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Claims  |
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I claim:
1. In an apparatus for measuring parameters associated with particles,
droplets and the like employing first and second Gaussian laser beams
caused to cross to establish an interference pattern forming a sample
volume, a method for detecting errors due to mixed components in light
scattered by said particles, droplets and the like passing through said
interference pattern, comprising the steps of:
(a) generating said first and second Gaussian laser beams and directing
said beams to cross at a known angle to form said sample volume;
(b) collecting said light scattered by said particles, droplets and the
like passing through said sample volume and determining the phase of said
scattered light;
(c) determining the size of said particles, droplets and the like from the
phase of said scattered light;
(d) determining the amplitude of said scattered light and comparing said
amplitude to predefined upper and lower amplitude limits for the particle
size, such that if said amplitude determined is outside said limits an
error is detected and said measurement is considered invalid.
2. The method as defined by claim 1, wherein said amplitude is further
compared to phase angle values stored in a look-up table, said table
providing a corresponding phase angle for an inputted amplitude and
determines if said amplitude corresponds to a phase angle greater than
2.pi..
3. The method as defined by claim 1, wherein said upper and lower amplitude
limits are stored in a look-up table for each size class of said
particles, droplets and the like.
4. The method as defined by claim 1, wherein said upper limit is determined
by computing a theoretical value for the size class of the particle size
determined and increasing the theoretical value by predetermined amount
indicative of a buffer zone.
5. The method as defined by claim 4, wherein the theoretical value is
computed using the Lorenz-Mie theory.
6. The method as defined by claim 4, wherein the theoretical value is
computed using a geometric technique which assumes that the signal
amplitude is equal to the particle diameter squared.
7. The method as defined by claim 4 wherein the predetermined amount is in
the range of 0-0.25 volts.
8. The method as defined by claim 1, wherein said lower limit is determined
by computing a theoretical value for the size class of the particle size
determined and decreasing the theoretical value by a predetermined amount.
9. The method as defined by claim 8, wherein the theoretical value is
computed using the Lorenz-Mie theory.
10. The method as defined by claim 8, wherein the theoretical value is
computed using a geometric technique which assumes that the signal
amplitude is equal to the particle diameter squared.
11. The method as defined by claim 8 wherein the predetermined amount is
approximately one-third of the theoretical value.
12. The method as defined by claim 1, wherein said collecting step includes
sensing said scattered light using two or more spaced apart
photodetectors.
13. The method as defined by claim 1, wherein said mixed components
comprise light reflected off of and refracted through said particles,
droplets and the like.
14. In a system for measuring parameters associated with particles,
droplets and the like employing laser light scattering, an apparatus for
detecting errors due to mixed components in said scattering, comprising:
laser generation means for generating first and second Guassian laser beams
and directing said beams to cross forming a sample volume;
collection means for collecting the scattered light due to said particles,
droplets and the like passing through said sample volume, and converting
said scattered light into electrical signals;
phase detection means coupled to said collection means for determining the
phase and amplitude of said signals;
sizing means coupled to said phase detection means for determining the size
of said particle, droplet and the like from the phase of said signals,
said sizing means further comparing said amplitude to predefined upper and
lower amplitude limits for the particle size, such that if said amplitude
is outside said limits an error is detected and said measurement is
considered invalid.
15. The apparatus as defined by claim 14, wherein said sizing means further
compares said amplitude to phase angle values stored in look-up table
means coupled to said sizing means, said look-up table means providing a
corresponding phase angle for an inputted amplitude, and determines if
said amplitude corresponds to a phase angle greater than 2.pi..
16. The apparatus as defined by claim 14, wherein said upper and lower
amplitude limits are stored in a look-up table for each class size of said
particles, droplets and the like.
17. The apparatus as defined by claim 14, wherein said upper limit is
determined by computing a theoretical value for the size class of the
particle size determined and increasing the theoretical value by a
predetermined amount indicative of a buffer zone.
18. The apparatus as defined by claim 17, wherein the theoretical value is
computed using the Lorenz-Mie theory.
19. The apparatus as defined by claim 17, wherein the theoretical value is
computed using a geometric technique which assumes that the signal
amplitude is equal to the particle diameter squared.
20. The apparatus as defined by claim 17 wherein the predetermined amount
is in the range of 0-0.25 volts.
