APPARATUS, METHOD AND COMPUTER-READABLE STORAGE MEDIUM FOR
DETERMINING THE RING-DOWN TIME 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 determining the ring-down
time in a spectrometer system.
BACKGROUND OF THE INVENTION
The concept of a ring-down cavity to perform spectroscopy has been developed
for application in the visible and infrared portions of the spectrum and discussed in the
technical literature. Cavity ring-down (CRD) spectrometers may generally be one of two
types, namely pulsed and continuous wave. In the pulsed case, a short pulse of light
may be injected into a resonant cavity (often referred to as a cavity resonator or sample
cell) which may include a pair of mirrors between which light may reflect. In
spectrometer applications, the space between the mirrors in these cavities may be filled
with a sample medium so that the absorption spectrum of the sample can be measured.
The mirrors may not be perfectly reflecting but may allow some light to pass
through the mirrors for entrance and exit of the light. If a short single pulse is injected
into an empty cavity, the pulse may reflect many times in the cavity, and on each
encounter with an exit mirror, a pulse may exit the cavity. Thus, a single pulse may
produce a train of pulses with each pulse subsequently reduced in pulse height as
energy leaks out of the exit mirror on subsequent passes. The multiple reflections may
be referred to as "ringing," and the time it takes the output pulse train to complete may be
referred to as the "ring-down time." This time constant is a property of the cavity geometry
and the medium between the reflecting mirrors. For more information on a pulsed ring-
down cavity, see for example, K. Lehmannn & D. Romanini, The Superposition Principle
and Cavity Ring-Down Spectroscopy, J. Chem. Phys., vol. 105 no. 23 (1996) (hereinafter
"Lehmannn & Romanini"), the content of which is hereby incorporated by reference in its
entirety.
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
determining the ring-down time in a cavity ring-down (CRD) spectrometer system.
According to one aspect of the present invention, a system is provided that includes a
cavity ring-down spectrometer and a processor. The spectrometer includes a transmitter,
modulator, cavity resonator and receiver. The transmitter, which may comprise a
photomixer or terahertz or millimeter wave transmitter, is configured to transmit a
continuous-wave electromagnetic signal at each of one or more selectable, transmission
frequencies in the Terahertz region of the electromagnetic spectrum; and the modulator is
configured to modulate (e.g., amplitude modulate) the electromagnetic signal at a
modulation frequency.
The cavity resonator is configured to receive the modulated electromagnetic
signal and pass at least a portion of the modulated electromagnetic signal. According to
this aspect, the transmitter and cavity resonator are configured so as to excite a single
resonant mode of the cavity resonator.
The receiver, which similar to the transmitter may comprise a photomixer or
terahertz or millimeter wave receiver, is configured to receive the portion of the modulated
electromagnetic signal passing the cavity resonator. The processor, in turn, is configured
to receive a measurement of the portion of the modulated electromagnetic signal received
by the receiver, and determine a phase shift of the modulated electromagnetic signal at
the modulation frequency based upon the measurement. The processor is also
configured to calculate a ring-down time of the cavity resonator as a function of the phase
shift. And further, when the cavity resonator houses a sample medium, the processor
may be configured to determine an absorption signature for the sample medium as a
function of the ring-down time and transmission frequency.
In a more particular exemplary embodiment, the processor may be configured to
calculate a ring-down time t in accordance with the following:
where fm' n' represents the phase shift at the modulation frequency for the single resonant
mode m'n', and ?md represents the modulation frequency. At terahertz frequencies,
devices like the photomixer may offer the unique ability to measure not only the intensity
but also the amplitude of radiation. Thus, the cavity resonator may have two ring-down
times, one for the intensity and one for the amplitude which is twice the intensity ring-
down time. In such instances, the aforementioned ring-down time may be considered the
intensity ring-down time. The processor, then, may be additionally or alternatively
configured to calculate an amplitude ring-down time Tamp in accordance with the following:
According to other aspects of the present invention, a method and computer-
readable storage medium are provided for determining the ring-down time in a
spectrometer system. Exemplary embodiments of the present invention therefore provide
an improved apparatus and method for determining the ring-down time in a spectrometer
system. As 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; and
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.
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 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 ?1 and ?2 (i.e., E?1 and E?2). Also note that frequencies ?1 and ?2, and
other frequencies described herein, may be expressed as radian angular frequencies, or
as corresponding temporal frequencies (f = ?l 2p).
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, the modulator producing an electric field EM
= Vmcos(?mdt), thereby amplitude modulating the transmitted signal at frequency ?md. 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 ?2, and a frequency ?1 that are
