires about 34 .mu.m of photosensitive material, if the
index difference is around 0.02.
[0042] In addition, it is necessary to also consider the spectral
properties of the hologram. It is preferred that the hologram have
appreciable diffraction efficiency over a range which is sufficient
to diffract substantially all of the energy of the radiation that
is desired to be deflected. In the case of routing the source
wavelengths to their appropriate destinations, the hologram need
only have high diffraction efficiency over a band larger than the
spectral width of the source radiation. In the case of the
scattered wavelengths, however, the hologram should diffract the
minimum of radiation not associated with the line to be detected.
In consequence, it is desirable to approximately match the band
over which the hologram has high diffraction efficiency to the
width of the spectral lines. Spectral lines have widths that can
vary considerably and Raman lines can have spectral widths as small
as 0.5 nm.
[0043] The following relationship governs the anticipated spectral
width: .xi. r = - .DELTA. .times. .times. .lamda. .lamda. a .times.
( 2 .times. .times. .pi. .times. .times. n o .lamda. a ) .times. T
.times. .times. sin .times. .times. .theta. o = 3.9 ( 6 ) ##EQU4##
where n.sub.o is the average refractive index of the medium and
where the specified condition corresponds to the location in
wavelength of the first null of reflectivity, and .xi..sub.r=3.9
corresponds to a hologram which exactly meets the inequality (5).
For reflection holograms of lower diffraction efficiency, the
number on the right hand side of (6) is smaller but still>3 for
a reflection hologram having diffraction efficiency of only 43%.
Using Eqn. (6) shows that for a hologram to have a half width of
0.5 nm, for n.sub.o=1.55, and angles of incidence near 90.degree.,
that T=650 .mu.m.
[0044] The foregoing suggests that a preferred media for the
holograms should be a photosensitive materials system of thickness
not less than 100 .mu.m and preferably approximately 1000 .mu.m. It
should be possible to create a change in the index of refraction of
the medium by photo-exposure of not less than 0.005, and preferably
0.02. If the preferred parameters are obtained, then it is possible
to achieve the objectives set forth in regard to diffraction
efficiency and spectral width. It is further possible to write up
to about 30 such holograms in a given volume.
[0045] It is sometimes desired to create holograms with broader
bandwidth, while maintaining a thick medium that is capable of
storing a multiplicity of high diffraction efficiency holograms. It
is possible to cause either the period of the hologram or the
background index of refraction to vary along a direction
perpendicular to the fringes. By doing so, however, inequality (5)
is no longer sufficient to guarantee high diffraction efficiency,
and it is preferable to design with larger n.sub.1 for each
hologram. That reduces the total number of holograms that can be
written before using up the total available index difference of the
media. Nevertheless, it can be shown by simulation that in a 1000
.mu.m thick medium, it is possible to write a hologram of>95%
diffraction efficiency with a bandwidth of 2 nm and an index
difference of 0.003. Hence, about six such holograms could be
written in a medium that has a total index difference range of
0.02. In this example, the background index of refraction was
varied linearly by a total of 0.003 from the front to the back of
the hologram. The various types of holograms described in the
foregoing examples are sufficient to create the essential functions
of the wavelength router 110.
[0046] In this embodiment, the router is composed of holographic
building blocks, which perform certain functions. One elementary
function is to diffract light through an angle and the requisite
hologram is shown in FIG. 3a. The index of refraction is
represented by the frequency of the lines in FIG. 3a. The index of
refraction change of the hologram is usually maximum where the
beams used to perform writing have constructive interference (a
medium in which the index changes negatively with exposure is also
possible and works equivalently). FIG. 3b shows two holograms
disposed at an angle in the same volume. If plane waves at two
wavelengths are incident on this device at the appropriate angles,
the plane waves will emerge at the same angle. This device is a
wavelength muliplexer, and can be used to combine beams at a
multiplicity of wavelengths. In the reverse direction it is a
wavelength demultiplexer.
[0047] It is also possible to divert different fractions of a
single wavelength into two different directions, the functionality
being described as a splitter. The concept is illustrated in FIG.
4. Using a combination of the types of holograms described in the
foregoing, it is possible to construct a wavelength router that can
divert arbitrary fractional linear combinations of wavelengths to
the desired destinations.
[0048] FIG. 5 is a drawing of a preferred embodiment, which can be
considered to be composed of the following sub-assemblies: [0049]
1. Source assembly which consists in this example of sources of
four different wavelengths and a collimating lens. [0050] 2.
Holographic optical element (HOE) which consists of multiple
reflection holograms, and performs the wavelength routing
functions. [0051] 3. Sample and the associated beam delivery and
collection optics. [0052] 4. Reference cell and associated beam
delivery and collection optics.