21. The apparatus as defined by claim 14, wherein said lower limit is
determined by computing a theoretical value for the size class of the
particle size determined and decreasing the theoretical value by a
predetermined amount.
22. The apparatus as defined by claim 21, wherein the theoretical value is
computed using the Lorenz-Mie theory.
23. The apparatus as defined by claim 21, wherein the theoretical value is
computed using a geometric technique which assumes that the signal
amplitude is equal to the particle diameter squared.
24. The apparatus as defined by claim 21 wherein the predetermined amount
is approximately one-third of the theoretical value.
25. The apparatus as defined by claim 14, wherein said collecting means
senses said scattered light using two or more spaced apart photodetectors.
26. In an apparatus for measuring or sensing parameters associated with
particles, droplets and the like employing first and second Gaussian laser
beams caused to cross to establish an interference pattern forming a
sample volume, a method for determining the change in the effective
cross-section of said sample volume, comprising the steps of:
(a) generating said first and second Gaussian laser beams and directing
said beams to cross at a known angle, said interference pattern having an
apparent spacing defined as .delta.;
(b) collecting the scattered signal created by said particles, droplets and
the like passing through said sample volume;
(c) determining the maximum (N.sub.max) and minimum (N.sub.min) number of
interference fringes crossed by said particles, droplets and the like, of
a class of particles having the same diameter passing through said sample
volume wherein N.sub.min is the number of fringes detected to produce a
signal reliable enough for later use;
(d) determining the change in the effective cross-section of said sample
volume due to size variations of said particles, droplets and the like
passing through said interference pattern, said change in said
cross-section being defined as:
T(d)=.delta.[N.sub.max (d).sup.2 -N.sub.min (d).sup.2 ].sup.1/2
where:
T=sample volume cross-section
d=diameter of said particle, droplet and the like
whereby the effective apparent cross-section of said sample volume is
determined for a class of said particles, droplets and the like having a
diameter d.
27. The method as defined by claim 26, wherein
.delta.=.lambda./2sin(.gamma./2)
where:
.lambda.=the wavelength of said first and second laser beams;
.gamma.=the known angle of the beam intersection.
28. The method as defined by claim 26, further including the steps of:
determining the number of particles in a size class measured; and
correcting the particle size distribution to account for the said change
of cross section of said sample volume due to a non-uniform sampling of
said cross-section such that:
n(d).sub.c =n(d)T(d.sub.max)/T(d)
where:
n(d)=number of particles measured in the size class d;
n(d).sub.c =corrected count for a particle, droplet and the like having
diameter d;
d.sub.max =maximum diameter of said particle, droplet and the like measured
in the size distribution.
29. The method as defined by claim 28, wherein said apparatus includes
collection means for collecting said scattered signal.
30. The method as defined by claim 29, wherein said collection means
includes at least two photo-detectors spaced apart from one another such
that said spacing of the finges formed by the scattered light is less than
the distance between said first and second photo-detectors.
31. The method as defined by claim 30, wherein said collection means
includes a third photo-detector spaced apart from said first and second
photo-detector.
32. The method as defined by claim 31, further including the step of
determining the phase shift of said scattered signal between said first
and second photo-detectors and said first and third photo-detectors to
determine the size range over which said particle, droplet and the like is
measured.
33. In a system for measuring or sensing parameters associated with
particles, droplets and the like employing laser scattering, an apparatus
for determining the change in the effective cross-section of two crossed
laser beams forming a sample volume, comprising:
laser generation means for generating first and second Gaussian laser beams
and directing said beams to cross at a known angle (.gamma.), said crossed
beams forming an interference pattern defining said sample volume, said
interference pattern having an apparent spacing (.delta.);
collection means for collecting the scattered signal created by said
particle, droplet and the like passing through said sample volume;
circuit means coupled to said collection means for determining the maximum
(N.sub.max) and minimum (N.sub.min) number of interference fringes crossed
by said particles, droplets and the like, of a class of particles having
the same diameter passing through said sample volume;
said circuit means further determining the change in the effective
cross-section of said sample volume due to size variations of said
particles, droplets and the like passing through said interference
pattern, said change in said cross section being defined as:
T(d)=.delta.[N.sub.max (d).sup.2 -N.sub.min (d).sup.2 ].sup.1/2
where:
T=sample volume cross-section;
d=diameter of said particle, droplet and the like;
whereby the effective apparent cross-section of said sample volume is
determined for a class of said particles, droplets and the like having a
diameter d.
