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BACKGROUND OF THE INVENTION
This invention relates to a method and apparatus for measuring the
temperature of gaseous materials through the selective transmission of
their periodic spectra.
DESCRIPTION OF THE PRIOR ART
In the apparatus conventionally used for spectroscopic measurement of gas
temperatures, light produced by scattering in the gas is collected and
transmitted to a spectrometer whose pass band is scanned to transmit
sequentially the rotational Raman spectra of the gas. The intensity of
each spectral line is recorded as a function of frequency and used to
calculate the temperature of the gas. It has also been proposed to
spectroscopically measure gas temperature by transmitting such scattered
light to a beam splitter associated with a pair of interference filters
adapted to transmit single spectral lines or bands thereof from
preselected portions of the rotational Raman spectrum of the gas. An
intensity ratio derived from the output signals of the interference
filters is used to calculate the temperature of the gas.
One of the major problems with such apparatus is the difficulty of
accurately measuring the temperature of gases present at remote locations.
The output signal from the spectrometer represents a relatively low
intensity signal that is frequently obscurred by spectral interference
between rotational Raman spectra of the gas being measured and spectra of
coexistent gases. Use of a beam splitter reduces the amount of light
transmitted to and hence the intensity of the output signal from each
interference filter associated therewith. Moreover, in order to minimize
the aforesaid spectral interference, the interference filters are adjusted
to transmit relatively low intensity signals derived from limited portions
of the spectrum. For the above reasons, rotational Raman scattering is
often too insensitive for measurement of temperatures of gases present at
remote locations.
SUMMARY OF THE INVENTION
The present invention provides apparatus having increased sensitivity for
spectroscopically measuring the temperature of gaseous materials. Such
apparatus has light conditioning means for collecting, collimating and
transmitting light produced by scattering in gaseous material and having
spectral components periodic in frequency. An interferometric means
adapted to receive such light selectively separates periodic spectra
therefrom and transmits the spectra in the form of a detectable signal
correlated with the temperature of the gaseous material. Such
interferometric means has interference-producing means for providing a
plurality of transmission windows regularly spaced in frequency. The
frequency spacing between adjacent windows, or spectral range, of the
interferometric means is adjusted to depart from an odd integral
submultiple, n, of the frequency difference between adjacent spectral
components of the periodic spectrum of a molecular species of the gaseous
material, said odd integral submultiple being at least three, so as to
produce a split-fringe containing first and second branches of the
components. Such interferometric means also has scanning means for causing
the transmission peaks for adjacent nth orders to substantially coincide
with the spectral lines of either branch of the components. Each branch of
the split-fringe is derived from a plurality of periodic spectral lines
and has an integrated intensity substantially equal to their sum. The
intensity of each of the branches of the split-fringe is measured by a
signal conditioning means, and the intensity ratio of the branches is
indicated and recorded by detecting means, the intensity ratio correlating
with the temprature of the gaseous material.
Further, the invention provides a method for determining the temperature of
a gaseous material by analyzing light having spectral components periodic
in frequency, comprising the steps of collecting, collimating and
transmitting the light in the form of a ray path; interferometrically
separating periodic spectra from the light by directing the light through
a plurality of transmission windows regularly spaced in frequency, the
frequency spacing between adjacent windows being adjusted to depart from
an odd integral submultiple, n, of the frequency difference between
adjacent spectral components of the periodic spectrum of the gaseous
material, or a constituent thereof if the gaseous material comprises a
mixture of gases, said odd integral submultiple being at least three, so
as to produce a split-fringe containing first and second branches of the
components, and scanning the ray path to cause the transmission peaks for
adjacent nth orders to substantially coincide with the spectral lines of
either branch of the components; transmitting a detectable signal composed
of the split-fringe, each branch of the split-fringe being derived from a
plurality of spectral lines and having an inegrated intensity
substantially equal to their sum; measuring the intensity of each of the
branches; and detecting and indicating the intensity ratio of the
branches, the intensity ratio being correlated with the temperature of the
gaseous material.
Although the light which is subjected to analysis can be received from an
external source, it is usually produced by the apparatus. Thus, the
apparatus preferably has light source means for generating monochromatic
light. A projecting means associated with the light source means directs
the monochromatic light through the gaseous material to produce scattered
light having spectral components periodic in frequency. Light conditioning
means are provided for collecting, collimating and transmitting the
scattered light to an interferometric means of the type described.