[0053] The source assembly illuminates the HOE with nominally
collimated light. Beams from each separate wavelength in the source
emerge from the lens at a different angle. Appropriate holograms in
the HOE reflect a portion of each of the separate beams in
substantially the same direction. Hence, when they pass through a
focusing lens, all beams will be focused at the same spot. The HOE
also performs the function of splitting off a fixed fraction of
each beam and diverting it either to the reference cell or the
sample. All beams with a common destination emerge parallel from
the HOE.
[0054] Upon being focused in the sample, the incident radiation
will generate scattering at one or more wavelengths substantially
different from that of the incident radiation, for each substance
present in the sample volume. The scattered wavelengths are
collected by the lens and directed back to the HOE. The HOE now
routes an appropriate fraction of each scattered wavelength to a
desired detector(s). A similar process transpires for the scattered
wavelengths emerging from the reference cell.
[0055] An example which illustrates the function of the HOE in FIG.
5 is presented in FIGS. 6a and 6b. In this example, four sources
are used, labeled .lamda..sub.1-.lamda..sub.4 on the lefthand side
of FIG. 6a. The two sources at .lamda..sub.1 and .lamda..sub.2 are
used to generate Raman signals from four spectral lines of the
analyte (the four spectral lines shown on the righthand side of
FIG. 6a). There are therefore a total of eight difference frequency
signals for the scattered light. FIG. 6b shows the spectral
response of the HOE. Each of the eight spectral curves on the
lefthand side of FIG. 6b represents a reflection hologram centered
at one of the difference frequencies. Thus, the eight difference
frequency signals are diverted by the HOE to the detector. The
remaining two sources at .lamda..sub.3 and .lamda..sub.4 are used
to measure the spectral line of water for calibration, as will be
described in more detail below. After interaction with the
sample/reference cell, both of these sources are shifted to the
same wavenumber. A single hologram (the righthand spectral curve in
FIG. 6b) diverts both signals to the detectors.
[0056] Calibration is an important feature of any device which is
designed to make a quantitative measurement of the concentration of
an analyte. In the example of FIG. 5, the analyte is assumed to be
dissolved in a solvent. Many other substances may also be dissolved
in the same volume of solvent. However, the quantity of the analyte
is expected to be proportional to the volume of solvent from which
light is collected. If all the water in the sample volume has the
same concentration of the analyte, then the scattered signal from
the analyte should be proportional to the scattered signal from the
solvent. The ratio of the signal size from appropriate spectral
lines of the solvent to the signal size from the appropriate lines
of the analyte should be a measure of the concentration of the
analyte. By measuring the solvent separately, and taking the
aforementioned ratio, the measurement will become insensitive to
changes in the observed sample volume which might arise from
mechanical motion, changes in the optical properties of materials
traversed by the light, or physiological changes in an
organism.
[0057] The reference cell preferentially contains, at minimum, a
quantity of a solvent identical to the solvent in which the analyte
is dissolved within the sample. As the geometry with respect to the
reference cell can be regarded as strictly fixed and stable, the
signal from the reference cell should be constant between
repetitive measurements. Any changes will be due to drifts in
optoelectronic components, and will thus be detected and extracted
from the measurement.
[0058] The provision of a fixed standard internal to the apparatus
allows a self-calibrating feature. In a preferred embodiment, the
solvent contains one or more dissolved analytes, in precisely
predefined concentrations. As with the solvent, the signals with
respect to these analytes can only change due to component drifts.
By making a measurement of the reference cell, the drifts may be
mathematically extracted, thus the reference cell measurement
permits an overall calibration of the apparatus.
[0059] In a preferred embodiment, which is applicable to
noninvasive measurement of analytes in human tissue, an additional
calibration is introduced which depends on the salinity of the
bodily fluids. The concentration of sodium chloride in human blood
is held in a very narrow range (approximately 6%) centered around
0.142 Moles/liter. The actual concentration can therefore
frequently be assumed to 0.142 Moles/liter. Salinity shifts the
absolute wavelength of the O--H stretching spectral line of water
by an amount proportional to the concentration of salt. The
dependence is described in an article entitled, "Raman
Spectroscopic Study of Sodium Chloride Water Solutions," by K.
Furic et al., in the Journal of Molecular Structure, Volume
550-551, p. 225-234 (2000). The authors describe a procedure
whereby the spectrum of water containing salt is mathematically
subtracted from the spectrum of pure water in order to calculate
the shift of the spectrum due to the presence of salt. The spectrum
is measured at a minimum of two wavelengths.
[0060] FIG. 6c shows the spectrum of water (the dashed line) and
the spectrum of a solution containing sodium chloride (the solid
line). FIG. 6d shows the difference signal between these two
spectra. The difference signal reaches its largest positive
amplitude at about 3140 cm.sup.-1 and its largest negative
amplitude at about 3506 cm.sup.-1. The difference between the
differential signal at these two wavelengths is marked by 620. It
is a good measure of the wavelength shift due to the salinity and
can be used to calculate the concentration of sodium ions in the
blood.
