APPARATUS, METHOD AND COMPUTER-READABLE STORAGE
MEDIUM FOR PROCESSING A SIGNAL IN A SPECTROMETER
SYSTEM
FIELD OF THE INVENTION
Exemplary embodiments of present invention generally relate to spectrometer
systems and methods of propagating electromagnetic signals and, more particularly, an
apparatus, method and computer-readable storage medium for processing a signal in a
spectrometer system.
BACKGROUND OF THE INVENTION
Spectrometry using continuous wave (CW) tunable sources with narrow spectral
linewidth and long coherence lengths has well-known advantages associated with high
spectral contrast, frequency selectivity and excellent sensitivity. Scanning CW terahertz
(THz) spectrometers are a prime example of this technology. In such systems, phase
stability in the transmitter-to-receiver demodulation processing may be required to obtain
an accurate measurement of the transmitted electric-field intensity and to characterize any
resulting absorption losses from samples in the spectrometer. However, the signal
generated by a THz spectrometer may contain a strong background signature created by
superimposed standing wave patterns within the spectrometer cavity or sample cell.
As the path length of the spectrometer increases, the variation in amplitude as a
function of measurement wavelength may also increase in frequency. A spectrometer
acquiring data at a discrete set of THz frequencies, then may under sample the background
pattern. The resulting background signature may be an aliasing of the actual standing wave
structure within the instrument, and change shape and amplitude as the measurement
frequency sampling is altered.
In the presence of small frequency calibration drifts occurring in a scanning
spectrometer, the sensitivity of the background structure to frequency sampling may cause
changes in that structure over multiple measurements. This variation in the background
between scans may reduce the effectiveness of a simple ratio technique — dividing a

measurement by a reference taken with no sample present — to accurately determine the
spectral features of a sample being tested.
SUMMARY OF THE INVENTION
In light of the foregoing background, embodiments of the present invention
provide an improved apparatus, method and computer-readable storage medium for
processing a signal in a spectrometer system. According to one aspect of the present
invention, a method is provided that includes receiving and processing a sample signal
scan. Processing the sample signal scan includes applying an inner-product operation on
the sample signal scan and each of a plurality of eigenvectors to generate a plurality of
corresponding coefficients, and subtracting the sample signal scan from a linear
combination of the eigenvectors and corresponding coefficients to thereby produce a
corrected sample signal scan. In this regard, the eigenvectors have been generated by
decomposing a plurality of background reference signal scans according to a singular
value decomposition technique; and as such, the method may also include receiving and
decomposing the plurality of background reference signal scans to generate the
eigenvectors.
The signal scans include a plurality of electromagnetic signal measurements at a
discrete set of frequencies, where each measurement has been taken by a spectrometer
system passing an electromagnetic signal through a sample cell including a base medium
with (for the sample signal scan) or without (for the background reference signal scans) a
sample medium.
The method may also include segmenting the sample signal scan into a plurality of
frequency segments, processing the sample signal scan segments to produce a respective
plurality of corrected sample signal scan segments, and assembling the corrected sample
signal scan segments. For each sample signal scan segment, processing the sample signal
scan segments may include applying an inner-product operation on the sample signal scan
segment and a respective set of eigenvectors to generate a respective set of corresponding
coefficients, and subtracting the sample signal scan segment from a linear combination of
the respective set of eigenvectors and corresponding coefficients to thereby produce a
respective corrected sample signal scan segment.
The aforementioned sets of eigenvectors may have been generated by segmenting a
plurality of background reference signal scans into a plurality of sets of background
reference signal scan segments, and decomposing each set of the background reference

signal scan segments according to a singular value decomposition technique. Thus, the
method may also include receiving and segmenting the plurality of background reference
signal scans into a plurality of sets of background reference signal scan segments, and
decomposing each set of the background reference signal scan segments to generate the
plurality of sets of eigenvectors.
The method may further include identifying an electromagnetic signal
measurement in the sample signal scan corresponding to an electromagnetic signal
measurement in the corrected sample signal that exceeds a specified absorption threshold.
The method may then include removing the identified electromagnetic signal
measurement to produce a modified sample signal scan, and processing the modified
sample signal scan. In such an instance, processing the modified sample signal scan may
include applying an inner-product operation on the modified sample signal scan and each
of a plurality of eigenvectors to generate a second plurality of corresponding coefficients,
and subtracting the sample signal scan from a linear combination of the eigenvectors and
second corresponding coefficients to thereby produce a further corrected sample signal
scan.
Moreover, the method may include calculating a ratio of the sample signal scan to
an average of the background reference signal scans, and adjusting the corrected sample
signal scan based on the ratio.
According to other aspects of the present invention, an apparatus and computer-
readable storage medium for processing a signal in a spectrometer system are provided.
Exemplary embodiments of the present invention therefore provide an improved
apparatus, method and computer-readable storage medium for processing a signal in a
spectrometer system. As indicated above, and explained below, exemplary embodiments
of the present invention may solve problems identified by prior techniques and provide
additional advantages.
BRIEF DESCRIPTION OF THE DRAWINGS
Having thus described the invention in general terms, reference will now be made
to the accompanying drawings, which are not necessarily drawn to scale, and wherein:
FIG. 1 is a schematic block diagram of a spectrometer system in accordance with
one exemplary embodiment of the present invention;