Several known interferometric means may be adapted for use with the above
apparatus. Preferably, the interferometric means is a Fabry-Perot
interferometer (FPI) having a mirror separation, d, adjusted to transmit
all rotational lines of a molecular species, or constituent, of the
gaseous material in the form of a detectable signal correlated with the
temperature thereof. This condition obtains when
##EQU1##
where d is the mirror separation of the FPI, n is an odd integer, .mu. is
the index of refraction of the medium between the mirrors, and B is the
molecular rotational constant of the species. For a given molecular
species, the rotational constant B and mirror separations d for
transmitting all the rotational Raman lines of the species are unique
quantities. The intensity distribution of the transmitted spectra varies
directly with the temperature of the species. Hence, the temperature of
the species producing a particular rotation Raman spectrum is determined
by adjusting the mirror sparation of the FPI to transmit all rotational
Raman spectra of the species in the form of a split-fringe containing a
first branch (composed of Stokes rotational lines) and a second branch
(composed of anti-Stokes rotational lines), measuring the peak intensity
of each branch and determining the intensity ratio of the branches.
Advantageously, the throughput of the FPI is considerably greater than
that for a spectrometer or for a beam splitter associated with a pair of
interference filters. Moreover, the detected signal has a pair of branches
each of which is derived from a plurality of spectral lines and has an
integrated intensity substantially equal to their sum. Spectral
interference is minimized. The sensitivity of the apparatus is increased
and highly sensitive forms and combinations of detectors, light sources,
filters and control systems are unnecessary. As a result, the method and
apparatus of this invention permits gas temperatures to be measured more
accurately and at less expense than systems wherein the spectra are
transmitted sequentially or from limited portions of the spectrum.
BRIEF 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:
FIG. 1 is a block diagram showing apparatus for determining the temperature
of gaseous material by analyzing light having spectral components periodic
in frequency;
FIG. 2 is a schematic diagram of the apparatus of FIG. 1 including,
additionally, means for producing light carrying such spectra;
FIG. 3 is a side view, partially cut away, showing means for modulating the
interferometric means of FIGS. 1 and 2;
FIG. 4 is a graph showing schematically the peak intensities of preselected
spectral components and their relative positions within a given fringe;
FIG. 5 is a graph showing schematically a split-fringe profile for the
spectral components of FIG. 4;
FIG. 6 is a graph showing a computed split-fringe profile for nitrogen gas;
FIG. 7 is a graph showing calculated intensity ratios for different fringe
numbers of the split-fringe for nitrogen gas at temperatures of
200.degree. K, 300.degree. K and 400.degree. K;
FIG. 8 is a graph showing calculated intensity ratios of split-fringes for
nitrogen gas within the range of 100.degree. K-600.degree. K and values of
the free spectral range in the vicinity of 4B/5;
FIG. 9 is a graph showing calculated intensity ratios of the split-fringes
for nitrogen gas within the temperature range of 100.degree. K-600.degree.
K and at values of the free spectral range in the vicinity of 4B.
FIG. 10 is a graph showing computed variations of the frequency differece
between peak portions of a split-fringe for nitrogen gas within the
temperature range of 100.degree.-1000.degree. K and at values of the free
spectral range in the vicinity of 4B; and
FIG. 11 is a graph showing computed variations of the frequency difference
between peak portions of a split-fringe for nitrogen gas within the
temperature range of 100.degree.-600.degree. K and at values of the free
spectral range in the vicinity of 4B/5.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Light scattered from gaseous material and having spectral components
periodic in frequency can be produced in each of the visible, infrared and
ultraviolet frequency regions at intensities sufficient to measure the
temperature of the gaseous material. As a consequence, the invention will
function with light having a relatively wide range of frequencies. For
illustrative purposes, the invention is described in connection with
apparatus for measuring temperature of gaseous material by analyzing
scattered light from the visible frequency region. When applied in this
manner, the invention is particularly suited to measure the temperature of
a gas mixture such as air. It will be readily appreciated that the
invention can be practiced using light from any of the foregoing frequency
regions, and that it can be employed for similar and yet diversified uses,
such as remote detection of clear air turbulence, weather forecasting, gas
stream analysis, industrial process control systems and the like.