selected to thereby select the difference, or transmission, frequency (e.g., ?2 - ?1).
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 cavity
resonator 26 or sample cell 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.
The cavity resonator 26 may have an actuator control to vary the length between
the reflectors 26a and 26b, which may permit changing the frequency sampling comb
and thereby lend flexibility to the system by providing continuous tuning across an
entire desired spectral range. The reflectors of the cavity resonator may be configured to
have a high reflectivity, such as on the order of 0.995 - 0.998 for certain THz bands. The
reflectors 26a and 26b may be configured in any of a number of different manners to
achieve a desired reflectivity and optical function. In one example embodiment, the
reflectors may include a gold grating polarizer coating. For a further discussion of suitable
coatings, see J. Auton, Infrared Transmission Polarizers by Photolithography, Applied
Optics, vol. 6, no. 6 (1967); and R. Ulrich et al., Variable Metal Mesh Coupler for Far
Infrared Lasers, Applied Optics, vol. 9, no. 11, (1970).
As the continuous-wave beam of radiation is introduced to the cavity resonator 26,
its intensity builds up as the beam reflects between the reflectors 26a and 26b. But as
the beam reflects between the reflectors, the sample and base medium in the cavity
resonator absorb at least a portion of the beam, or more particularly at least a portion of
the electric field of the beam; and a remaining, unabsorbed portion of the beam of
radiation (i.e., received signal) then exits the cavity resonator. 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. 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 Id, 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 Id 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.
When 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 ?md to thereby recover the amplitude of the down-converted signal.
In operation as a continuous wave CRD spectrometer, the sample signal exiting
the cavity resonator 26 may be monitored until it reaches a particular threshold intensity,
the transmitter 12 may be shut-off or otherwise controlled to cease transmission of the
beam into the cavity resonator. In this regard, the shut-off switch may be configured such
that its falling-edge is short compared to the ring-down time of the excited modes. With
the transmitter ceasing transmission of the beam into the cavity resonator, the intensity of
the beam propagating within the cavity resonator, and thus the portion of the beam
exiting the cavity resonator, decays exponentially (i.e., "rings down") until no more of the
beam exits the cavity resonator or the exiting portion of the beam becomes
immeasurable. The time between the transmitter ceasing transmission of the beam into
the cavity resonator and the last of the beam exiting the cavity resonator (or the last of
the exiting beam being measurable), then, may be measured as the "ring-down time," as
shown in block 50 of FIG. 2. The ring-down time may be measured in a number of
different manners, one of which is more particularly described below.
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 ?2, and frequency ?1 that are scanned through a
number of frequencies, as shown in blocks 54 and 56. 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 or otherwise determine the ring-
down time t. The resulting collection of ring-down times, and associated transmission
frequencies, may be used to determine absorption or dispersion signature for the sample
in the cavity resonator 26, from which the sample may be identified, as shown in block 58
of FIG. 2. For example, an absorption or dispersion signature may be determined by
plotting cavity loss (1/CT, where c represents the speed of light) as a function of
transmission frequency.
By implementing a phase shift cavity ring-down technique, many of the typical
problems of spectroscopic characterization and detection may be avoided. Again, in
the ring-down method, a beam of radiation may be injected into the cavity resonator 26
as an amplitude modulated carrier. The cavity resonator presents a delay to the traveling
wave, which may introduce a phase shift (delay) for both the carrier and modulated
(envelope) waves. The presence of an absorber changes the intrinsic cavity decay time
and presents a different delay. This can be measured in two ways: a decay time or
through a phase shift at the modulation frequency (see FIG. 2, block 50). By measuring
delay times or phase shifts, issues associated with energy normalization may be reduced
over the pulsed method, if not obviated.
The analysis of Lehmannn & Romanini shows that each transverse cavity mode
m, n has an exponential decay (ring-down time) td that may be expressed - for intensity
measurements - as follows:
(1)
In the preceding, Rmn, eff= Rmn exp(-K(?mnq)L), with Rmn representing the modal reflectivity
of the cavity reflectors 26a, 26b (the mode dependence of the reflectivity comes from the
coefficient of the input field expanded in terms of the cavity modes). Also, L represents
the cavity length, tr represents the round trip travel time of light in a single cycle, ?mnq
represents the angular frequency of the m, n transverse and q longitudinal modes of the
cavity resonator 26, and k represents the absorption coefficient of the sample medium in
the cavity. Given the following assumptions with c representing the speed of light: t1/2 =
L/c, kL<<1; Rmn ~ R0,0 ~ 1; and r = td,00 (?0,0,q), the intensity ring-down time at longitudinal
frequency vq may be given by:

Lehmannn & Romanini point out that if Rmn is not constant due to mode dependent loss,
the ring-down time may have a non-exponential dependence with or with out a sample
medium in the cavity resonator. They also indicate for the pulsed case, the input pulse
should have a falling edge less than the decay time of the excited longitudinal mode.
Unlike the pulsed case of Lehmannn & Romanini where the input pulse width may
be short and the frequency spectrum may be wide, a continuous wave (CW) case may
have a long time span and an impulse frequency input. The modulated CW case may
lead to a cavity response that, in the observed signal, produces a phase shift that is
related to the ring-down time. In this case, a modulated input beam may emerge from the
cavity resonator 26 shifted in phase f (at the modulation frequency fmd), and with a
corresponding intensity ring-down time, which may be given by:
(2)
In accordance with example embodiments of the present invention, a
measurement of the ring-down time may be achieved when the input continuous wave
beam is modulated. Thus, when the input beam to the cavity is modulated with an
angular frequency ?md, the ring-down time may be measured in terms of a phase shift of
the modulated continuous wave current. This may be done by representing the cavity
input field in terms of the cavity resonant modes which may be assumed to be the
Hermite-Gaussian modes. The analytic 2-dimensional modal transfer function may then
be calculated and used to determine the output field coefficients from the input field
coefficients. This transfer function may include both the effects of the transverse and
longitudinal modes.
Consider a cavity resonator 26 including reflectors 26a and 26b that have an
identical or substantially-identical radius of curvature Rc, amplitude transmittance T and
reflectance R. Assuming a monochromatic beam of radiation and a sinusoidal
modulation of that beam, the analysis may begin by describing the relationship between a
cavity input (c) and output (c°) transverse mode coefficients of the input and output fields,
and the cavity mode transfer function Gmn, all evaluated at some temporal frequency f =
col 2%. This relationship may be expressed as follows (cf. Lehmannn & Romanini,
equation (26)):
(3)
where the cavity mode transfer function Gmn may be as provided by equation (27) in
Lehmannn & Romanini.
For the modulated input beam coefficients, the coefficients may be taken as

