INFRARED GAS ANALYSIS OF MOLECULAR SPECIES

ANALYSE PAR INFRAROUGE DE LA COMPOSITION MOLECULAIRE D'UN GAZ

English Abstract

INVENTION: INFRARED GAS ANALYSIS
INVENTOR: JOSEPH J. BARRETT
ABSTRACT OF THE DISCLOSURE
A method and apparatus for detecting and quantitatively
measuring a molecular species of gaseous material in a sample to
be analyzed are provided. Light containing incoherent infrared
radiation is collected, collimated and transmitted by a light
conditioning means to a primary filtering means. The primary
filtering means selectively transmits light having a frequency
range in the region of an absorption band for a molecular species
to be detected. A secondary filtering means, adapted to receive
the filtered light, transmits light at a plurality of discrete
frequencies, providing a detectable signal, through the gaseous
material. The intensity of the signal changes in proportion to
the concentration of the molecular species. Means are provided
for measuring and recording the magnitude of the signal intensity
change. The intensity of the detectable signal is not affected
by molecular species other than the species appointed for detection,
and the intensity differential represents a relatively large
change in a small signal. Hence, gaseous constituents are
detected in an accurate and economical manner.

Claims

I claim:
1. Apparatus for detecting and quantitatively measuring
a molecular species of gaseous material in a sample to be analyzed,
comprising:
(a) light source means for generating incoherent
infrared radiation;
(b) light conditioning means for collecting, colli-
mating and transmitting said light;
(c) primary filtering means adapted to receive said
light and selectively transmit light having a
frequency range in the region of an absorption
band for the molecular species to be detected;
(d) secondary filtering means adapted to receive said
filtered light and transmit light having a
plurality of discrete frequencies forming a
plurality of fringes which provide a detectable
signal, said secondary filtering means having
interference producing means for providing a
plurality of transmission windows regularly spaced
in frequency, the frequency spacing between
adjacent windows being adjusted to equal sub-
stantially the product of the frequency difference
between adjacent spectral lines of the absorption
spectrum for the molecular species to be detected
and the factor <IMG>, where n and n' are integers and
n does not equal n' and scanning means for causing
the transmission peaks for adjacent n'th orders to
coincide substantially with the spectral lines of
said absorption spectrum, whereby said detectable
signal has an intensity substantially equal to the
sum of said fringes;
21

(e) means for transmitting said detectable signal
through said gaseous material, whereby the intensity
of said detectable signal changes in proportion
to the concentration of said molecular species;
(f) signal conditioning means for converting to
measurable form said intensity change; and
(g) detecting means for indicating the magnitude of
said intensity change.
2. Apparatus as recited in claim 1, wherein said signal
conditioning means includes modulating means for modulating the
phase difference between interfering rays of said light so as to
shift the frequency of each fringe, the modulating range being no
greater than the frequency spacing between adjacent orders, and
synchronous detection means for detecting the intensity variation
of the signal, whereby the magnitude of the signal intensity
change can be identified.
3. Apparatus as recited in claim 2, wherein said modu-
lating means has a modulating range of about 1/2 the frequency
width of each fringe.
4. Apparatus as recited in claim 3, including indica-
ting and recording means for displaying said signal.
5. Apparatus as recited in claim 3, wherein said
modulating means is a piezoelectric cylinder and said synchronous
detection means is a phase sensitive detection system.
6. Apparatus as recited in claim 1 wherein said
secondary filtering means is a Fabry-Perot interferometer.
7. Apparatus as recited in claim 1 wherein said
secondary filterinq means is a solid etalon having temperature
control means associated therewith for adjusting the optical
path length thereof.
8. Apparatus as recited in claim 5 including means for
applying to said cylinder a voltage having a square wave form,
22

the limits of said voltage being adjusted so that the intensity
of said detectable signal alternates between its maximum and
minimum values, means for determining for each cycle of said
voltage the difference in amplitude between said maximum and
minimum values of said detectable signal to produce an electrical
output signal proportional to the maximum and minimum values of
the detectable signal.
9. Apparatus as recited in claim 7, wherein said solid
elaton is composed of optically transparent material selected from
the group consisting of potassium bromide, potassium chloride,
lithium fluoride, magnesium fluoride, calcium fluoride, cesium
bromide, cesium iodide, barium fluoride, sodium chloride and
sodium bromide.
10. Apparatus as recited in claim 3, wherein said
modulating means is a piezoelectric cylinder and said synchronous
detection means is a lock-in amplifier.
11. Apparatus as recited in claim 1, wherein the
frequency spacing between adjacent windows of said interference
producing means is adjusted to equal substantially the product of
the frequency difference between adjacent spectral lines of the
absorption spectrum for the molecular species to be detected and
the factor <IMG>, where n' is an integer greater than one.
12. Apparatus as recited in claim 1, wherein the
frequency spacing between adjacent windows of said interference
producing means is adjusted to equal substantially the product
of the frequency difference between adjacent spectral lines of the
absorption spectrum for the molecular species to be detected and
the factor <IMG>, where n is an integer greater than one and
n' is equal to one.
13. Apparatus for detecting and quantitatively measuring
a molecular species of gaseous material in a sample to be analyzed
comprising:
23