34. The apparatus as defined by claim 33, wherein
.delta.=.lambda./2sin(.gamma./2)
where:
.lambda.=the wavelength of said first and second laser beams;
.gamma.=the known angle of the beam intersection.
35. The apparatus as defined by claim 34, wherein said circuit means
utilize the number of particles in a size class measure and includes
correction means for correcting said change of cross-section of said
sample volume due to a non-uniform sampling of said cross-section, such
that:
n(d).sub.c =n(d)T(d.sub.max)/T(d)
where:
n(d)=number of particles measured in the size class d;
n(d).sub.c =corrected count for a particle, droplet and the like having
diameter d;
d.sub.max =maximum diameter of said particle, droplet and the like measured
in the size distribution.
36. The apparatus as defined by claim 35, wherein said collection means
includes at least two photo-detectors spaced apart from one another such
that the fringe spacing produced by the scattered light signal in the
plane of the detectors is less than the distance between said first and
second photodetectors.
37. The apparatus as defined by claim 36, wherein said collection means
includes a third photo-detector spaced apart from said first and second
photo-detector.
38. The apparatus as defined by claim 37, wherein said circuit means
determines a first phase shift of said scattered signal between said first
and second photodetectors and a second phase shift of said first and third
photo-detectors to determine the size range over which said particle,
droplet and the like is measured.
39. The apparatus as defined by claim 38, wherein said circuit means
further comprises:
means for determining that the signals collected by two photodetectors are
approximately 360 degrees out of phase;
a phase shifting means to shift the phase of one of the signals collected
by one of the photodetectors 180 degrees such that errors due to ambiguity
of overlapping signals is minimized. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Related Applications
This application is a continuation in part of U.S. Pat. application Ser.
No. 162,053, filed Feb. 29, 1988, entitled "Improved Method for Measuring
The Size And Velocity of Spherical Particles Using The Phase And Intensity
of Scattered Light", now abandoned.
2. Field of the Invention
The present invention relates to particle size and velocity measurements
using scattered laser light detection and, more specifically, relates to
such measurements utilizing the Doppler difference frequency, relative
signal phase, and intensity of the scattered light.
3. Art Background
There is a need for the detailed measurement of the size and velocity of
spherical particles, drops, bubbles, and the like. Areas of application
for such measurements include spray nozzle manufacturing, spray combustion
research, application of agricultural pesticides and irrigation, aircraft
icing studies, atmospheric aerosol research, planetary studies, fuel
analysis, and numerous other applications. Several techniques employing
laser light scattering have been considered and developed to determine the
size and velocity of particles, drops, bubbles, or the like. These
techniques include using the intensity of scattered light by particles,
particle visibility and the phase/doppler technique for measuring particle
size. Each method has had varying degrees of success when applied in real
world environments.
Particle size is determinable from the intensity of the light scattered by
particles. The higher the intensity of scattered light, the larger the
particle size. In one intensity measurement method, the particle size is
computed by assuming that a particle scatters light in proportion to the
diameter of the particle squared (d.sup.2). A more precise method is the
well known Lorenz-Mie theory. Using the Lorenz-Mie theory, the light
scattering intensity can be predicted for uniformly illuminated spherical
particles of arbitrary size. For further information on particle
measurements using the intensity technique, see van de Hulst, Light
Scattering By Small Particles (Dover Publications, 1957). However,
particle size measurements which use the intensity of scattered light to
determine particle size are quite imprecise because there are a number of
unknown parameters such as the incident intensity on the particle, the
crosssection of the incident laser light and the particle trajectory
through the laser beam. Another method based on light scattering
interferometry, referred to as visibility, has been used to measure
spherical particles, drops, bubbles, or the like. This method is described
by William D. Bachalo, in an article entitled, "Method for Measuring the
Size and Velocity of Spheres by Dual-Beam Light-Scatter Interferometry",
Applied Optics, Vol. 19, Feb. 1, 1980 and in U.S. Pat. No. 4,329,054 which
issued on May 11, 1982. The spatial period of the interference fringe
pattern generated by a spherical particle, drop, bubble, or the like as it
passes through a sample volume defined by the intersection of crossed
laser beams is used in determining the particle size and velocity. Several
methods have been devised for measuring the spatial period of the fringe
pattern. In the above cited references, the fringe pattern was integrated
over the receiver lens aperture to obtain the spacing or spatial period of
the fringe pattern. The signal visibility which resulted could then be
related to the particle size. This method has drawbacks since the dynamic
range of the system was limited, and the combined light scattering by the
mechanisms of refraction and reflection produced uncertainties in the
measurements. Furthermore, other particles passing through the crossed
beams produce extinction pulses that tend to distort the signals and
hence, compromise the measurement accuracy.