where d represents the standard mathematical delta function, cmn represents the
transverse mode coefficients of the input field, and ?0 represents the CW transmission
frequency (e.g., ?2 - ?1). Given the cavity mode transfer function Gmn may, then, the
output field coefficients CL may be found from equations (3) and (4); and together with an
expression for the total output field (e.g., Lehmannn & Romanini, equation (31)), the
output field coefficients may provide an expression for the output field ER in the time
domain.
When the receiver 30 is an electric-field (or amplitude) detector such as a
photomixer receiver (homodyne receiver) that collects the entire output field, this spatially
integrated field may be viewed as a current at the receiver and may be expressed as the
following complex function (/' representing the imaginary unit):

In the preceding, Km,n represents mode constants such as those given in equation (21) of
Lehmannn & Romanini evaluated at the output face of the cavity resonator 26, Fm and Fn
each represent a component of the 2-dimensional integral of each cavity mode, and ?r
represents radian longitudinal mode frequency of the cavity resonator closest to the
transmission frequency ?0. Also in the preceding, dkm,n describes the transverse m, n
modes defined by

The function Fm (and similarly Fn) may be notationally expressed by the
integrated amplitude modes as follows:

where Hm represents the mth Hermite-Gaussian amplitude mode, w(L/2) represents the
Gaussian beam waist at the output reflector 26b, and RW(L/2) represents the beam
radius of curvature at the output reflector. And further to the above, k represents the
wave vector of the beam of radiation, and may be expressed as:

where ncav represents the complex refractive index of the sample medium between the
reflectors.
Equation (5) may be simplified if the following substitutions are made:

The variable ?mn represents the modal reflectivity of the cavity reflectors 26a, 26b, ?mn
represents a phase shift associated with reflection, and ymn represents a dummy variable
that collects phase shifts due to misalignment of the transmission frequency ?0 from a
cavity longitudinal mode, phase shifts of the mode itself and/or phase shifts associated
with the mirrors of the cavity. Further, the complex variable coefmn represents a dummy
variable that collects some of the parts in equation (5) to permit rewriting equation (5) in
the desired form of equation (8).
Defining the amplitude of the current at the receiver 30 as gives the following complex demodulated signal

where qmn represents the entire phase of the complex variable coefmn (qmn representing
the imaginary part of the natural log of the complex variable coefmn). As coefmn depends
on , it may be seen that qmn depends on F, and consequently, qmn depends on the ring-
down time.
Converting ld(t) to a real signal using /(t) = 2 Re(ld (t)) and trigonometric identities
yields the sinusoidal signal sum:

In the preceding, (?mn represents a phase shift of the current at the receiver 30 (shifted
from the frequency-modulated, input signal). The variable rmn represents a real number
that contributes only to the amplitude in equation (10); it does not depend on time or the
phase of the cosine.
When the transmission frequency ?0 is on a particular /', m', n' cavity resonance
mode, ym'n' = 0; and when qm'n' = 0(i.e., coefmn is real), equation (11) simplifies to:

For small F and ?m'n' close to unity, the last part of equation (12) shows how the phase
shift of the demodulated current fm'n' is related to the ring-down time of the cavity through
tr and equation (2) may be recovered using the - intensity - ring-down time from equation
(1) written as:
The p in the numerator may be set to one when the reflectors 26a, 26b are highly
reflecting; and thus, substituting the above expression into equation (12) may yield
equation (2):

At THz frequencies, a photomixer receiver 30 may offer the unique ability to measure not
only the intensity but also the amplitude of radiation. Thus, the cavity resonator 26 may
have two ring-down times, one for the intensity and one for the amplitude which is twice
the intensity ring-down time. In terms of the amplitude ring-down time, Tamp equation (13)
may be expressed as follows:

When the m'n' mode is the only cavity mode excited by the input beam, then measuring
the phase in equation (13) may provide a measure of the ring-down time of the cavity as
defined in equation (13). Given all the conditions used to arrive at equation (13) from
equation (11), it may be seen that equation (13) is a particular result of the more general
equation (11), which also relates fmn to the intensity decay time t.