FIG. 2 is a flowchart illustrating various steps in a method of sweeping a
spectrometer system through a frequency spectrum, according to exemplary embodiments
of the present invention; and
FIGS. 3 and 4 are block diagrams illustrating operations that a processing
apparatus may be configured to perform according to exemplary embodiments of the
present invention.
DETAILED DESCRIPTION OF THE INVENTION
The present invention now will be described more fully hereinafter with reference
to the accompanying drawings, in which preferred embodiments of the invention are
shown. This invention may, however, be embodied in many different forms and should
not be construed as limited to the embodiments set forth herein; rather, these embodiments
are provided so that this disclosure will be thorough and complete, and will fully convey
the scope of the invention to those skilled in the art. In this regard, reference may be made
herein to a number of mathematical or numerical expressions that may be related by
equality. It should be understood, however, that this equality may refer to an absolute or
approximate equality, such that exemplary embodiments of the present invention may
account for variations that may occur in the system and method, such as those due to
engineering tolerances. Further, although a number of variables may be reflected by
mathematical symbols including subscripts at various instances, it should be understood
that these symbols and subscripts are presented solely for illustrative purposes, and should
not be construed as limiting the scope of the invention. Like numbers refer to like
elements throughout.
FIGS. 1 and 2 illustrate a spectrometer system and method that may benefit from
exemplary embodiments of the present invention ("exemplary" as used herein referring to
"serving as an example, instance or illustration"). It should be understood, however, that
the spectrometer system and method illustrated and hereinafter described are merely
illustrative of one type of system and method that may benefit from exemplary
embodiments of the present invention and, therefore, should not be taken to limit the scope
of the present invention. For an example of another spectrometer system and method that
may benefit from exemplary embodiments of the present invention is described in U.S.
Patent Application No. 12/712,736, entitled: System and Method for Magnitude and Phase
Retrieval by Path Modulation, filed February 25, 2010. The content of the 12/713,736
application is hereby incorporated by reference in its entirety.

While several embodiments of the spectrometer system and method are illustrated
and will be hereinafter described for purposes of example, other types of systems and
methods of propagating electromagnetic signals may readily employ the present invention.
Moreover, the system and method of the present invention will be primarily described in
conjunction with signals in the THz (or mmW) region of the electromagnetic spectrum.
But the system and method of embodiments of the present invention may be utilized in
conjunction with a variety of other applications, both within and outside the THz region of
the electromagnetic spectrum.
As shown, a spectrometer system 10 of one exemplary embodiment of the present
invention includes a transmitter 12 configured to transmit a beam of coherent radiation
(electromagnetic wave) at a given frequency. The transmitter can comprise any of a
number of different transmitters known to those skilled in the art. In one exemplary
embodiment, for example, the transmitter comprises a photomixer transmitter. In such
instances, the transmitter includes a high-speed photoconductive diode (i.e., photomixer),
which may be pumped with two laser sources 14a, 14b via a beam combiner/splitter 16
and an optically coupled first optical path 18 (e.g., optical fiber). In this regard, the laser
sources may be configured to emit signals with electric fields having offsetting
frequencies at a>\ and a>2 (i.e., Eai and Ea2). Also note that frequencies coi and a>2 may be
expressed as angular frequencies, or as corresponding temporal frequencies (f= colln).
The transmitter 12 may be coupled to a transmitter bias modulator 20 including a
voltage source 22 configured to generate a sinusoidal modulated voltage with which the
photomixer of the transmitter may be biased, although it should be understood that the
system need not frequency modulate the signal. By locating the photomixer at the driving
point of an antenna, such as a spiral, dipole or slot antenna, the difference-frequency
current is converted to difference-frequency photons. The result is a highly-tunable,
continuous-wave (CW), highly-coherent source of radiation contained in a single (quasi-
Gaussian) spatial mode, and having a transmitted electric field ETM- For more information
on such a transmitter, see U.S. Patent No. 6,348,683 entitled: Quasi-Optical Transceiver
Having an Antenna with Time Varying Voltage, issued February 19, 2002.
Thus, the method of one exemplary embodiment includes selecting a transmission
frequency, thereafter transmitting a beam of radiation (i.e., source beam) at that frequency
from the transmitter 12, as shown in blocks 42 and 48 of FIG. 2. The transmission
frequency can be selected in any of a number of different manners. To detect a sample