(a) light source means for generating incoherent
infrared radiation, said light source means
being adapted to emit light having a frequency
range in the region of an absorption band for
the molecular species to be detected;
(b) light conditioning means for collecting,
collimating and transmitting said light;
(c) filtering means adapted to receive said light
and transmit light having a plurality of
discrete frequencies forming a plurality of
fringes which provide a detectable signal, said
filtering means having interference producing
means for providing a plurality of transmission
windows regularly spaced in frequency the
frequency spacing between adjacent windows being
adjusted to equal substantially the product of
frequency difference between adjacent spectral
lines of the absorption spectrum for the molecular
species to be detected and the factor <IMG>, where n
and n' are integers and n does not equal n', and
scanning means for causing the transmission peaks
for adjacent n'th orders to coincide substantially
with the spectral lines of said absorption spectrum,
whereby said detectable signal has an intensity
substantially equal to the sum of said fringes;
(d) means for transmitting said detectable signal
through said gaseous material, whereby the
intensity of said detectable signal changes in
proportion to the concentration of said molecular
species;
(e) signal conditioning means for converting to
measurable form said intensity change; and
24

(f) detecting means for indicating the magnitude of
said intensity change.
14. Apparatus as recited in claim 13 wherein said light
source means is a light emitting diode.
15. Apparatus as recited in claim 13, wherein the
frequency spacing between adjacent windows of said interference
producing means is adjusted to equal substantially the product of
the frequency difference between adjacent spectral lines of the
absorption spectrum for the molecular species to be detected and
the factor <IMG>, where n' is an integer greater than one.
16. Apparatus as recited in claim 13, wherein the
frequency spacing between adjacent windows of said interference
producing means is adjusted to equal substantially the product of
the frequency difference between adjacent spectral lines of the
absorption spectrum for the molecular species to be detected and
the factor <IMG>, where n is an integer greater than one and
n' is equal to one.
17. A method for detecting and quantitatively measuring
a molecular species of gaseous material in a sample to be analyzed,
comprising the steps of
generating light in the form of incoherent infrared
radiation;
collecting, collimating and transmitting the light;
filtering said light so as to selectively transmit light
having a frequency range in the region of an absorption band for
the molecular species to be detected;
interferometrically filtering said filtered light and
transmitting light at a plurality of discrete frequencies to form
a plurality of fringes which provide a detectable signal by
directing the light through a plurality of transmission windows
regularly spaced in frequency, the frequency spacing between

adjacent windows being equal substantially to the product of the
frequency difference between adjacent spectral lines of the absorp-
tion spectrum for the molecular species to be detected and the
factor <IMG>, where n and n' are integers and n does not equal n',
and scanning said light to cause the transmission peaks for
adjacent n'th orders to coincide substantially with the spectral
lines of said absorption spectrum, said signal having an intensity
substantially equal to the sum of said fringes;
transmitting said detectable signal through said gaseous
material, whereby the intensity of said detectable signal changes
in proportion to the concentration of said molecular species; and
detecting and indicating the intensity change of said
signal.
18. A method as recited in claim 17, including the
steps of modulating the phase difference between interfering rays
of said light so as to vary the intensity of the signal, the
modulating range being no greater than the frequency spacing
between adjacent absorption lines of said molecular species.
19. A method as recited in claim 17, wherein the
frequency spacing between adjacent windows is adjusted to equal
substantially the product of the frequency difference between
adjacent spectral lines of the absorption spectrum for the
molecular species to be detected and the factor <IMG>, where n' is
an integer greater than one.
20. A method as recited in claim 17, wherein the
frequency spacing between adjacent windows is adjusted to equal
substantially the product of the frequency difference between
adjacent spectral lines of the absorption spectrum for the
molecular species to be detected and the factor <IMG>, where n is
an integer greater than one and n' is equal to one.
26

Description

~'7~
BACKGROUND OF THE INVENTION
This invention relates to the field of infrared gas
analysis and more particularly to a method and apparatus in which
light is transmitted through a gas sample at discrete frequencies
correlated with the absorption spectrum of a gaseous constituent
thereof to detect and quantitatively measure the constituent.
DESCRIPTION OF THE PRIOR ART
In the apparatus conventionally used for non-dispersive
infrared gas analysis, a beam of infrared radiation having an
emission spectrum embracing the absorption spectrum of the gas to
be analyzed is directed through a gas sample to a transducer.
The output signal from the transducer is compared with that
produced by passing the beam through the series combination of
the sample and a reference gas of the type appointed for analysis.
A signal intensity differential, produced by absorption in the
sample, is converted to a detectable signal and displayed.
One of the major problems with such analyzers is the
difficulty of analyzing quantities of gaseous constituents present
in the low parts per million range. The signal intensity differ-
ential represents a relatively small change in a large signal and
is frequently obscured by spectral interference between absorption
spectra of the constituent being analyzed and absorption spectra
of coe~istent constituents. Another problem with such analyzers
is the decreased sensitivity which results unless the temperature
and pressure of the reference gas are carefully controlled. To
alleviate these p,roblems, it has been necessary to provide the
analyzers with hig~lly sensitive forms and combinations of detec-
tors, sources, filters, control systems and the like, which are ~-
~ ~g
. . . . . .. ., ~. :