An alternative approach to the visibility method, referred to as the
"phase/doppler method", was described by F. Durst and M. Zare in a paper
entitled, "Laser Doppler Measurements in Two-Phase Flows", Proceedings of
the LDA Symposium, Copenhagen, 1975. The authors provided a basic analysis
using a simple geometrical approach to show that the shape and spacing of
the fringes formed by the scattered light through reflection and
refraction are functions of the angle between the incident laser beams,
their wavelength, as well as the direction of light collection and
particle diameter. Although the authors claimed that spherical particles
could be measured using a double photo-detector apparatus, they later
recognized that size measurements required that the distance between the
photo-detectors be matched to the expected fringe spacing produced by the
scattered light. They concluded that the method was not practical for
particle field measurements.
More recently, the method was discussed by, W. D. Bachalo and M. J. Houser
in an article entitled "Phase/Doppler Spray Analyzer for Simultaneous
Measurements of Drop Size and Velocity Distributions", Optical
Engineering, Vol. 23, No. 5, 1984. In this article, a more rigorous
description of the light scattering theory described by W. D. Bachalo in
an earlier article entitled, "Method for Measuring the Size and Velocity
of Spheres by Dual-Beam Light Scatter Interferometry", Applied Optics,
Vol. 19, 1980, was used in the analysis. The theoretical description and
experimental verification showed that the method of using signal phase
measurements could be used for practical particle field measurements. This
was made possible with the selection of appropriate detector separations,
on-line observation of the measurements, the use of pairs of detectors,
and a single lens system for scattered light detection. The technique was
disclosed in U.S. Pat. No. 4,540,283. A similar method was disclosed in
U.S. Pat. No. 4,701,051. However, the latter disclosure describes a system
using three or more separate receiver lenses and detector systems. The
approach disclosed in U.S. Pat. No. 4,701,051 has proved very difficult
to operate since each receiver must be carefully aligned to the same
measurement point.
Both approaches suffer from the effects of combined light scattering due to
reflection and refraction by the particle. This problem was addressed by
W. D. Bachalo and M. J. Houser in their report entitled, "Analysis and
Testing of a New Method for Drop Size Measurement Using Laser Light
Scatter Interferometry", NASA Contract Report No. 174636. The problem was
later addressed by Saffman in a report entitled, "The Use of Polarized
Light for Optical Particle Sizing", presented at the Third International
Symposium on Applications of Laser Anemometry to Fluid Mechanics held in
Lisbon, Portugal on July 7-9, 1986. Saffman suggested that a light scatter
detection angle of approximately 70.degree. was necessary to avoid errors
due to mixed component light scatter detection. This method has the
disadvantage of relatively low scattering intensity, lower sensitivity to
particle size and inconvenience in applications requiring traversing the
sample volume with restricted optical access. Often, backscatter light
detection is desirable. Although off-axis backscatter detection has been
demonstrated as a viable configuration, errors can occur as a result of
the multiple component scattering of reflection and refraction.
The problem is exacerbated when using highly focused laser beams having
Gaussian beam intensity distributions. Highly focused beams are required
to reduce the sample volume size when coping with high particle number
densities. For example, at a light detection angle of 30.degree. with the
appropriate polarization, the scattered coefficient for refraction is
approximately 80 times that for reflection. However, with a focused beam
diameter similar to the sphere diameter and on certain trajectories, the
relative incident intensities can be such that the light scattering by
reflection and refraction are nearly equal. Because the sign of the phase
shift for the fringe pattern produced by reflected light is opposite to
that produced by refracted light, the fringes produced by reflection move
in the opposite direction.