Referring to FIG. 1 of the drawings, there is shown preferred apparatus for
measuring the temperature of gaseous material. The apparatus, shown
generally at 10, has light conditioning means 12 for collecting,
collimating and transmitting light 14 having spectral components periodic
in frequency. An interferometric means 16 receives the light 14,
selectively separates preselected spectra therefrom and transmits the
spectra in the form of a split-fringe containing first and second branches
of the spectra which provides a detectable signal 18. Generally, such
preselected spectra are those produced by scattering of a major
constituent of the gaseous material as, for example, the rotational Raman
spectra of oxygen or nitrogen in a sample of air. A signal conditioning
means 20 associated with the interferometric means 16 measures the
intensity of each branch. The intensity ratio of the branches is measured
by a detecting means 22, and used to calculate the temperature of the
gaseous material.
More specifically, as shown in FIG. 2, the interferometric means 16 has
interference-producing means for providing a plurality of transmission
windows regularly spaced in frequency. In addition, the interferometric
means 16 has scanning means for variably controlling the frequency of each
order. The frequency spacing between adjacent windows of the
interferometric means 16 is adjusted to depart from an odd integral
submultiple, n, of the frequency difference between adjacent spectral
components of the periodic spectrum of a molecular species of the gaseous
material, said odd integral submultiple being at least three, so as to
produce the split-fringe. The scanning means is then adjusted so that the
transmission peaks for adjacent nth orders substantially coincide with the
spectral lines of either branch of the components. When the
interferometric means 16 is adjusted in the above manner, each branch of
the split-fringe is derived from a plurality of periodic spectral lines
and has an integrated intensity substantially equal to their sum.
As previously noted, the light 14 which is subjected to analysis can be
received from an external source. Generally, however, the light 14 is
produced by the apparatus 10. Hence, the apparatus 10 has light source
means 26, such as a conventional argon ion laser, a frequency doubled,
pulsed ruby laser or the like, for generating a highly monochromatic,
coherent, collimated beam of radiation. The resolving power of the
interferometric means 16 is best utilized when the light source means 36
is provided with means for projecting light having a line width and
frequency stability about equal to or less than the instrumental width,
described hereinafter in greater detail, of the interferometric means 16.
The use of a pulsed laser as the light source means 36 together with a time
gated electronic detection system permits determination of temperature and
location of a sample of gaseous material remote from the apparatus 10. For
example, by providing the apparatus 10 with (1) means for measuring the
time interval required to send a laser pulse into the sample and receive a
return signal caused by light scattered therein and (2) means for
measuring the amplitude of the return signal, the distance of the sample
from the apparatus 10 as well as the temperature thereof is readily
obtained. A pulsed laser adapted to determine temperature and location in
the above manner preferably has means for projecting light having a line
width and frequency stability about equal to or less than the instrumental
width of the interferometric means associated therewith. Such means
typically includes a mode selecting etalon disposed in the laser cavity.
A projecting means associated with the light source means 36 introduces the
radiation, schematically represented by ray path 38, into gaseous material
in sample compartment 40 in one direction, which will be considered to be
substantially vertical for convenience in referencing direction, but may,
of course, be in any direction desired. Raman scattered radiation,
hereinafter referred to as light 14, from the gaseous material in sample
compartment 40 is collected, collimated and transmitted to the
interferometric means 16 by the light conditioning means 12, which may be
a lens, or other suitable optical system. As long as the gaseous material
contains molecules which are of the linear or symmetric top variety, the
light 14 will exhibit spectral components periodic in frequency.
The signal conditioning means 20 has modulating means 42 for modulating the
phase difference between interfering rays of light 14 transmitted by the
interferometric means 16 so as to compare the peak intensities of the
branches of the split-fringe transmitted thereby. Signal conditioning
means 20 also has synchronous (e.g., phase sensitive) detecting means for
detecting the intensity ratio of the latter split-fringe, whereby the
intensity ratio of the split-fringe can be indicated by the detecting
means 22.
Several known interferometric means may be adapted to selectively separate
periodic spectra from the light 14. Preferably, the interferometric means
is a Fabry-Perot Interferometer (FPI) having a mirror separation, d,
adjusted to transmit all rotational lines of a molecular species of the
gaseous material. The transmission function of an FPI (I.sub.t) can be
given by the Airy formula: I.sub.t = .tau..sup.2 [1+R.sup.2
-2Rcos.phi.].sup.-1.I.sub.o where .tau. + R + A = 1, I.sub.o is the
intensity of the incident light, and the phase difference .phi. is
expressed as .phi. = 4.pi..mu..omega.d for rays normal to the FPI mirrors.