relatively expensive. For the above reasons, gas analyzers of
the type described have low sensitivity and high operating costs.
SUl~MARY OF THE I NVENTI ON
The present invention provides apparatus wherein light
from the infrared frequency region is transmitted through a sample
of gaseous material at discrete frequencies correlated with the
absorption spectrum of a molecular species thereof to detect and
quantitatively measure the species. Briefly stated, the apparatus
has light source means for generating incoherent infrared radia-
tion. A light conditioning means collects, collimates and trans-
mits the light to a primary filtering means. The primary filtering
means is adapted to receive the light and selectively transmit
light having a frequency range in the region of an absorption band
for the molecular species to be detected. A secondary filtering
means, adapted to receive the fil~ered light, transmits light at
a plurality of discrete frequencies forming a plurality of fringes
which provide a detectable signal. The secondary filtering means
has interference producing means for providing a plurality of
transmission windows regularly spaced in frequency. The frequency
spacing between adjacent windows is adjusted to equal substantially
the product of the frequency difference between adjacent spectral
lines of the absorption spectrum for the molecular species to be
detected and the factor nn,, where n and n' are integers and n does
not equal n'. Under these circumstances, the interference
producing means forms a comb filter. ~he secondary filtering
means also has scanning means for causing the transmission peaks
for adjacent n'th orders to coincide substantially with the
spectral lines of such absorption spectrum. Means are provided
for transmitting the detectable signal through the gaseous
material, whereby the intensity of the detectable signal changes
in proportion to the concentration of the molecular species.
--2--

The intensity change of the detectable signal is converted to a
measurable form by a signal conditioning means, and the
magnitude thereof is indicated by detecting means.
Further, the invention provides a method for detecting
and quantitatively measuring a molecular species of gaseous
material in a sample to be analyzed, comprising the steps of
generating light in the form of incoherent infrared radiation;
collecting, collimating and transmitting the light; filtering said
light so as to selectively transmit light having a frequency range
in the region of an absorption band for the molecular species to
be detected; interferometrically filtering said filtered light and
transmitting light at a plurality of discrete frequencies to form
a plurality of fringes which provide a detectable signal by
directing the light through a plurality of transmission windows
regularly spaced in frequency, the frequency spacing between
adjacent windows being equal substantially to the product of the
frequency difference between adjacent spectral lines of the
absorption spectrum for the molecular species to be detected and
the factor n,, where n and n' are integers and n does not
equal n', and scanning said light to cause the transmission peaks
for adjacent n'th orders to coincide substantially with the
spectral lines of said absorption spectrum, said detectable
signal having an intensity substantially equal to the sum of
said fringes; transmitting the detectable signal through said
gaseous material, whereby the intensity of the detectable signal
changes in proportion to the concentration of the molecular
species; and detecting and indicating the intensity change of
the signal.
Several known filtering means may be adapted for use
with the above apparatus. Preferably, the secondary filtering
means is a Fabry-Perot interferometer (FPI) having a mirror
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,
. :.

74~
separation, d, adjusted to transmit the filtered light at aplurality of discrete frequencies correlated with the absorption
spectrum of a molecular species of the gaseous material. This
condition is obtained when
d 4~Bn
~here d is the mirror separation of the FPI, ~ is the index of
refraction of the medium between the mirrors. B is the molecular
rotational constant of the species n and n' are integers and
~ does not equal n'. For a given molecular species, the rotational
constant B is a unique quantity. Thus, identification of the
species having a particular absorption spectrum is made positively
by adjusting the mirror separation of the FPI such that the
discrete frequencies transmitted coincide substantially with the
absorption lines o the molecular species to be detected.
Advantageously, the intensity of the detectable signal is not
affected by molecular species other than the species appointed
for detection and the intensity differential represents a
relatively large change in a small signal. Spectral interference
is minimized and no reference gas is needed. The sensitivity
of the apparatus is increased and highly sensitive forms and
combinations of detectors, sources, filters and control systems
are unnecessary. As a result, the method and apparatus of this
i invention permits gaseous constituents to be detected more
accurately and at less expense than systems wherein the emission
spectrum of light passed through the sample contains a continuum
of frequencies.
BRIEE` DESCRIPTION OF THE DRAWINGS ~-
..... _ . __ .
The invention will be more fully understood and further
advantages will become apparent when reference is made to the
following detailed description of the preferred embodiments of
the invention and the accompanying drawings in which:
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, , . . . . - - . - , : .