The present invention discloses a method to overcome this source of error
and to provide an alternative means to test the measurements for their
accuracy. In addition, the method can provide an alternate means to allow
the measurements over several fringes (N.times.2.pi.) without ambiguity,
and without using additional phase measurements which can complicate the
signal processing. A method is also described for measuring the sample
volume cross section which is known to vary with particle size.
SUMMARY OF THE INVENTION
An improved apparatus and method for determining the change in the
effective cross-section of a sample volume defined by two crossed laser
beams is disclosed. A laser generation means is provided for generating a
pair of coherent laser beams and means are provided to change the
separation, intersection angle, and focused diameter of the beams. These
beams are directed along an axis, and are caused to cross the axis at a
given angle to define an interference pattern constituting a sample
volume. A collection apparatus for sensing the light scattered by
particles, droplets, bubbles, or the like travelling through the sample
volume is provided. In the presently preferred embodiment, the collection
apparatus is disposed at preferred off-axis angles including off-axis
backscatter with the angle predetermined, and the angle defined by the
direction of beam propagation. The collected scattered light is directed
onto photo-detectors which are coupled to a signal phase determining
means, for measuring the relative phase between the signals produced by
each photo-detector and a signal amplitude determining means to measure
the relative amplitude of the signals produced as the particle, drop,
bubble, or the like passes through the sample volume. Sizing means are
coupled to the signal phase and amplitude determination means for
determining the size of the particle, drop, bubble, or the like from phase
and amplitude changes in the received signals.
The present invention determines particle size by the phase of the
scattered light signals but overcomes problems associated with this
technique, that is, the ambiguity due to the combined light scattering
effect by the mechanisms of refraction and reflection. The ambiguity is
reduced by examining the amplitude of the scattered light signals to
ensure that the amplitudes fall within a certain range of signal
amplitudes considered to be reliable. Signals not falling within
prescribed maximum and minimum values are rejected from the measurement
calculations leaving only those signals which result in meaningful
calculations.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagrammatical representation of the presently preferred
embodiment of the invention.
FIG. 2 is a schematic illustrating a Gaussian intensity laser beam incident
on a sphere.
FIG. 3 is a table illustrating theoretical amplitude values computed using
a geometric technique and their corresponding particle sizes.
FIG. 4 is a logarithmic graph illustrating the theoretical amplitude values
computed for particle size classes using the Lorenz-Mie theory.
FIG. 5 is a graph of signal voltage variation versus particle size.
FIG. 6 is a graph of Gaussian laser beam intensity illustrating the
variation in sampling cross-section with particle diameter.
FIG. 7 is a graph illustrating theoretical and experimental results of
change in sample volume cross-section versus particle size.
FIG. 8 illustrates a cross-section of the sample volume showing the
interference fringe pattern with spacing of .delta.=.lambda./2sin
.gamma./2.
FIG. 9(a) and 9(b) schematically illustrate orthogonal fringe patterns for
measuring sample volume.
FIG. 10 schematically illustrates the phase for particle sizing over
multiple fringe cycles.
FIG. 11 is a table illustrating phase and amplitude values for classes of
particle size.
FIG. 12 is a graph of phase and corresponding size distribution when
particle size exceeds selected range.
FIG. 13 is a graph of phase and corresponding size distribution after size
range adjustment.
FIG. 14 schematically illustrates the use of redundant phase measurements
to measure greater than 360.degree. of phase shift at high sensitivity.
DETAILED DESCRIPTION OF THE INVENTION
An apparatus and method for determining the size and velocity of particles,
droplets, bubbles, or the like (hereinafter sometimes collectively
referred to as "particles") using laser light scattering is disclosed. In
the following description for purposes of explanation, numerous details
are set forth such as specific wavelengths, angles, frequencies, etc. in
order to provide a thorough understanding of the present invention.
However, it will be apparent to one skilled in the art that the invention
may be practiced without these specific details. In other instances, well
known components, structures and electrical processing means have not been
described in detail in order not to obscure the present invention
unnecessarily.