based upon a measured absorption signature, however, the transmission frequency may be
typically selected within a range of frequencies over which the absorption signature is
defined. In a photomixer transmitter, then, the photomixer can be pumped with tunable
laser sources at a frequency ω2, and a frequency ω1 that are selected to thereby select the
difference, or transmission, frequency (i.e.,ω2 - ω1).
The beam of radiation from the transmitter 12 may pass through a collimating lens
24 to produce a collimated beam of radiation. The beam may then pass through a sample
cell 26 that may be bounded by reflectors 26a and 26b through which the beam passes,
and that may include a sample medium to be analyzed and a base medium, such as
ambient air. As will be appreciated, the sample and base medium can have any of a
number of different forms through which the beam of radiation is at least partially
transmissive. For example, the sample and base medium can comprise a solid, liquid, gas,
plasma or aerosol. More particularly, in various advantageous embodiments, the base
medium of ambient air may be in gas form, while a sample may be in gas or aerosol form.
As the beam of radiation passes through the sample cell 26, the sample and base
medium in the sample cell absorb at least a portion of the beam, or more particularly at
least a portion of the electric field of the beam. The remaining, unabsorbed portion of the
beam of radiation (i.e., received signal) then exits the sample cell. The sample signal then
propagates to a focusing lens 28, from which the focused signal is picked up or otherwise
received by a receiver 30 as a received signal ERP.
The receiver obtains a measurement representative of the received electric field
ERP, as shown in block 50 of FIG. 2. Similar to the transmitter 12, the receiver may
comprise an electric-field detector such as a photomixer receiver (homodyne receiver).
The photomixer receiver may include an antenna configured to receive the electric field
and generate a corresponding voltage in response thereto, which may be directed to a high-
speed photoconductor. The photoconductor is also electrically coupled to a second optical
path 32 for pumping the photoconductor with beams from the same two laser sources 14a,
14b pumping the photomixer transmitter 12. In this regard, the beam combiner/splitter 16
may separate each of the signals from the laser sources into the aforementioned first
optical path 18, as well as another, second optical path (e.g., optical fiber) for pumping the
receiver photomixer. These signals, then, may modulate a conductance of the photomixer.
The voltage generated by the receiver antenna may be applied to the photomixer
active material, and produce a current through the modulated conductance. The difference
frequency result of the product is the down-converted signal current IDown, which may have

a corresponding down-converted electric-field ER, either or both of which may constitute
or otherwise represent a signal. For more information on such a receiver, see the
aforementioned '683 patent.
The down-converted signal current IDown and/or electric-field ER may be applied to
receiver signal conditioning circuitry 34 including, for example, an anti-aliasing filter 36.
The output of the signal conditioning circuitry may then be input to a processing apparatus
38, such as for performing digital signal processing operations thereon. In this regard, the
processing apparatus can comprise any of a number of different devices capable of
operating in accordance with exemplary embodiments of the present invention. For
example, the processing apparatus may comprise a computer (e.g., personal computer,
laptop computer, server computer, workstation computer) or other computing apparatus.
The processing apparatus may include a processor and computer-readable storage
medium. The processor may include, for example, one or more programmed or
programmable general-purpose processors, microprocessors, coprocessors, controllers,
specialized digital signal processors and/ or various other processing devices including one
or more integrated circuits (e.g., ASICs, FPGAs), hardware accelerators, processing
circuitry or the like.
The computer-readable storage medium of the processing apparatus 38 may
include volatile and/or non-volatile memory, which may be embedded and/or removable,
and may include, for example, read-only memory, flash memory, magnetic storage devices
(e.g., hard disks, floppy disk drives, magnetic tape, etc.), optical disc drives and/or media,
non-volatile random access memory (NVRAM), and/or the like. The computer-readable
storage medium may store any of a number of different data, content or the like, according
to exemplary embodiments of the present invention. For example, the computer-readable
storage medium may be configured to store executable or other computer-readable
instructions that may be executed or otherwise processed by the processor.
If the spectrometer system 10 frequency modulates the signal, the signal
processing operations performed by the processor 38 may include recovering the
amplitude of the down-converted signal ER such as by an analog-to-digital converter (A/D)
40 direct sampling of the signal at the modulating frequency, and the processor Discrete
Fourier Transformation (DFT) processing of the sampled data. Alternatively, for example,
the spectrometer system may further include a synchronous demodulator such as a lock-in
amplifier (not shown) for further processing the down-converted signal ER. In this regard,