~Q74~
Figure 1 is a block diagram showing apparatus for
detecting and quantitatively measuring a molecular species of
gaseous material;
Figure 2 is a schematic diagram of the apparatus of
Figure l;
Figure 3 i5 a side view, par~ially cut away, showing
means for modulating the secondary filtering means of Figures
1 and 2;
Figure 4 is a schematic diagram showing an alternate
embodiment of the apparatus of Figure l; and
Figure 5 illustrates the absorption spectrum of a
particular molecular species.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring to Figure 1 of the drawings, there is shown
preferred apparatus for detecting and quantitatively measuring a
molecular species of gaseous material. The apparatus, shown
generally at 10, has light source means 12 for generating light
15 containing incoherent inrared radiation. A light conditioning
means 14 collects, collimates and transmits the light 15 to a
primary filtering means 16. The primary filtering means 16 is
adapted to receive the light 15 and selectively transmit light 17
; having a frequency range in the region of an absorption band for
the molecular species to be detected. A secondary filtering
means 18, adapted to receive the filtered light 17, transmits
light at a plurality of discrete frequencies forming a plurality
of fringes which provide a detectable signal 30. The detectable
signal 30 is transmitted through gaseous material in sample 20.
A signal conditioning means 22 converts to measurable form
intensity changes created in the signal 30 by said molecular
species of the samp:Le 20. The magnitude of the intensity change
is indicated by detecting means 24.
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- - - - . . .
- - . .. . . . . . ~ . . . -
- . - . . .

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More specifically, as shown in Figure 2, the primary
filtering means 16 is a narrow band pass filter composed of
multiple layers of dielectric thin films, and the secondary
filtering means 18 has interference producing means for providing
a plurality of transmission windows regularly spaced in frequency.
In addition, the secondary filtering means 18 has scanning means
for variably controlling the frequency of each order. The inter-
ference producing means is adjusted so that the frequency spacing
between adjacent windows equals substantially the product of the
frequency difference between adjacent spectral lines of the
absorption spectrum for the molecular species to be detected and
the factor n~j, where n and n' are integers and n does not equal n'.
Under these circumstances, the detectable signal 30 transmitted
by the secondary filtering means 18 has an intensity substantially
equal to the sum of the fringes. Moreover, the intensity of the
signal 30 is not affected by molecular species other than the
species appointed for detection, referred to hereinafter as the
preselected species.
~pon transmission of the detectable signal 30 through
; 20 gaseous material in sample 20, its intensity changes in proportion
to the concentration of the preselected species. Such intensity
change is converted to measurable form by the signal conditioning
means 22. The latter has modulating means 26 for modulating the
phase difference between interfering rays of light transmitted by
the secondary filtering means 18 so as to shift the frequency of
each fringe transmitted thereby. Signal conditioning means 22
also has synchronous (e.g. phase sensitive) detecting means 28
for detecting the intensity variation of the signal 30, whereby
the magnitude of the intensity change can be identified by
detecting ~eans 24.
Several known filtering means may be used as the
secondary filtering means with the apparatus lOo Preferably,
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~74~4~3
the secondary filtering means is a Fabry-Perot interferometer
having a mirror separation, d, adjusted to transmit filtered light
from the primary filtering means 16 at a plurality of discrete
frequencies correlated with the absorption spectrum of the
preselected species. The transmission ~unction of an FPI (It) can
be given by the Airy formula: It = T2[l+R2-2cos~] l I where
T + R + A = 1, Io is the intensity oE the incident light, and the
phase difference ~ is expressed as ~ = 4~wd for rays normal to
the FPI mirrors. The symbols A, R and T represent, respectively,
the absorbance, reflectance and transmittance of the FPI mirrors,
~ is the refractive index of the medium between the FPI mirrors,
d is the FPI mirror separation, and ~ is the frequency of the
incident light expressed in wavenumbers. When cos ~ is equal to
unity, transmission maxima for It occur. Hence, ~ = 2~m, where m
takes on integral values and represents the order of interference.
The transmission maxima for It are referred to in the specification
and claims as transmission windows. For a specific value of the
mirror SeparatiQn~ d, the FPI provides a plurality of transmission
windows regularly spaced in frequency. The frequency spacing, ~f,
between adjacent windows (or spectral range) of the FPI is
af = (2~d) 1. For a simple diatomic molecule such as carbon
monoxide, the frequency spacing between adjacent absorption lines
of the infrared rotation~vibration absorption spectrum is
approximately equal to 2B. By varying the mirror spacing, d, of
the FPI, ~f can be adjusted to substantially equal the frequency
difference between adjacent spectral lines of part or all of the
absorption spectrum for the preselected species. That is,
continuous scanning of the FPI in the vicinity of
d ~ 41B
produces an absorption interferogram having a plurality of fringes
corresponding to a superposition of substantially all the absorption
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lines of the preselected species. When ~f=2B, the transmission
peaks for adjacent orders coincide substantially with the adjacent
spectral lines of said absorption spectrum so as to produce a
l-to-l correspondence therewith, and the amplitude oE the signal
from gas sample 20 is a minimum. For values of Af slightly
different from 2B, the transmission peaks for adjacent orders will
not perectly coincide with the absorption lines and the amplitude
of the signal from gas sample 20 will increase.
Other absorption interferograms are produced for values
of the interferometer mirror separation
d ~ n'
4~Bn
where n and n' are integers and n does not equal n'. These absorp-
tion interferograms are produced when ~f is equal to certain
multiples of the rotational constant, B. The principal inter-
ferograms are produced when every absorption line coincides with
a different transmission window of the FPI. 5uch principal inter-
ferograms are obtained for values of interEerometer mirror
separation
d ~ 4n
where n is equal to one and n' is an integer greater than one.
More specifically, for values of interferometer mirror separation
d = n'/(4~B) where n' is an integer greater than one, the principal
interferograms are obtained. For example, with n'=3, radiation is
transmitted by the interferome~er not on]y at frequencies corre-
sponding with those of adjacent absorption lines of the molecular
species to be detected but also at two discrete frequencies located
between each pair of the absorption lines. Secondary inter-
ferograms are obtained when every other absorption line or everythird absorption line (and so on) coincides with the transmission
. . - ,:
~, ~.. .
.