[0061] In a preferred embodiment, the reference cell contains a
quantity of salt free water and the spectrum is sampled at the two
wavenumbers 3140 and 3506 cm.sup.-1. These values have a nominal
ratio and the actual readings are scaled mathematically to preserve
this nominal value. The scaling factor is then applied to an
identical measurement made using the sample rather than the
reference cell. These measurements are used to estimate the
salinity in the sample.
[0062] The mathematics is now described. Let R.sub.1 be the signal
measured at wavenumber 3140 cm.sup.-1 in the reference cell and
R.sub.2 be the signal measured at wavenumber 3506 cm.sup.-1 in the
reference cell. The ratio R.sub.1//R.sub.2 is a fixed property of
water once the wavelengths have been chosen. However, some
variation may occur due to the differences in the optics or the two
detectors used in the measurement. The value A is calculated such
that R.sub.2'=AR.sub.1 and the ratio A R.sub.1/R.sub.2'=1.
[0063] The same measurement is applied to the sample, which has the
shifted curve of FIG. 6c due to its salinity. If S.sub.1 and
S.sub.2 are the signals obtained at the two wavenumbers 3140 and
3506 cm.sup.-1 respectively from the sample, then the same factor,
A, is applied to the signal S.sub.2. Furthermore, the sums of the
signals for the reference and sample preferably is scaled to be the
same as follows: R.sub.1+AR.sub.2=C(S.sub.1+AS.sub.2) (7) where C
is a mathematical constant which is calculated to satisfy Eqn. 7.
The mathematical function of Eqn. 7 is referred to as
normalization.
[0064] The difference signals are D.sub.1=R.sub.1-CS.sub.1 (8a) and
D.sub.2=AR.sub.2-CAS.sub.2 (8b) where now the quantity
(D.sub.1-D.sub.2)/R.sub.1 is proportional to the salinity of the
sample. The constant of proportionality can be obtained by
measuring a standard saline solution with the apparatus. The above
algorithm can yield an additional calibration for all other analyte
measurements as now signal amplitudes have been absolutely related
to a known concentration.
[0065] It is desirable that light used for calibration traverse as
much of the same optical path as the light from the sample as
possible, and it is preferred that it be detected by the same
detectors. In a preferred embodiment, the router diverts the water
spectral lines to a single detector which is also the detector used
to measure the sum of all powers in all the desired analyte lines.
Referring to FIGS. 5, 6a, and 6b, the process for measurement of
water is as follows: [0066] 1. Shutter 1 is opened and shutter 2 is
closed so that only the reference cell is illuminated. [0067] 2.
Source .lamda..sub.3 is turned on to illuminate the reference cell.
Scattered light is diverted by the corresponding hologram (i.e.,
the hologram designed for the particular wavelength(s)) and is
measured in a single detector. [0068] 3. Source .lamda..sub.3 is
turned off and source .lamda..sub.4 is then turned on. This source
wavelength is chosen to satisfy the following relationship:
1/.lamda..sub.3-1/.lamda..sub.4=.DELTA.K.sub.w (9) where
.DELTA.K.sub.w the difference in wavenumbers between the two
measurement wavelengths and is preferred to be approximately 366
cm.sup.-1. As Stokes Raman scattering works on the basis of
generating the difference frequency between the source and the
characteristic vibrational frequency of the molecule, two sources
obeying Eqn. 9 will generate a scattering signal which appears at
the same wavelength, but which has sampled two distinct wavenumbers
in the desired Raman line. In other words, the difference component
between source .lamda..sub.3 and wavenumber 3140 cm.sup.-1 will be
located at the same wavelength as the difference component between
source .lamda..sub.4 and wavenumber 3506 cm.sup.-1. The same
hologram as in step 2 will therefore divert the desired light to
the same detector. [0069] 4. Shutter 1 is closed and shutter 2 is
open such that the sample is measured. [0070] 5. Sources
.lamda..sub.3 and .lamda..sub.4 are sequenced in the same manner as
in the reference cell measurement, in order to make the sample
measurement. [0071] 6. The results of the .lamda..sub.3 and
.lamda..sub.4 measurements of the reference cell and sample are
used to calibrate the salinity of the sample, as described
above.
[0072] To measure the analyte, sources .lamda..sub.1 and
.lamda..sub.2 are simultaneously actuated. In a preferred
embodiment, the analyte is also present in the reference cell, and
can be measured separately by opening shutter 1 and closing shutter
2. In this embodiment, the router deflects each scattered
wavelength to the same detector. Hence, the power at each
wavelength is summed. By opening shutter 2 and closing shutter 1,
the same measurement can be performed for the sample. One advantage
of using a multiplicity of sources is to obtain more source power
from relatively inexpensive lasers. Note that this system permits a
very large number of scattered wavelengths all to be deflected to a
single detector. The signal increases proportionately. The variance
of the dark current of the detector is independent of the signal.