such a synchronous demodulator may include a local oscillator operating at the
modulating frequency ωm to thereby recover the amplitude of the down-converted signal.
In operation as a spectrometer, the system 10 scans through a number of
transmission frequencies in a range of frequencies, such as by pumping the photomixers of
the transmitter 12 and receiver 30 with tunable laser sources at frequency ω2, and
frequency ω1 that are scanned through a number of frequencies, as shown in blocks 54 and
56 of FIG. 2. For each transmission frequency in the range of frequency, and thus each
beam of radiation having a different transmission frequency, the processor 38 may
measure the amplitude and/or phase of the down-converted signal current IDown. The
resulting collection of transmissions amplitudes and/or phases, and associated
transmission frequencies, may define a measured absorption or dispersion signature for the
sample in the sample cell 26, from which the sample may be identified, as shown in block
58 of FIG. 2.
As explained in the background section, the signal generated by a spectrometer
(e.g., THz spectrometer) may contain a strong background signature created by
superimposed standing wave patterns within a sample cell (e.g., sample cell 26). As the
path length of the spectrometer increases, the variation in amplitude as a function of
measurement wavelength may also increase in frequency. A spectrometer acquiring data
at a discrete set of THz frequencies over a spectrum of interest, then may under sample the
background pattern. The resulting background signature may be an aliasing of the actual
standing wave structure within the instrument, and change shape and amplitude as the
measurement frequency sampling is altered.
As also explained in the background, in the presence of small frequency calibration
drifts occurring in a scanning spectrometer, the sensitivity of the background structure to
frequency sampling may cause changes in that structure over multiple measurements.
This variation in the background between scans may reduce the effectiveness of a simple
ratio technique - dividing a measurement by a reference taken with no sample present - to
accurately determine the spectral features of a sample being tested.
In view of the foregoing, the processing apparatus 38 of exemplary embodiments
of the present invention may be configured to process acquired measurement according to
an orthogonal background subtraction or suppression (OBS) technique to at least partially
separate a complex and varying background structure from an acquired measurement, and
thereby reveal the spectrum of a sample under test. As described herein, the acquired
measurements may be in the form of the down-converted electric-field (or signal) ER

measured at a discrete set of frequencies in a spectrum of interest, but it should be
understood that the measurements may equally be in the form of the down-converted
signal current IDown measured over a similar discrete set of frequences. As also described
herein, the processing OBS technique may but need not be implemented in logarithm
space so that division of a reference measurement is equivalent to subtraction.
Reference is now made to FIGS. 3 and 4, which illustrate block diagrams of
operations that the processing apparatus 38 may be configured to perform according to
exemplary embodiments of the present invention. The illustrated block diagrams include a
number of scans to illustrate signals or measurements of signals received or calculated by
the processing apparatus. It should be understood that references to a "signal" may be
used interchangeably with references to a "measurement of a signal," as may be received
by the processing apparatus. It should also be understood that the illustrated scans are
presented merely for illustration, and that signals, measurements or other data may be
received, calculated or presented in any of a number of different forms without departing
from the spirit and scope of the present invention.
According to exemplary embodiments of the present invention, the processing
apparatus 38 may be configured to process a signal scans by a process that includes
obtaining or otherwise retrieving N background reference signal scans 60. As described
herein, each a signal scan includes signal measurements at a discrete set of frequencies in a
spectrum of interest. In the context of a background reference signal scan, each
measurement is taken of a transmitted signal passing through the sample cell 26 with the
base medium (e.g., ambient air) but without the sample medium. The processing
apparatus may then be configured to decompose the background reference signal scans,
such as in accordance with a singular value decomposition (SVD) technique 62, to
generate a set of N orthogonal eigenvectors 64. The resulting eigenvectors may
represent a set of basis functions as a function of frequency, whose linear combinations
may reproduce each of the N background reference signal scans. The eigenvectors may
then be utilized by the processing apparatus to process a subsequent sample signal scan. It
should be understood that the background reference signal scans may be obtained and
decomposed at any time prior to processing a sample signal. Consequently, the
background reference signal scans or resulting eigenvectors may be stored in memory
embodied within or otherwise associated with the processing apparatus, and retrieved at an
appropriate time for use in generating the eigenvectors and/or processing a sample signal
scan.

At some time after generating the eigenvectors 64, and with the sample medium
having been inserted into the sample cell 26, a sample signal scan 66 may be obtained,
where each measurement of the scan may be taken of a transmitted signal passing through
the sample cell including the sample and base mediums. The processing apparatus 38 may
be configured to receive and project the sample signal scan on each of the eigenvectors to
generate corresponding coefficients 70. This projection may be accomplished, for
example, by applying an inner-product (dot-product) operation 68 on the eigenvectors and
sample signal scan, which itself may be accomplished by multiplying the transpose of the
eigenvectors and sample signal scan. Regardless of the manner by which the sample
signal scan is projected onto each of the eigenvectors, the eigenvectors may be linearly
combined 72 with their corresponding coefficients to generate a correction value or values
74, which may be subtracted 76 from the sample signal scan to produce a corrected sample
signal scan.
The OBS technique implemented by the processing apparatus 38 may reveal the
content of the sample signal scan that is orthogonal to the space of spectra spanned by
the background reference eigenvectors. The technique implemented by the processing
apparatus may be able to remove a background signature including superimposed
standing waves of time-varying amplitudes. In addition, consider that at terahertz, the gas
spectra of interest may be spectral lines caused by the rotational characteristics of the
molecule. The resolution of the spectrometer system of exemplary embodiments of the
present invention may be sufficient to resolve many of these lines which may require
sampling rich spectra with a large number of samples.
As will be appreciated, performing SVD on a set of N background reference signal
scans 60, each with M measurement frequencies, may require the allocation and
manipulation of an N x M matrix. A typical THz spectrum may include 10,000 to 100,000
measurement points (frequencies), and as many as 50 background reference signal scans
may be acquired. As shown more particularly in FIG. 4, to relieve at least a portion of
the otherwise high computing and storage resources that may otherwise be required to
process such signal scans, the processing apparatus 38 of various example
embodiments may be configured to segment, process and then stitch back together
signal scans. More particularly, the processing apparatus may be configured to
segment the background reference signal scans and sample signal scan 66 into a
plurality of overlapping frequency segments, each of which may be individually processed