Referring now to FIG. 1, the apparatus for determining the size and
velocity of particles includes a sample volume denoted generally by the
numeral 16. The sample volume 16 is defined as the overlap region of a
first laser beam 18 and a second laser beam 20 which are caused to cross
at an angle gamma with respect to an axis defined through the intersection
of the two beams 18 and 20. The laser beams employed by the present
invention are generated in the preferred embodiment by a single laser 25.
The primary beam 28 generated by laser 25 is passed through a beam
splitter 30, thereby forming first and second beams 32 and 34,
respectively. Beams 32 and 34 are reflected off of reflectors 36 and 38,
and are passed through a focussing lens 40 which causes the beams to cross
at the desired angle and form sample volume 16. It should be noted
however, that reflectors 36 and 38 are not necessary to practice this
invention and an "in-line" system accomplishes the same result.
Note that in FIG. 1, the beams have been broken and then shown in enlarged
form in the region of the sample volume. Particles passing through the
sample volume 16 scatter light from each beam and the scattered light
interferes to form interference fringe patterns in the space surrounding
the particle. As previously discussed (see for example, the references to
Durst and Zare; and Bachalo), the phase of the scattered light forms the
interference fringe pattern at a specific spatial frequency. This spatial
frequency is inversely proportional to the particle diameter. The
scattered light intensity and hence, the signal amplitude, depends on the
particle diameter squared, the incident intensity as well as other
parameters that are determined by the optical geometry. The scattered
light is sensed by a collection apparatus which includes lenses 46 and 48,
which focus the light onto photo-detectors 50. Two or more photodetectors
may be used. Photo-detectors 50 are coupled through amplifiers 52 to phase
detection means 54 and sizing means 56. A circuit means 57 is coupled to
the sizing means 56, to determine the change in the effective
cross-section of the sample volume 16 due to size variations of particles,
droplets and the like passing through the interference pattern 42, as will
be described below.
FIG. 2 is a schematic illustration of the laser beam with Gaussian
intensity incident on a particle or droplet in the shape of a sphere.
Phase measurements as described by the inventor, W. Bachalo in U.S. Pat.
No. 4,540,283 provide measurements of the particle diameter. However, due
to the Gaussian intensity distribution of the laser beam operating in the
fundamental mode (TEM.infin.), and the random particle trajectories
through the beam, the combined light scattering by reflection and
refraction can produce significant error. This problem occurs, for
example, for particles passing on trajectories as illustrated in FIG. 2.
At a light scatter detection angle of 30.degree., light intensity
scattered by refraction is approximately 80 times that scattered by
reflection. However, on trajectories as shown in FIG. 2, the difference
can be much less due to the nonuniform beam intensity with the greater
incident intensity falling on the point reflecting light to the detector.
When the light scattering by the undesired component (reflection when
refraction is expected) is significant, the interference fringe pattern is
no longer sinusoidal, but becomes a complex superposition of several
spatial frequency components.
The interference fringes produced by reflection also move in the opposite
direction to the fringes produced by refraction. This can lead to large
measurement errors.
In the present invention, the intensity or signal amplitude information is
used as a means of preventing gross errors due to the effect of the
aforementioned mixed scattering components that occurs for certain
particle trajectories through the beam. More specifically, the amplitude
information is used to determine the range of signal values considered
reliable enough to result in accurate calculations. If the amplitude
measurements falls outside the range of signal values considered to be
reliable, the signal measurements (phase and amplitude) are rejected and
not utilized in the computation of the particle size.
Preferably the Gaussian beam is first clipped to remove light on the wings
of the Gaussian curve at some desired level (e.g., I/I.sub.o =1/e.sup.2).
Although it is not necessary to actually clip the Gaussian beam, this
approach the advantage of reducing the size of the sample volume 16 and
decreasing the number of signals to be processed that will ultimately be
rejected. Particles of a given size passing on all trajectories through
the beam will produce a range of light scattering intensities of
1/e.ltoreq.I/I.sub.max .ltoreq.1.
Preferably the range of reliable signal values is determined empirically by
measuring the range of amplitude values (also referred to as intensity
values) for a known particle size class. The range of reliable signal
values may also be derived from the calculation of the theoretical
amplitude range of classes of particle size. A range of acceptable
amplitude values is then determined by computing an upper limit above the
theoretical value and a lower limit below the theoretical value.