peaks o~ the FPI. Such secondary interferograms are obtained for
values of the interferometer mirror separation
d ~ n'
where n is an integer greater than one and n' is equal to one.
.~lore specifically, for values of interferometer mirror separation
d l~n where n is an integer greater than one, the secondary
interferograms are obtained. For example, with n-3, radiation is
transmitted by the interferometer at frequencies corresponding
with those of every third absorption line of the molecular species
to be detected.
Use of the apparatus 10 for infrared gas analysis may
be exemplified in connection with the detection of a diatomic
molecule such as carbon monoxide. Carbon monoxide (CO) has a
vibration-rotation absorption band in the wavelength region of
about ~.5 - 4.9~ with its band center at about 4.6~. This
absorption band corresponds to transitions from the ground
vibrational state (v = 0) to the first vibrational state (v = 1).
As shown in Figure 5, the absorption band consists of two
branches: an "R-branch" corresponding to rotation-vibration
transitions for which the rotational quantum number J changes by
+l and a "P-branch" corresponding to rotation vibration transitions
for which the rotational quantum number J changes by -1. The
frequencies, in units of wavenumbers, of the rotational transitions
for the R and P branches are given by the formulas
~ R = ~o + 2Bl + (3Bl-Bo)J + (Bl Bo)J
with J = 0, 1, 2, ....
p o (Bl+Bo)J + (Bl-Bo)J
with J = 1, 2, 3, ....
The quantities ~0, Bo and Bl represent the absorption band center
frequency, the ground state rotational constant and the first
_g_
.
- . . .. ..

~'7~
vibrational state rotational constant, respectively. The rota-
tional constants Bo and Bl are related according to the equation
0 Bl ~ e
where ae is the rotation-vibration interaction constant. Values
for the rotational constants of carbon monoxide listed in American
Institute of Physics Handbook, Third Edition, p. 7-173, are:
Bo = 1.9225145cm
Bl = 1.9050015cm 1
ae = 0.017513cm 1
The intensity distribution for the R and P branches is given by
the equation
~ b = Qbs SJ exp[-BoJ(J+l)kT]
Where Cabs is a constant factor, QR is the rotational partition
function (-kT/hcB), ~ is the frequency, in wavenumbers, of the
individual rotation-vibration absorption lines, h is Planck's
constant, c is the speed of lightt k is the Boltzmann constant,
T is the absolute temperature and the line strengths SJ are:
SJ = J + 1 for the R-branch
SJ = J for the P-branch
Using these equations for line positions and intensities, a sche-
matic representation of the CO absorption spectrum shown in
Figure 5, was constructed. The representation is termed schematic
as, in reality, each rotational absorption line of the spectrum
has a small but finite width.
In order to utilize a Fabry-Perot interferometer to
provide discrete frequencies of light at the frequencies of the
absorption lines of the band, it is necessary to determine the
effect of the non-periodic spacing of the rotational absorption
lines on the operation of the apparatus 10. For this purpose the
Fabry-Perot interferometer is adjusted such that the J = 5 and
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J = 7 R-branch rotational absorption lines coincide exactly with
two adjacent discrete frequencies from the Fabry-Perot interfero-
meter. These two rotational absorption lines are the strongest
lines in the band. Their frequencies are:
(J=6) = 2169.169975cm
~ R(J=7) = 2172.734796cm 1
The wavenumber difference between these lines is 3.564821cm 1.
The free spectral range of the interferometer is adjusted to be
equal to this wavenumber difference between adjacent lines. In
order to determine the manner in which the mismatch of the light
frequencies from the interferometer and the individual rotational
absorption lines occur the quantity QR=~R(J+l)-~R(J) is calculated.
The quantity QR may be evaluated as follows:
R R(J+l) R(J)=(3Bl-Bo)-~e[(J~l) -J ]=(3Bl-Bo)-~e(2J+l).
Therefore, the frequency difference between adjacent rotational
absorption lines in the R-branch changes in direct proportion with
the rotational quantum number J and the rotation-vibration inter-
action constant ~ . The halfwidth, A, of the Fabry-Perot
transmission windows is given by the equation
~ = l-R
2~d~R
where R is the reflectivity of the Fabry-Perot mirrors and ~d is
the optical path length between the mirrors. Assuming that the
reflectivity R~0.85, then A = 0.185cm 1. The frequency mismatch
, with the ~R(J=5) line is 0.035cm 1, which is well within the
transmission halfwidth of the Fabry-Perot interferometer. The
frequency mismatch with thè`~R(J=3) line is 0.210cm 1, which is
; just slightly larger than the FPI halfwidth. The frequency mis-
match with the ~R(J=10) line is 0.210cm 1, which is also just
slightly larger than the FPI halfwidth. Therefore, the R-branch
lines from J=3 to J=10 will coincide substantially with the
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:. ., :- . . ,. . . .. . :.. ............ .