such as in accordance with the OBS technique explained above with respect to FIG. 3.
The overlapping spectra segments resulting from individually processing the segments
may be assembled (or stitched together) and averaged, such as according to a least
squares minimization of discrepancy technique with respect to spectra bias and tilt.
In implementing the OBS technique according to exemplary embodiments of the
present invention, the processing apparatus 38 may be configured to apply a bias
correction to any OBS residual. In this regard, in the generated eigenvectors 64 (or set of
eigenvectors for each segment), the mean of the background may be represented as a linear
combination of eigenvectors. As a result, the OBS technique implemented by the
processing apparatus 38 may alter the mean of each segment. In addition, during the
stitching reconstruction process, one segment may be held constant while the processing
apparatus optimally recombines the others with respect to bias and tilt based on the
segment being held constant. As a consequence, if not corrected, the absolute bias of the
measured spectrum may be lost during this processing.
Accurate detection of broadband absorbing gas species may require that the
absolute absorption magnitude be restored to the processed measurement. Thus, the
processing apparatus 38 of exemplary embodiments of the present invention may be
configured to calculate the ratio between the sample and background signals, and then
set the average signal of the final spectrum to match this ratio, thereby correcting the bias
due to any OBS residual. More particularly, for example, the processing apparatus may be
configured to calculate the difference between the average sample signal and the average
background signal - the averages performed over all frequencies. The processed final
spectrum may then be adjusted so that its average over all frequencies matches the
calculated difference. When these calculations are performed on the logarithms of the
sample and background amplitudes, this has the effect of setting the average transmission
of the processed data to the ratio of the sample signals to the background signals.
Even further, in the presence of high slopes in the sample signal spectrum, the
projection of segments onto the corresponding eigenvectors can result in anomalously high
coefficients 70, which in turn can result in a failure to accurately suppress the background
signal in the segments containing the high slope features. To address this condition, the
processing apparatus 38 of exemplary embodiments may employ the OBS technique in an
iterative manner. For example, after initially processing a sample signal scan (see FIG.
3), data points in the sample signal scan corresponding to points in the corrected sample
signal scan exceeding a specified absorption threshold may be identified and temporarily

removed from the original sample signal scan. The modified raw sample signal scan may
then be projected (e.g., applying the inner-product operation 68) a second time on to the
eigenvectors to determine more-accurate coefficients. The resulting linear combination of
eigenvectors with the more-accurate coefficients may then be subtracted from the original
sample signal scan (including the high absorption points) to yield a further, more-accurate
corrected sample signal scan.
According to one aspect of the example embodiments of present invention, the
operations performed by the processing apparatus 38, such as those illustrated by the block
diagrams of FIGS. 3 and 4, may be performed by various means. It will be understood
that each block or operation of the block diagrams, and/or combinations of blocks or
operations in the block diagrams, can be implemented by various means. Means for
implementing the blocks or operations of the block diagrams, combinations of the blocks
or operations in the block diagrams, or other functionality of example embodiments of the
present invention described herein may include hardware, and/or a computer program
product including a computer-readable storage medium having one or more computer
program code instructions, program instructions, or executable computer-readable
program code instructions stored therein. In this regard, program code instructions may be
stored on a computer-readable storage medium and executed by a processor, such as those
of the processing apparatus.
As will be appreciated, program code instructions may be loaded onto a computer
or other programmable apparatus (e.g., processor, memory, or the like) from a computer-
readable storage medium to produce a particular machine, such that the particular machine
becomes a means for implementing the operations specified in the block diagrams'
block(s) or operation(s). These program code instructions may also be stored in a
computer-readable storage medium that can direct a computer, a processor, or other
programmable apparatus to function in a particular manner to thereby generate a particular
machine or particular article of manufacture. The instructions stored in the computer-
readable storage medium may produce an article of manufacture, where the article of
manufacture becomes a means for implementing the functions specified in the block
diagrams' block(s) or operation(s). The program code instructions may be retrieved from
a computer-readable storage medium and loaded into a computer, processor, or other
programmable apparatus to configure the computer, processor, or other programmable
apparatus to execute operations to be performed on or by the computer, processor, or other
programmable apparatus. Retrieval, loading, and execution of the program code