The symbols A, R and .tau. represent, respectively, the absorbance,
reflectance and transmittance of the FPI mirrors, .mu. is the refractive
index of the medium between the FPI mirrors, d is the FPI mirror
separation, and .omega. is the frequency of the incident light expressed
in wavenumbers. When cos .phi. is equal to unity, transmission maxima for
I.sub.t occur. Hence, .phi. =2.pi.m, where m takes on integral values and
represents the order of interference. The transmission maxima for I.sub.t
are referred to in the specification and claims as transmission windows.
For a specific value of the mirror separation d, the FPI provides a
plurality of transmission windows regularly spaced in frequency. The
frequency spacing, .DELTA.f, between adjacent windows (or spectral range)
of the FPI is .DELTA.f = (2.mu.d(.sup.-1. By varying the mirror spacing,
d, of the FPI, .DELTA.f can be adjusted to depart from the frequency
difference between adjacent spectral components of a specific periodic
spectrum by a preselected frequency difference as in the order of about
160B.sup.2 /.omega..sub.o n to 480B.sup.2 /.omega..sub.o n and preferably
about 240B.sup.2 /.omega..sub.o n to 320b.sup.2 /.omega..sub.o n. If the
rotational Raman spectrum of a gas is used as the periodic spectrum, the
FPI will behave as a comb filter having its transmission windows matched
to the given periodic spectrum so as to transmit all of the Raman lines of
the spectrum in the form of a split-fringe containing first and second
branches of the lines and block the Rayleigh line when the mirror spacing
is adjusted so that
.DELTA.f = (4B/n .+-.240B.sup.2 /.omega..sub.o n (2)
where B is the rotational constant of a molecular species, or constituent
of the gas. The Rayleight line is blocked because it falls between two FPI
transmission windows. Moreover, in the Raman spectrum, the Stokes and
anti-Stokes Raman lines are symmetrically positioned around the Rayleigh
line (at.omega.=.omega..sub.o). The first two Raman lines (having
rotational quantum number, J, equal to zero) are shifted away from
.omega..sub.o by a frequency of 6B, whereas the frequency separation of
successive rotational lines is 4B. Continuous scanning of the FPI in the
vicinity of
##EQU2##
produces an interferogram having equally spaced vertical lines of constant
amplitude, which represent Rayleigh fringes at .omega..sub.o, and a
plurality of split-fringes, positioned between such vertical lines, each
of the split-fringes containing a first branch (composed of the Stokes
rotational lines) and a second branch (composed of the anti-Stokes
rotational lines). When .DELTA.f = 4B/n, the transmission peaks for
adjacent orders coincide with the adjacent rotational Raman lines so as to
produce a 1:1 correspondence therewith, and the amplitude of the Raman
fringe transmitted is a maximum. For values of .DELTA.f slightly different
from 4B/n, the transmission peaks for adjacent orders will not perfectly
coincide with the Raman spectrum and the profile of the Raman fringe
transmitted by the FPI will split into such first and second branches.