discrete frequencies from the FPI and therefore will be most effec-
tive in the operation of the apparatus 10. The absorption line
positions can be determined relative to the FPI transmission
windows. From the equation for QR, ~.he non-periodicity of the
absorption line positions is given by the term ~e(2J+l). Equating
this to the FPI transmission halfwidth yields
A = ~e(2JR+l)
R ` ~
J ~ e ( 2 JR+l ),
2~d~
Since 21d = free spectral range, is set to be equal to the
product of the periodic contribution in the equation for QR,
namely, 3Bl-Bo, and the factor n'
n~3Bl-Bo)~ e(
Solving for JR
JR = ~. _G ( 1 R ~ _ 1/2.
The equilibrium value of the rotational constant Be is given as
Be = Bv + ~e(V+l/2)
where B is the rotational constant of the v-th vibrational state.
Hence 3Bl-Bo = 2B -4~ , and
n [ e ~ 1/2.
For CO, B = 1.931271cm 1 and assuming a FPI mirror reflectivity
of 0.85,
R ~ 5-~ n/n' - 0.5
Similarly, for the P-branch
Qp = ~p(J+l)-~p(J) = -(Bl+Bo)-~e(2J+l)
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4~
and the same reasoning yields
n ( ~e ~ 1/2.
Since Be/~e 1, JR~Jp. The values of JR and Jp can be denoted
by Jopt. Therefore, the optimum banclwidth of the primary filtering
means 16 should be equal to approximately 2BeJopt and no greater
than 4BeJopt. The value f Jopt for the principal interferograms
having n'=3, for example, is equal to 1.4. Thus,it is always possible
to match the transmission windows of the interferometer with at
least two absorption lines of the species appointed for detection.
For the principal interferogram of CO with n'=3/ the
interferometer will transmit radiation through transmission windows
corresponding to the frequencies of at least two of the absorption
lines appointed for analysis and, in addition, through two extra
transmission windows spaced at equal frequency intervals with and
between the absorption lines appointed for analysis. In situations
where the absorption lines of the gas being analyzed are relatively
narrow and exist in a frequency region that does not contain
interfering absorption lines from other gases, use of principal
inteferograms of the type wherein n'=3 provides increased
sensitivity. The increase in sensitivity is produced by the
better match created between absorption linewidth and the widths
of the interferometer's transmission windows. The decrease in
; sensitivity otherwise resulting from the presence of additional
FPI transmission windows is offset by the increase in sensitivity
achieved by reducing the width of the FPI transmission windows.
The increase in sensitivity which is realized in a particular
situation depends on the value of n' selected, which, in turn,
is governed by the experimental conditions associated with the gas
sample under investigation. It is significantly greater than
that produced by increasing the reflectivity of the ~PI mirrors.
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~7~8
The latter approach permits narrowing the width of the FPI trans-
mission windows without introducing additional radiation not
absorbed by the gas, and would, at first, appear to be a better
way to improve the match between absorption linewidth and FPI
transmission linewidth. In practice, however, for high mirror
reflectivities the transmissivity of the FPI is decreased by small
absorption and/or scattering losses in the FPI mirrored surfaces.
This reduction in transmissivity will result in a decrease in
sensitivity that is greater than the sensitivity loss produced by
introduction of additional transmission windows discussed above.
Further, the use of lower reflectivity FPI mirrors with high
transmissivity will result in a device that can be used for a
larger number of experimental applications.
For the secondary interferograms of CO with n=3, a
value of 16 is obtained for the quantity Jopt This value for
Jopt indicates that absorption of radiation transmitted by the
~PI occurs over a frequency range that contains approximately
16 absorption lines. In use of a secondary interferogram having
n=3, FPI transmissions windows occur at every third absorption
line, so that absorption will take place at only 5 absorption
lines. The usefulness of these secondary interferograms is
anticipated for the cases where gas mixtures are being analyzed.
In such cases strong absorption lines from a gas other than the
one appointed for analysis can interfere with the measurement of
the gas appointed for analysis. This interference can be reduced
or eliminated by selecting a secondary interferogram which does not
provide radiation at the absorption frequencies of the interfering
gas.
As previously noted, the modulating means 26 modulates
the phase difference, ~, so as to vary the intensity of the trans-
mitted signal 30. In order to obtain the maximum modulated
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~a74~4~3
signal, the modulating range is adjus~ed to approximately 1/2 thefrequency spacing between adjacent fringes. The modulating range
can, alternatively, be restricted to preselected portions of the
absorption spectrum of the preselect~ed species in order to
increase the intensity of the modulated signal. Generally speaking,
the modulating range should be no greater than the frequency
spacing between adjacent absorption lines of the preselected
species.
The resultant signal 30 from secondary filtering means