instructions may be performed sequentially such that one instruction is retrieved, loaded,
and executed at a time. In some example embodiments, retrieval, loading and/or
execution may be performed in parallel such that multiple instructions are retrieved,
loaded, and/or executed together. Execution of the program code instructions may
produce a computer-implemented process such that the instructions executed by the
computer, processor, or other programmable apparatus provide operations for
implementing the functions specified in the block diagrams' block(s) or operation(s).
Accordingly, execution of instructions associated with the blocks or operations of
the block diagrams by a processor, or storage of instructions associated with the blocks or
operations of the block diagrams in a computer-readable storage medium, supports
combinations of operations for performing the specified functions. It will also be
understood that one or more blocks or operations of the block diagrams, and combinations
of blocks or operations in the block diagrams, may be implemented by special purpose
hardware-based computer systems and/or processors which perform the specified
functions, or combinations of special purpose hardware and program code instructions.
Many modifications and other embodiments of the invention will come to mind to
one skilled in the art to which this invention pertains having the benefit of the teachings
presented in the foregoing descriptions and the associated drawings. Therefore, it is to be
understood that the invention is not to be limited to the specific embodiments disclosed
and that modifications and other embodiments are intended to be included within the
scope of the appended claims. Although specific terms are employed herein, they are used
in a generic and descriptive sense only and not for purposes of limitation.

WHAT IS CLAIMED IS:
1. An apparatus comprising:
a processor configured to receive a sample signal scan that includes a plurality of
electromagnetic signal measurements at a discrete set of frequencies, each respective
measurement having been taken by a spectrometer system passing an electromagnetic
signal through a sample cell including a sample medium and a base medium,
wherein the processor is configured to segment the sample signal scan into a
plurality of frequency segments,
wherein the processor is configured to process the sample signal scan segments to
produce a respective plurality of corrected sample signal scan segments, wherein the
processor being configured to process the sample signal scan segments includes, for each
sample signal scan segment, being configured to:
apply an inner-product operation on the sample signal scan segment and a
respective set of eigenvectors from a plurality of sets of eigenvectors to generate a
respective set of corresponding coefficients, the sets of eigenvectors having been
generated by segmenting a plurality of background reference signal scans into a
plurality of sets of background reference signal scan segments, and decomposing
each set of background reference signal scan segments according to a singular
value decomposition technique, each background reference signal scan including a
plurality of electromagnetic signal measurements at a discrete set of frequencies,
each respective measurement having been taken by the spectrometer system
passing an electromagnetic signal through the sample cell including the base
medium but without the sample medium, and
subtract the sample signal scan segment from a linear combination of the
respective set of eigenvectors and corresponding coefficients to thereby produce a
respective corrected sample signal scan, and
wherein the processor is configured to assemble the corrected sample signal scan
segments.
2. The apparatus of Claim 1, wherein the processor is further configured to
receive and segment the plurality of background reference signal scans into a plurality of
sets of background reference signal scan segments, and decompose each set of the
background reference signal scan segments to generate the plurality of sets of
eigenvectors.

3. The apparatus of Claim 1, wherein the processor is further configured to
identify an electromagnetic signal measurement in the sample signal scan corresponding to
an electromagnetic signal measurement in the corrected sample signal that exceeds a
specified absorption threshold,
wherein the processor is configured to remove the identified electromagnetic signal
measurement to produce a modified sample signal scan, and
wherein the processor is configured to process the modified sample signal scan,
including being configured to:
apply an inner-product operation on the modified sample signal scan and
each of a plurality of eigenvectors to generate a second plurality of corresponding
coefficients, and
subtract the sample signal scan from a linear combination of the
eigenvectors and second corresponding coefficients to thereby produce a further
corrected sample signal scan.
4. The apparatus of Claim 1, wherein the processor is further configured to
calculate a ratio of the sample signal scan to an average of the background reference signal
scans, and adjust the corrected sample signal scan based on the ratio.
5. An apparatus comprising:
a processor configured to receive a sample signal scan that includes a plurality of
electromagnetic signal measurements at a discrete set of frequencies, each respective
measurement having been taken by a spectrometer system passing an electromagnetic
signal through a sample cell including a sample medium and a base medium,
wherein the processor is configured to process the sample signal scan, including
being configured to:
apply an inner-product operation on the sample signal scan and each of a
plurality of eigenvectors to generate a plurality of corresponding coefficients, the
plurality of eigenvectors having been generated by decomposing a plurality of
background reference signal scans according to a singular value decomposition
technique, each background reference signal scan including a plurality of
electromagnetic signal measurements at a discrete set of frequencies, each
respective measurement having been taken by the spectrometer system passing an