In order to illustrate the manner in which the Raman fringe splits to form
a Stokes branch and an anti-Stokes branch, the positions and peak
intensities of the individual rotational Raman lines were plotted for a
mirror separation slightly larger than the mirror separation corresponding
to the center of the 4B/5 interference pattern for nitrogen. The result is
shown in FIG. 4. This figure shows schematically the relative positions of
the individual rotational Raman lines between two 514.5 nm Raleigh fringes
corresponding to the fringe numbers 12263 and 12264. The peak rotational
line intensities were calculated for a gas temperature of 300 K and the
nitrogen ground state rotational constants of B.sub.o = 1.989506 cm.sup.-1
and D.sub.o = 5.48.times.10.sup.-6 cm.sup.-1. For the Stokes branch lines,
the Raman frequency of the rotational line with quantum number J is
.omega..sub.s = .omega..sub.o - (4B.sub.o - 6D.sub.o)(J + 3/2) + 8D.sub.o
(J + 3/2).sup.3
and the corresponding peak line intensity is
##EQU3##
where K is a proportionality constant, T is the absolute temperature and
h, c, and k are Planck's constant, the speed of light and Boltzmann's
constant, respectively. For the anti-Stokes branch, the corresponding
Raman frequency and peak intensity are given by
.omega..sub.A = .omega..sub.o + (4B.sub.o -6D.sub.o)(J + 3/2) - 8D.sub.o (J
+ 3/2).sup.3
and
##EQU4##
The rotational lines shown in FIG. 4 are depicted as having zero
linewidth. In reality, each line has a finite width which is due to the
combined effects of the laser linewidth, Doppler broadening by the
scattering process and instrumental broadening by the Fabry-Perot
interferometer. In order to determine the fringe profile, a computer
program was written and tested which takes into account the aforementioned
factors. For the purpose of calculation, it is asumed that the laser line
is gaussian shaped with a width of .DELTA..omega..sub.o. This laser line
was convolved with the Doppler broadened profiles for the Rayleigh line
and the individual Raman lines. A convolution was then performed with the
instrumental transfer function of the interferometer. At specified fringe
intervals, the contributions from the Rayleigh line and all the individual
Raman lines were summed to yield the fringe profile at that particular
mirror position.
The Fabry-Perot transfer function may be written as
I(.omega.) = G.sub.A (.omega.) * G.sub.D (.omega.) * G.sub.S (.omega.) (5)
where
G.sub.A (.omega.) = the Airy function
G.sub.D (.omega.) = the mirror defect function, and
G.sub.S (.omega.) = the scanning aperture function.
It can be shown mathematically that the Fourier transform of the
convolution of two or more functions is equal to the product of the
Fourier transforms of the individual functions. Therefore, the Fourier
transform of I(.omega.) is
i(X) .tbd. F.T. [ I(.omega.)] = g.sub.A (X) . g.sub.D (X) . g.sub.S (X) (6)
where g.sub.A, g.sub.D and g.sub.S are the Fourier transform of G.sub.A,
G.sub.D and G.sub.S, respectively.
The Airy function, G.sub.A (.omega.), can be written as
##EQU5##
where .gamma.= 2.mu.d = the optical path between interfering rays. The
Fourier transform of G.sub.A (.omega.) is
##EQU6##
This transform is non-zero only for the discrete values of X = N.gamma..
The mirror defect function, G.sub.D (.omega.) can be expressed as
G.sub.D (.omega.) = 1 for -[2.gamma. F.sub.D ].sup.-1
.ltoreq..omega.<[2.gamma.F.sub.D ].sup.-1 = o for all other .omega.(9)
where F.sub.D = Defect finesse = 1/2 m for .lambda./m flatness figure. The
Fourier transform of G.sub.D (.omega.) is
##EQU7##
Similarly, the scanning aperture function can be written as
G.sub.S (.omega.= 1 for -[2.gamma.F.sub.S ].sup.-1 .ltoreq..omega.<
[2.gamma.F.sub.S ].sup.-1 = 0 for all other .omega.. (11)
The scanning finesse, F.sub.S, is defined as
##EQU8##
where .theta..sub.p is the pinhole angle in radius. The Fourier transform
of G.sub.S (.omega.) is
##EQU9##
A broadened line profile, H (.omega.), is of the form
H (.omega.) = H (.omega..sub.R) exp [-(4 ln 2)
(.omega.-.omega..sub.R).sup.2 /(.DELTA..omega..sub.R).sup.2 ](14)
where .omega..sub.R = Raman frequency (cm.sup.-1)
H(.omega..sub.R)= peak intensity of the individual Raman lines and
.DELTA..omega..sub.R = the Doppler line width.
##EQU10##
where T = the absolute temperature (K)
M = the molecular weight
R = the gas constant, and
.phi. = the scattering angle.
The Fourier transform of H (.omega.) is
##EQU11##
A pressure broadened line profile, L(.omega.), may be represented by an
Lorentzian function given by the equation:
L(.omega.) = (.DELTA..omega..sub.p /2)[(.omega.- .omega..sub.R).sup.2 +
(.DELTA..omega..sub.p /2).sup.2 ].sup.-1 (17)
where .omega..sub.R = the Raman frequency (cm .sup.-1)
.DELTA..omega..sub.R = the full width at half maximum of the pressure
broadened line.