18 and gas sample 20 is focused in the plane of pinhole stop 32
by lens 34. Lens 34 is adjusted so that the center of the signal
is positioned on the pinhole 36. The intensity of the portion of
signal 30 passing through the pinhole 36 is detected by an infra-
red detector 38. Phase sensitive detection means 28, such as a
lock-in amplifier, is adapted to receive the signal from infrared
detector 38 and detect the intensity variation thereof. The
output o the phase sensitive detection means 28, representing
the signal intensity change, is displayed by an indicating and
recording means 40, which can comprise an oscilloscope and a
chart recorder.
In Figure 3, the secondary filtering means 18 and the
modulating means 26 are shown in greater detail. The secondary
filtering means shown is a Fabry-Perot interferometer (FPI) which
is scanned by varying the phase difference, ~, between inter-
fering beams of light in a conventional way. Scanning methods
such as those wherein the pressure of gas between the mirrors of
the FPI is altered so as to change the optical path therebetween
can also be used. Accordingly, the secondary filtering means 18
shown in Figure 3 should be interpreted as illustrative and not
in a limiting sense. Such means has cylindrical air bearings 56
and 58 which normally operate at about 30 psi and collectively
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4~8
support a hollow metal cylinder 60 approximately 35 cm. long and
constructed of stainless steel or the like. The outer diameter
of the cylinder 60 is centerless ground to about 4 cm. The inner
diameter of the cylinder 60 is about 3.5 cm. Each of the air
bearings 56 and 58 is about 8 cm. long and has outer and inner
diameters of about 5 cm. and about 4 cm., respectively. The
separation between centers of the air bearings is approximately
20 cm. One of the mirrors 62 of the secondary filtering means 18
is fixedly mounted on end 64 of cylinder 60 as by a suitable
adhesive or the like. The plane surface of the mirror 6~ is sub-
stantially perpendicular to the translational axis of the cylinder.
The other mirror 66 is fixedly mounted to the modulating means 42
as hereinafter described. Each of the air bearings 56 and 58
rests in precise v-blocks of a base plate (not shown) treated
so as to dampen external vibrations. Filtered light 17 from
primary filtering means 16 enters the secondary filtering means
18 at end 68 of cylinder 60~ A carriage 70 caused to move
horizontally by means of a precision screw 72 and having a
coupling arm 8~ fixedly secured thereto by mechanical fastening
means, such as screws 88, and to cylinder 60 as described here-
ina~ter provides the cylinder 60 with the linear motion needed
to scan the secondary filtering means 18. Precision screw 72
is coupled to a digital stepping motor 74 through gear assembly
76. The scan rate of the interferometer is controlled either
by changing the gear ratio of assembly 76, as by means of magnetic -
clutches or the like, or by varying the pulse rate input to the
digital stepping motor 74. With apparatus of the type described,
the scan rate can be varied over a range as great as 106 to 1 or
more.
In order to transmit precisely the linear motion to
cylinder 60, a collar 78 having glass plate 80 adhesively secured
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aS8
thereto, is fixedly attached to the cylinder 60. The coupling
arm 82 has a ball 86 comprised of stainless steel, or the like,
associated with an end 84 thereof. A permanent magnet 90 is
attached to end 84 of coupling arm 82 near the ball 86. Due to
the magnetic attraction between the collar 78 and the magnet 90,
the ball is held in contact with the glass plate 80. A low
friction contact point is thereby provided. The contact force
produced at such contact point by linear movement of the carriage
70 can be adjusted either by varying the separation between the
magnet 90 and the collar 78, or by decreasing the strength of
the magnet 90.
A sectional view of one form of modulating means 26 is
shown in Figure 3. Other forms of the modulating means 26 can
al~o be used. Preferably, the modulating means 26 has a hollow
cylindrical body 92 of piezoelectric ceramics. The inner and
outer wall 94 and 96 of the cylindrical body 92 are coated with
an electrically conductive material such as silver or the like.
Insulating members 98 and 100 comprised of an insulating
material such as ceramic or the like are secured to the cylin-
drical body 92, at ends 10~ and 104, respectively~ by a suitable
; adhesive such as an epoxy resin. Mirror 66 is fixedly attached
to insulating member 93 by an adhesive of the type used to secure
mirror 62 to the end 64 of cylinder 60. In order that mirror 66
be maintained in parallel with mirror 62, the insulating member
100 is adhesively secured to face 106 of holding member 108. The
outer face 110 of the holding member 108 has connected thereto a
plurality of differential screw micrometers 112, which can be
adjusted in the conventional way to provide for precise angular
alignment of the mirror 66. Electrodes 114 and 116 are attached
to the inner wall 94 and the outer wall 96, repectively. Voltage
having a wave form such as a sine wave or a square wave impressed
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~(~74~4~3