electromagnetic signal through the sample cell including the base medium but
without the sample medium, and
subtract the sample signal scan from a linear combination of the
eigenvectors and corresponding coefficients to thereby produce a corrected sample
signal scan,
wherein the processor is further configured to identify an electromagnetic signal
measurement in the sample signal scan corresponding to an electromagnetic signal
measurement in the corrected sample signal that exceeds a specified absorption threshold,
wherein the processor is configured to remove the identified electromagnetic signal
measurement to produce a modified sample signal scan, and
wherein the processor is configured to process the modified sample signal scan,
including being configured to:
apply an inner-product operation on the modified sample signal scan and
each of a plurality of eigenvectors to generate a second plurality of corresponding
coefficients, and
subtract the sample signal scan from a linear combination of the
eigenvectors and second corresponding coefficients to thereby produce a further
corrected sample signal scan.
6. The apparatus of Claim 5, wherein the processor is further configured to
calculate a ratio of the sample signal scan to an average of the background reference signal
scans, and adjust the corrected sample signal scan based on the ratio.
7. A method comprising:
receiving a sample signal scan that includes a plurality of electromagnetic signal
measurements at a discrete set of frequencies, each respective measurement having been
taken by a spectrometer system passing an electromagnetic signal through a sample cell
including a sample medium and a base medium;
segmenting the sample signal scan into a plurality of frequency segments;
processing the sample signal scan segments to produce a respective plurality of
corrected sample signal scan segments, wherein processing the sample signal scan
segment comprises, for each sample signal scan segment:
applying an inner-product operation on the sample signal scan segment and
a respective set of eigenvectors from a plurality of sets of eigenvectors to generate

a respective set of corresponding coefficients, the sets of eigenvectors having been
generated by segmenting a plurality of background reference signal scans into a
plurality of sets of background reference signal scan segments, and decomposing
each set of background reference signal scan segments according to a singular
value decomposition technique, each background reference signal scan including a
plurality of electromagnetic signal measurements at a discrete set of frequencies,
each respective measurement having been taken by the spectrometer system
passing an electromagnetic signal through the sample cell including the base
medium but without the sample medium; and
subtracting the sample signal scan segment from a linear combination of
the respective set of eigenvectors and corresponding coefficients to thereby
produce a respective corrected sample signal scan; and
assembling the corrected sample signal scan segments.
8. The method of Claim 7 further comprising receiving and segmenting the
plurality of background reference signal scans into a plurality of sets of background
reference signal scan segments, and decomposing each set of the background reference
signal scan segments to generate the plurality of sets of eigenvectors.
9. The method of Claim 7 further comprising:
identifying an electromagnetic signal measurement in the sample signal scan
corresponding to an electromagnetic signal measurement in the corrected sample signal
that exceeds a specified absorption threshold;
removing the identified electromagnetic signal measurement to produce a modified
sample signal scan; and
processing the modified sample signal scan, wherein processing the modified
sample signal scan comprises:
applying an inner-product operation on the modified sample signal scan
and each of a plurality of eigenvectors to generate a second plurality of
corresponding coefficients, and
subtracting the sample signal scan from a linear combination of the
eigenvectors and second corresponding coefficients to thereby produce a further
corrected sample signal scan.

10. The method of Claim 7 further comprising:
calculating a ratio of the sample signal scan to an average of the background
reference signal scans; and
adjusting the corrected sample signal scan based on the ratio.
11. A method comprising:
receiving a sample signal scan that includes a plurality of electromagnetic signal
measurements at a discrete set of frequencies, each respective measurement having been
taken by a spectrometer system passing an electromagnetic signal through a sample cell
including a sample medium and a base medium;
processing the sample signal scan, wherein processing the sample signal scan
comprises:
applying an inner-product operation on the sample signal scan and each of
a plurality of eigenvectors to generate a plurality of corresponding coefficients, the
plurality of eigenvectors having been generated by decomposing a plurality of
background reference signal scans according to a singular value decomposition
technique, each background reference signal scan including a plurality of
electromagnetic signal measurements at a discrete set of frequencies, each
respective measurement having been taken by the spectrometer system passing an
electromagnetic signal through the sample cell including the base medium but
without the sample medium; and
subtracting the sample signal scan from a linear combination of the
eigenvectors and corresponding coefficients to thereby produce a corrected sample
signal scan;
identifying an electromagnetic signal measurement in the sample signal scan
corresponding to an electromagnetic signal measurement in the corrected sample signal
that exceeds a specified absorption threshold;
removing the identified electromagnetic signal measurement to produce a modified
sample signal scan; and
processing the modified sample signal scan, wherein processing the modified
sample signal scan comprises:
applying an inner-product operation on the modified sample signal scan
and each of a plurality of eigenvectors to generate a second plurality of
corresponding coefficients; and

subtracting the sample signal scan from a linear combination of the
eigenvectors and second corresponding coefficients to thereby produce a further
corrected sample signal scan.
12. The method of Claim 11 further comprising calculating a ratio of the
sample signal scan to an average of the background reference signal scans, and adjusting
the corrected sample signal scan based on the ratio.
13. A computer-readable storage medium having computer-readable program
code portions stored therein, the computer-readable program portions comprising:
a first executable portion configured to receive a sample signal scan that includes a
plurality of electromagnetic signal measurements at a discrete set of frequencies, each
respective measurement having been taken by a spectrometer system passing an
electromagnetic signal through a sample cell including a sample medium and a base
medium; and
a second executable portion configured to segment the sample signal scan into a
plurality of frequency segments;
a third executable portion configured to process the sample signal scan segments to
produce a respective plurality of corrected sample signal scan segments, wherein the third
executable portion being configured to process the sample signal scan segments includes,
for each sample signal scan segment, being configured to:
apply an inner-product operation on the sample signal scan segment and a
respective set of eigenvectors from a plurality of sets of eigenvectors to generate a
respective set of corresponding coefficients, the sets of eigenvectors having been
generated by segmenting a plurality of background reference signal scans into a
plurality of sets of background reference signal scan segments, and decomposing
each set of background reference signal scan segments according to a singular
value decomposition technique, each background reference signal scan including a
plurality of electromagnetic signal measurements at a discrete set of frequencies,
each respective measurement having been taken by the spectrometer system
passing an electromagnetic signal through the sample cell including the base
medium but without the sample medium, and