The fourier transform of L(.omega.) is
l(X) = F.T. [L(.omega.)]= exp [-.pi..DELTA..omega..sub.p X]. (18)
the convolution of all these functions is achieved by forming the product
of the Fourier transforms and then taking the inverse Fourier transform of
the product. The calculation is simplified by the presence of the
.delta.-function in the Fourier transform of the Airy function, since it
is necessary to compute the product only for discrete values of X
=N.gamma. where N = 1, 2, 3, etc.
The computer program begins by calculating the frequencies and peak
intensities of the individual Raman lines. For a given optical path
difference, .gamma., an array A(N) is calculated. The array A(N) is the
product of the Fourier transforms of the FPI transfer function, a gaussian
lineshape for the exciting laser light, a gaussian lineshape for the
Doppler broadened scattered light and a Lorentzian lineshape for the
pressure broadened scattered light. The intensity of the interferogram for
a given .gamma. is
##EQU12##
where the index i runs over all spectral lines. The value of .gamma. is
incremented and the calculation is repeated.
This computer program was used to calculate the fringe profile for the
fringe interval shown in FIG. 4. The results of the calculation are shown
in FIG. 5. The open circles represent the calculated profile for this
particular fringe interval and the five triangular points which represent
experimental data indicate that the agreement between the experimental and
calculated fringe profiles is quite good.
A computed fringe profile for a fringe interval corresponding to a mirror
separation slightly less than the mirror separation for the center of the
4B/5 interference pattern in nitrogen is shown in FIG. 6. Since the
positions of the individual Raman lines within a given fringe changes as
the mirror separation is changed, this ratio of the Stokes branch
intensity to the anti-Stokes branch intensity shown in FIG. 6 differs from
that shown in FIG. 5. In order to investigate the variation of this Raman
intensity ratio as a function of fringe number (mirror separation), fringe
profiles were calculated for three different temperatures for the fringe
numbers 12250 to 12273 inclusive. The Raman intensity ratios were
calculated from the computer fringe profiles and the results are plotted
in FIG. 7 for nitrogen gas. The change in the Raman intensity ratio as a
function of temperature was determined by arbitrarily selecting a fringe
interval (12260 to 12261) and calculating the Raman fringe profiles for
several different temperatures. FIG. 8 is a graphic representation showing
the variation of the calculated split fringe ratio over the temperature
range 100K to 600K. Also shown in FIG. 8 is the variation of the
calculated split fringe ratio for the fringe 12170 within the same
temperature range.
A similar computer investigation was carried out for the 4B interference
pattern of nitrogen for selected fringe intervals on either side of the 4B
interference maxima (which occurs at the 514.5 nm order number of 2443).
These results are shown in FIG. 9. In practice, the Raman fringe intensity
ratio is measured from a fringe number produced by an experimentally
determined mirror separation. For that particular fringe, a computer
calculation is then performed using .gamma. values coresponding to peak
portions of the stokes and anti-stokes branches of the split-fringe to
give the Raman fringe intensity ratio as a function of temperature
according to equation 19. Alternatively, the Raman fringe intensity ratio
is experimentally measured for several known gas temperatures in the range
of interest in order to calibrate the apparatus 10. FIGS. 8 and 9 show
that the Raman intensity ratio for the split fringe varies inversely with
gas temperature, i.e., the ratio is greater at lower temperatures than at
higher temperatures.
The temperature of a preselected constituent of gaseous material can also
be determined by measuring the frequency difference between preselected
portions (preferably the peak portions) of first and second branches of
the split fringe. Such a frequency difference is produced when the
spectral range of the interferometric means is adjusted to depart from an
odd integral submultiple, n, of the frequency difference between adjacent
spectral components of the periodic spectrum of a molecular species of the
gaseous material appointed for analysis, and the scanning means is
adjusted to cause transmission peaks for adjacent nth orders to
substantially coincide with the spectral lines of either branch of the
components. The frequency difference between the preselected portions of
the first and second branches is measured by the signal conditioning
means, indicated and recorded by detecting means and correlated with the
temperature of the gaseous material.