In implementation, the expression equation (15) may be desired for increased accuracy.
In such instances, a calibration of the instrument could determine the coefficient of the
tangent on the right side of equation (15) as a short polynomial in t, but it may require the
processing apparatus 38 to invert equation (15). The choice of using either equation (13)
or (15) may therefore rest on the desired performance requirements imposed on the
system spectrometer 10. It may be expected that in most cases of interest, however,
equation (15) provides only minor modifications to equation (13). The fact that the phase
in equation (13) may be measured means that, as long as the phase of the cosinusoid is
measured, the result is nearly independent of the amplitude.
It should be noted that when the demodulation contains degenerate transverse
modes, the sum in equation (10) may not contain just one term; and each term in the sum
may contribute a phase factor adding to the phase noise in the system. It may therefore
be beneficial to excite a single cavity mode for ring-down measurements. Single mode
cavity excitation requirements may demand care in source beam spatial filtering and
frequency control. These can be accomplished, for example, with well established
beam alignment and filtering methods using narrow-band spectral sources derived in a
variety of ways that include phase-lock loop frequency references and up-conversion by
diode multipliers. On the other hand, there are two ways in which several cavity modes
may be excited, and for which it may be desirable to avoid. The first is with a
monochromatic input source and a degenerate cavity such as confocal cavity resonator;
and the second is with a quasi-monochromatic source whose linewidth spans multiple
cavity modes. In the second case, each mode may be excited in proportion to the input
energy of the source at the different mode frequencies. In addition, the current at the
receiver 30 may see phase noise associated with the linewidth of the source. In the first
case, the confocal cavity may produce degenerate transverse modes of the sort labeled
above by the m, n indecies. Because of this degeneracy, several spatial modes may
have the same frequency as the longitudinal mode so their selection may depend on
mode shape overlap with the input profile. Moving the cavity away from confocal, may
remove the degeneracy and provide a more robust selection by frequency discrimination.
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 diagram of FIG. 2, may be performed by various means. It will be understood that
each block or operation of the block diagram, and/or combinations of blocks or operations
in the block diagram, can be implemented by various means. Means for implementing
the blocks or operations of the block diagram, combinations of the blocks or operations in
the block diagram, 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
diagram's 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 diagram's 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 diagram's block(s) or operation(s).
Accordingly, execution of instructions associated with the blocks or operations of
the block diagram by a processor, or storage of instructions associated with the blocks or
operations of the block diagram 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 diagram, and combinations
of blocks or operations in the block diagram, 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. A system comprising:
a cavity ring-down spectrometer comprising:
a transmitter configured to transmit a continuous-wave electromagnetic
signal at each of one or more selectable, transmission frequencies in the
Terahertz region of the electromagnetic spectrum;
a modulator configured to modulate the electromagnetic signal at a
modulation frequency;
a cavity resonator configured to receive the modulated electromagnetic
signal and pass at least a portion of the modulated electromagnetic signal,
wherein the transmitter and cavity resonator are configured so as to excite a
single resonant mode of the cavity resonator; and
a receiver configured to receive the portion of the modulated
electromagnetic signal passing the cavity resonator; and
a processor configured to receive a measurement of the portion of the modulated
electromagnetic signal received by the receiver, and determine a phase shift of the
modulated electromagnetic signal at the modulation frequency based upon the
measurement, and wherein the processor is configured to calculate a ring-down time of
the cavity resonator as a function of the phase shift.
2. The system of Claim 1, wherein the processor being configured to
calculate a ring-down time includes being configured to calculate an intensity ring-down
time t in accordance with the following:
wherein fm'n' represents the phase shift at the modulation frequency for the single
resonant mode m'n', and ?md represents the modulation frequency.
3. The system of Claim 1, wherein the processor being configured to
calculate a ring-down time includes being configured to calculate an amplitude ring-down
time Tamp in accordance with the following:
wherein fm'n' represents the phase shift at the modulation frequency for the single
resonant mode rn'n', and ?md represents the modulation frequency.
4'. The system of Claim 1, wherein the cavity resonator is configured to house
a sample, and
wherein the processor is configured to determine an absorption signature for the
sample medium as a function of the ring-down time and transmission frequency.
5. The system of Claim 1, wherein the transmitter comprises a photomixer
transmitter, and the receiver comprises a photomixer receiver.
6. The system of Claim 1, wherein the transmitter comprises a terahertz or
millimeter wave transmitter, and the receiver comprises a terahertz or millimeter wave
receiver.
7. A method comprising:
transmitting a continuous-wave electromagnetic signal at each of one or more
selectable, transmission frequencies in the Terahertz region of the electromagnetic