subtract the sample signal scan segment from a linear combination of the
respective set of eigenvectors and corresponding coefficients to thereby produce a
respective corrected sample signal scan; and
a fourth executable portion configured to assemble the corrected sample signal
scan segments.
14. The computer-readable storage medium of Claim 13, wherein the
computer-readable program portions further comprise:
a fifth executable portion configured to receive and segment the plurality of
background reference signal scans into a plurality of sets of background reference signal
scan segments; and
a sixth executable portion configured to decompose each set of the background
reference signal scan segments to generate the plurality of sets of eigenvectors.
15. The computer-readable storage medium of Claim 13, wherein the
computer-readable program portions further comprise:
a fifth executable portion configured to identify an electromagnetic signal
measurement in the sample signal scan corresponding to an electromagnetic signal
measurement in the corrected sample signal that exceeds a specified absorption threshold;
a sixth executable portion configured to remove the identified electromagnetic
signal measurement to produce a modified sample signal scan; and
a seventh executable portion configured to process the modified sample signal
scan, including being configured to:
apply an inner-product operation on the modified sample signal scan and
each of a plurality of eigenvectors to generate a second plurality of corresponding
coefficients, and
subtract the sample signal scan from a linear combination of the
eigenvectors and second corresponding coefficients to thereby produce a further
corrected sample signal scan.
16. The computer-readable storage medium of Claim 13, wherein the
computer-readable program portions further comprise:
a fifth executable portion configured to calculate a ratio of the sample signal scan
to an average of the background reference signal scans; and

a sixth executable portion configured to adjust the corrected sample signal scan
based on the ratio.
17. A computer-readable storage medium having computer-readable program
code portions stored therein, the computer-readable program portions comprising:
a first executable portion configured to receive a sample signal scan that includes a
plurality of electromagnetic signal measurements at a discrete set of frequencies, each
respective measurement having been taken by a spectrometer system passing an
electromagnetic signal through a sample cell including a sample medium and a base
medium;
a second executable portion configured to process the sample signal scan,
including being configured to:
apply an inner-product operation on the sample signal scan and each of a
plurality of eigenvectors to generate a plurality of corresponding coefficients, the
plurality of eigenvectors having been generated by decomposing a plurality of
background reference signal scans according to a singular value decomposition
technique, each background reference signal scan including a plurality of
electromagnetic signal measurements at a discrete set of frequencies, each
respective measurement having been taken by the spectrometer system passing an
electromagnetic signal through the sample cell including the base medium but
without the sample medium, and
subtract the sample signal scan from a linear combination of the
eigenvectors and corresponding coefficients to thereby produce a corrected sample
signal scan;
a third executable portion configured to identify an electromagnetic signal
measurement in the sample signal scan corresponding to an electromagnetic signal
measurement in the corrected sample signal that exceeds a specified absorption threshold;
a fourth executable portion configured to remove the identified electromagnetic
signal measurement to produce a modified sample signal scan; and
a fifth executable portion configured to process the modified sample signal scan,
including being configured to:
apply an inner-product operation on the modified sample signal scan and
each of a plurality of eigenvectors to generate a second plurality of corresponding
coefficients, and

subtract the sample signal scan from a linear combination of the eigenvectors and
second corresponding coefficients to thereby produce a further corrected sample signal
scan.
18. The computer-readable storage medium of Claim 17, wherein the
computer-readable program portions further comprise a sixth executable portion
configured to calculate a ratio of the sample signal scan to an average of the background
reference signal scans, and adjust the corrected sample signal scan based on the ratio.

A method is provided that includes receiving and processing a sample signal scan.
Processing the sample signal scan includes applying an inner-product operation on the
sample signal scan and each of a plurality of eigenvectors to generate a plurality of
corresponding coefficients, and subtracting the sample signal scan from a linear
combination of the eigenvectors and corresponding coefficients to thereby produce a
corrected sample signal scan. In this regard, the eigenvectors have been generated by
decomposing a plurality of background reference signal scans according to a singular
value decomposition technique. The signal scans include a plurality of electromagnetic
signal measurements at a discrete set of frequencies, where each measurement has been
taken by a spectrometer system passing an electromagnetic signal through a sample cell
including just a base medium (for the background reference signal scans), or both a base
medium and a sample medium (for the sample signal scan).