thereon is applied from a high voltage low current power supply101 to the electrodes 114 and 116. Upon application of the
voltage the cylindrical body 92 is caused to modulate in a linear
direction, whereby the intensity of signal 30 is varied. When
the voltage applied from power supply 101 to electrodes 114 and
116 has the form of a square wave, the voltage limits of the wave
form can be adjusted so that the intensity of the signal 30
alternates between its maximum and minimum values. A synchronous
detection means is provided for determining the difference in
amplitude between the maximum and minimum values of the signal
30 for each cycle of the square wave to produce an electrical
output signal proportional to the maximum and minimum values of
the signal 30. As a result, the accuracy of the detecting means
and hence the sensitivity of the apparatus 10 is increased by a
factor in the order of about 100 or more.
The apparatus 10 which has been disclosed herein can,
of course, be modified in numerous ways without departing from the
scope of the invention. For example, secondary filtering means
18 can be a fixed etalon tuned by controlling the temperature
thereof. One type of fixed etalon which is suitable is comprised
of optically transparen~ material, such as potassium bromide,
potassium chloride, lithium fluoride, magnesium fluoride, calcium
fluoride, cesium bromide, sodium bromide, cesium iodide, barium
fluoride, sodium chloride, and the like, having high transmission
characteristics in the frequency region oE the absorption band of
the preselected species. In addition, such an etalon has opposed
surfaces which are polished, flat, parallel and coated with
silver, dielectric material or the like for high reflectivity at
a preselected frequency region. For a preselected species such
as carbon mono~ide, having an absorption spectrum in the frequency
region of about 2050 to 2250 wavenumbers, preEerred optically
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transparent materials include potassium bromide, lithium fluorideand magnesium fluoride. The thickness of the solid etalon can be
chosen so that the free spectral range of the etalon corresponds
approximately to the frequency difference between spectral compo-
nents of the given absorption spectrum. Fine tuning of the solid
etalon is affected by providing means for controlling the tempera-
ture, and hence the optical path length, thereof so as to cause the
transmission peaks for adjacent orders to coincide with the
components of the given absorption spectrum. Lenses 14 and 34 can
be replaced with off-axis parabolic mirrors (not shown) to enhance
the optical through-put of the apparatus 10. As shown in Figure
4, the signal intensity change can be determined without modulating
the phase difference of the secondary filtering means 18 by
transmitting a second beam of light from source 1~' through con-
ditioning means 14', primary and secondary filtering means 16' and
18', sample 20, lens 34', pinhole 3~' of pinhole stop 32' to
infrared detector 38' and indicating and recording means 40'~ In
the latter embodiment, the secondary filtering means 18 and 18'
each receive light having the same frequency range and are adjusted
to transmit the light at two different sets of discrete frequencies,
the first set of frequencies being shifted from the second set of
frequencies by an amount no greater than the frequency spacing
between adjacent absorption lines of the preselected species, and
preferably about 1/2 of such frequency spacing. Other similar
modifications can be made which fall within the scope of the
t~ present invention. It is, accordingly, intended that all matter
contained in the above description and shown in the accompanying
dr~awings be interpreted as illustrative and not in a limiting
sense.
In operation, light 15, containing incoherent, infrared
radiation, is collected, collimated and transmitted by light
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~074~48
conditioning means 14 to primary filtering means 16. The primary
filtering means 16 receives the light 15, selectively separates
therefrom light 17 having a frequency range in the region of an
absorption band for the preselected molecular species, and sends
the separated light 17 to the secondary filtering means 18. The
secondary filtering means 18 receives the light 17 and transmits
light having a plurality of discrete frequencies which provides
a detectable signal 30. The detectable signal is transmitted
through gaseous material in sample 20, whereby the intensity of
the signal changes in proportion to the concentration of the
preselected species. A modulating means 26 operates to modulate
the phase difference of the secondary filtering means so as to
vary the intensity of the signal 30. The intensity variation of
the signal 30 is detected by a phase sensitive detection means 28.
The resultant signal from the phase sensitive detection means 28
is displayed by the indicating and recording means 40.
Having thus described the invention in rather full
detail, it will be understood that these details need not be
strictly adhered to but that various changes and modifications
may suggest themselves to one skilled in the art, all falling
within the scope of the present invention as defined by the
subj~ined claims.
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