spectrum, the electromagnetic signal being transmitted from a transmitter in a cavity ring-
down spectrometer;
modulating the electromagnetic signal at a modulation frequency;
passing at least a portion of the modulated electromagnetic signal through a cavity
resonator, wherein the transmitter and cavity resonator are configured so as to excite a
single resonant mode of the cavity resonator;
receiving a measurement of the portion of the modulated electromagnetic signal
passing the cavity resonator;
determining a phase shift of the modulated electromagnetic signal at the
modulation frequency based upon the measurement; and
calculating a ring-down time of the cavity resonator as a function of the phase
shift.
8. The method of Claim 7, wherein calculating a ring-down time comprises
calculating an intensity ring-down time r in accordance with the following:
wherein fm'n' represents the phase shift at the modulation frequency for the single
resonant mode m'n', and ?md represents the modulation frequency.
9. The method of Claim 7, wherein calculating a ring-down time comprises
calculating an amplitude ring-down time Tamp in accordance with the following:
wherein fm'n' represents the phase shift at the modulation frequency for the single
resonant mode m'n', and ?md represents the modulation frequency.
10. The method of Claim 7, wherein the cavity resonator houses a sample,
and
wherein the method further comprises determining an absorption signature for the
sample medium as a function of the ring-down time and transmission frequency.
11. The method of Claim 7, wherein transmitting a continuous-wave
electromagnetic signal comprises transmitting a continuous-wave electromagnetic signal
from a photomixer transmitter, and wherein receiving a measurement comprises receiving
a measurement from a photomixer receiver.
12. The method of Claim 7, wherein transmitting a continuous-wave
electromagnetic signal comprises transmitting a continuous-wave electromagnetic signal
from a terahertz or millimeter wave transmitter, and wherein receiving a measurement
comprises receiving a measurement from a terahertz or millimeter wave receiver.
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 measurement, the measurement
having been received from a spectrometer system configured to:
transmit a continuous-wave electromagnetic signal at each of one or more
selectable, transmission frequencies in the Terahertz region of the
electromagnetic spectrum, the electromagnetic signal being transmitted from a
transmitter in a cavity ring-down spectrometer;
modulate the electromagnetic signal at a modulation frequency; and
pass at least a portion of the modulated electromagnetic signal through a
cavity resonator, wherein the transmitter and cavity resonator are configured so as
to excite a single resonant mode of the cavity resonator, the measurement
comprising a measurement of the portion of the modulated electromagnetic signal
passing the cavity resonator;
a second executable portion configured to determine a phase shift of the
modulated electromagnetic signal at the modulation frequency based upon the
measurement; and
a third executable portion configured to calculate a ring-down time of the cavity
resonator as a function of the phase shift.
14. The computer-readable storage medium of Claim 13, wherein the third
executable portion being configured to calculate a ring-down time includes being
configured to calculate an intensity ring-down time r in accordance with the following:
wherein fm'n' represents the phase shift at the modulation frequency for the single
resonant mode m'n', and ?md represents the modulation frequency.
15. The computer-readable storage medium of Claim 13, wherein the third
executable portion being configured to calculate a ring-down time includes being
configured to calculate an amplitude ring-down time Tamp in accordance with the following:
wherein fm'n' represents the phase shift at the modulation frequency for the single
resonant mode m'n', and ?md represents the modulation frequency.
16. The computer-readable storage medium of Claim 13, wherein the cavity
resonator houses a sample, and
wherein the computer-readable program portions further comprise a fourth
executable portion configured to determine an absorption signature for the sample
medium as a function of the ring-down time and transmission frequency.
17. The computer-readable storage medium of Claim 13, wherein the
spectrometer system being configured to transmit a continuous-wave electromagnetic
signal includes being configured to transmit a continuous-wave electromagnetic signal
from a photomixer transmitter, and wherein the spectrometer system being configured to
receive a measurement includes being configured to receive a measurement from a
photomixer receiver.
18. The computer-readable storage medium of Claim 13, wherein the
spectrometer system being configured to transmit a continuous-wave electromagnetic
signal includes being configured to transmit a continuous-wave electromagnetic signal
from a terahertz or millimeter wave transmitter, and wherein the spectrometer system
being configured to receive a measurement includes being configured to receive a
measurement from a terahertz or millimeter wave receiver.

A system is provided that includes a cavity ring-down spectrometer and a
processor. The spectrometer is configured to pass, through a cavity resonator, a
modulated, continuous-wave electromagnetic signal at each of one or more selectable,
transmission frequencies in the Terahertz region of the electromagnetic spectrum. The
spectrometer includes a transmitter that, with the cavity resonator, is configured so as to
excite a single resonant mode of the cavity resonator. The processor is configured to
receive a measurement of the passed portion of the modulated electromagnetic signal,
and determine a phase shift of the modulated electromagnetic signal based upon the
measurement. The processor is then configured to calculate a ring-down time of the
cavity resonator as a function of the phase shift.