Hence, the S/N ratio with respect to dark current noise increases
proportionately to the signal.
[0073] Because the concentration of the analyte in the reference
cell is known, the signal from the reference cell is a good
calibration for the signal from the sample. In the case when more
than one analyte is to be measured, a preferred embodiment consists
of adding additional detectors for each analyte and of adding each
analyte to the solution in the reference cell.
[0074] The presence of the sources, sample, reference cell and
detectors on the same side of the optical system with respect to
the HOE can produce crowding. This can be somewhat ameliorated by
moving one or more assemblies out of the plane of the drawing
(along the x direction referring to FIG. 5). Nevertheless when
compactness is critical, a problem of crowding can still arise.
[0075] The issue arises from the dependence of the acceptance angle
of the holograms as a function of the incident angle. For
reflection holograms, the angular deviation .delta. from nominal
for which the diffraction efficiency will go to zero is given by:
.delta. = .DELTA. .times. .times. .lamda. .lamda. a .times. tan
.times. .times. .theta. ( 10 ) ##EQU5## where .DELTA..delta. is the
wavelength deviation from nominal which causes the diffraction
efficiency to go to zero. Note that this calculation emerges from a
first order expansion of the Bragg condition, and as .theta.
approaches 90.degree., it is preferable to carry out the expansion
to second order as the first term vanishes. If the hologram is to
have a narrow wavelength band, which is optimal for narrow spectral
lines from the analytes, it will also have a narrow field of view
unless the incident angle is relatively close to .pi./2 radians.
The angular diversion between the incident and diffracted light is
just 2(.pi./2-.theta.), which becomes small as .theta. becomes
large.
[0076] For collimated light incident on a lens of focal length f,
the translation deviation between the spot emitting the light and
the spot in which scattered light is focused is 2f (.pi./2-.theta.)
which also becomes small. Hence, sources and detectors would be
crowded together unless the focal lengths are large. The optical
system, however, preferably collects as large a fraction of the
light emanating from the sample as possible. In addition, it is
undesirable to magnify the size of the spot in the sample because
then larger detectors would be required, which would have higher
dark current. As a result, the size of the optics scale with the
focal length. Hence, in the design of FIG. 5, the relief of
crowding typically results in larger optics.
[0077] A solution to the problem of crowding for compact devices is
presented in FIG. 7. Here a second HOE is introduced. The second
HOE performs the function of reflecting substantially all of the
radiation incident upon it from the reflections arising from HOE1.
HOE2 is disposed at an angle with respect to HOE1. In consequence,
light propagating back from HOE2 towards HOE1 is outside the field
of view of the holograms in HOE1 and is not diffracted a second
time by HOE1. Such an arrangement is possible because the field of
view of the hologram, .delta. can be much smaller than the angle
through which the light is diverted and hence the light will not be
diffracted a second time.
[0078] As a result, the source can be on the opposite side of the
system from both the sample and reference cell. A long wave pass
filter (LWP) is used to reflect source light while passing the
scattered light to the detectors. This arrangement is appropriate
for Stokes Raman Scattering. For Anti-Stokes Raman scattering, a
short wave pass filter should be chosen. Aside from further
relieving the crowding, the filter also helps deflect source light
that might be scattered off of the optics, or other index
discontinuities in the optical path, from reaching the
detectors.
[0079] To preferentially illuminate either the sample or reference
cell, a moveable dual aperture with reflecting prism is employed.
When it is desired to illuminate the sample, the device is
positioned in the Y direction (see FIG. 7 for axis definitions)
such that focused light from the sources and focused light from the
scattering passes through the lower of the two apertures. To
illuminate the reference cell, the dual aperture with turning prism
is translated in Y such that the light passes through the upper
aperture. FIG. 7 shows the apertures in this position. Rays which
are shown that traverse the apertures in the direction of the
sample are presented to show the path of the source and scattered
light when the light passes through the lower aperture. The prism
deflects both source and scattered light through approximately
90.degree., allowing the reference cell to be disposed away from
the sample.
[0080] In FIG. 7, marginal and central rays are presented for the
illumination and scattering signals. Angles have been exaggerated
for clarity. Rays which are at slightly different Y positions have
been positioned so as to be visible in the drawing and can in
practice overlap. Some rays that would exist between the two HOE's
have been suppressed so as not to produce an excessively tangled
view of the rays between the HOE's.
[0081] FIG. 7 shows a case where the scattered light from both the
reference cell and sample would be brought back to a single
detector but that is not a requirement of the design. It is
possible to combine the functions of HOE1 and HOE2 in a single
medium. The two functions have been separated here for clarity of
presentation.
* * * * *