The variation in frequency difference as a function of temperature was
determined by means of the fringe profile computor program for nitrogen
gas. FIG. 10 is a graphic representation showing the computed variation of
the frequency difference between the peak portions of the split-fringe
over a temperature range of 100.degree.-1000.degree. K for the 514.53 nm
order number of 2410. FIG. 11 is a graphic representation showing the
computed variation of the frequency difference between the peak portions
of the split-fringe over a temperature range of 100.degree.-600.degree. K
for the 514.53 nm order number of 12,260. For nitrogen gas at room
temperature the frequency difference between the peak portions of the
split-fringe was determined experimentally to be 0.556 cm.sup.-1. From the
computed data shown in FIG. 11, the temperature corresponding to the
frequency difference of 0.556 cm.sup.-1 is equal to 297 K, or 24.degree.
C., which equaled, approximately, the ambient temperature.
For certain molecules, such as oxygen and carbon dioxide, spectral
components of the rotational Raman spectra having either even or odd
rotational quantum numbers (J) will have zero intensity. This alternation
in the intensity of the rotational Raman lines is produced by the effects
of nuclear spin. For such molecules, adjacent rotational lines in the
Stokes and anti-stokes branches are separated by a frequency substantially
equal to 8B. Secondary interferograms are produced for values of the
interferometer spectral range equal substantially to 8B/n, where n is an
odd integer. The secondary interferograms which are produced, consist of
two Raman fringes between adjacent Rayleigh fringes: one Raman fringe
being due to the simultaneous transmission by the FPI of only Stokes Raman
lines and the other Raman fringe being due to the simultaneous
transmission by the FPI of only anti-Stokes Raman fringes. By measuring
the intensity ratio of the peaks of these two fringes, gas temperatures
may be deduced. This technique will be useful for only molecules with
either odd or even J value lines missing.
As previously noted, a modulating means 42 is associated with the
interferometric means 16 for modulating the phase difference, .phi., so as
to compare the peak intensities of the branches of the split-fringe
transmitted thereby. In order to obtain the maximum modulated signal from
the split-fringe appointed for analysis, the modulating means is adjusted
to modulate between the peak portion of each branch thereof. Generally
speaking, the modulating range should be no greater than the frequency
spacing between adjacent orders.
The resultant signal 18 from the inerferometric means 16 is collected and
focused in the plane of pinhole stop 44 by a lens 46. Lens 46 is adjusted
so that the center of the signal 18 is positioned on the pinhole 48. The
intensity of the portion of signal 18 passing through the pinbhole 48 is
detected by a photomultiplier 50. A phase sensitive detection means 52,
such as a lock-in amplifier, is adapted to receive the signal from the
photomultiplier 50 and detect the intensity variation of the fringe
appointed for analysis. The output of the phase sensitive detection means
52 is displayed by an indicating and recording means 54, which can
comprise an oscilloscope and a chart recorder.
In FIG. 3, the interferometric means 16 and the modulating means 42 are
shown in greater detail. The interferometric means shown is a Fabry-Perot
Interferometer (FPI) which is scanned by varying the phase difference,
.phi., between interfering beams of light in a conventional way. Scanning
methods such as those wherein the pressure of gas between the mirror of
the FPI is altered so as to change the optical path therebetween can also
be used. Accordingly, interferometric means 16 shown in FIG. 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 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
interferometric means 16 is fixedly mounted on end 64 of cylinder 60 as by
a suitable adhesive or the like. The plane surface of the mirror 62 is
substantially perpendicular to the rotational 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. The light 14 to be analyzed enters the interferometric means
16 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 82 fixedly secured
thereto by mechanical fastening means, such as screws 88, and to cylinder
60 as described hereinafter provides the cylinder 60 with the linear
motion needed to scan the interferometric means 16. 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 10.sup.6 to 1 or more.
In order to transmit precisely the linear motion to cylinder 60, a collar
78 having glass plate 80 adhesively secured 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 42 is shown in FIG. 3.
Other forms of the modulating means 42 can also be used. Preferably, the
modulating means 42 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 cylindrical body 92, at ends 102
and 104, respectively, by a suitable adhesive such as an epoxy resin.
Mirror 66 is fixedly attached to insulating member 98 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, respectively. Voltage having a wave form such as a sine wave or a
square wave impressed thereon is applied from a high voltage low current
power supply 101 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 18 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 split-fringe to be analyzed from signal 18 alternates
between the maximum values of the branches. A detection means is provided
for determining the photon cokunt at the peak of each branch of the
split-fringe for each half | | |