The theoretical amplitude values may be determined by assuming that a
particle scatters light in proportion to the diameter of the particle
squared (d.sup.2). An exemplary table containing the theoretical values
computed is shown in FIG. 3. Alternatively, the values can be computed
using the Lorenz-Mie theory which is computationally intensive but
produces accurate results for particle sizes less than 3 microns, where
the geometric calculation (d.sup.2) breaks down. A logarithmic graph
showing the intensity values (volts) for corresponding particle diameters
(um) is illustrated in FIG. 4. The theoretical values may be computed as
the signal value measurements are taken or may be computed for a range of
particle size classes and stored in lookup tables for quick and easy
reference.
The upper limit may be the theoretical value computed. Preferably, the
upper limit is slightly greater than, for example, 0-.25 volts, the
theoretical value to provide a buffering zone. The lower limit on the
accepted light scattering intensity may be selected depending upon the
requirements for measurement accuracy, the possibility for mixed component
light scattering, and other considerations. For example, if as described
above, the Gaussian beam is clipped at 1/e, particles of a given size
passing on all trajectories through the beam will produce a range of light
scattering intensities of 1/e.ltoreq.I/I.sub.max .ltoreq.1. Thus, the
uncertainty in the particle diameter due to particle trajectory through
the clipped Gaussian beam is 1/e to 1 or 0.368 to 1, and the lower limit
would preferably be set to approximately 1/3 of the theoretical value.
Again assuming that the light scattering intensity is proportional to
d.sup.2, an example of the diagram of acceptable scattered intensities is
shown in FIG. 5. The detector gain is set automatically such that the
maximum signal amplitude for each particle size class falls on the d.sup.2
curve passing through the maximum allowable signal. The gain is set with
the assumption that the phase Doppler method measures the size accurately
of most particles passing through the center of the Gaussian beam. This
assumption has been shown to be correct by experiment. An acceptable error
limit which functions as a buffer, is set on the maximum value shown as
the dashed curve marked "upper" on FIG. 5. The dashed curve marked "lower
limit" on FIG. 5 can be adjusted to select the range of scattered
intensities over which particles will be accepted for each size class.
This corresponds to a range of particle trajectories through the Gaussian
beam and diameters that will produce signals of acceptable intensities for
each size class. The vertical line on the plot is an example of this
acceptable band for a specific size (e.g., d/d.sub.min =20 for this
example). The acceptable limits for particle size classes may be computed
as the measurements are taken or are preferably computed prior to the
measurements and stored in a lookup table for quick reference.
The sample volume cross section is known to vary with particle diameter
when using Gaussian laser beams [see, D. W. Roberds, Appl. Optics, Vol.
16, pg. 1861, (1977)]. Smaller particles must pass through regions of
greater beam intensity (near to the center of the Gaussian) to be
detected, whereas larger particles may pass on trajectories further out on
the Gaussian intensity profile and still be detected. This results in a
bias favoring the measurement of the larger particles (i.e. larger
particles are measurable over a larger cross-section and are thus more
likely to be measured). This bias and the correcting technique employed
are discussed later. FIG. 6 illustrates the variation in sampling
cross-section with particle diameter for a Gaussian laser beam. Thus, it
can be seen that the sampling cross section increases with particle
diameter. The change in sampling volume can be predicted knowing that the
beam has a Gaussian intensity distribution and the scattering
characteristics of the particles. The equation for the intensity of a
Gaussian beam at a certain distance, r, from the center of the beam is
given as:
I=I.sub.o exp[-2r.sup.2 /b.sup.2 ]
where:
I.sub.0 =Maximum intensity of the beam.
r=Radius beam coordinate (distance between particle and center of beam)
b=Radius at which I/I.sub.0 =1/e.sup.2
Assuming that the particles scatter in proportion to their diameter squared
(although a more precise value could also be used when appropriate), the
resultant expression for the change in sampling cross section, r, with
particle diameter, d, is
##EQU1##
where:
.sup.d min=minimum diameter of the distribution of particles measured
(smallest particle size to measure)
and V.sub.0 refer to signal visibility. (See, U.S. Pat. No. 4,329,054,
incorporated herein by reference, for determining signal visibility.) This
illustrates the bias effect which occurs because a larger particle
scatters more light than a smaller particle. It follows that a larger
particle can be detected a farther distance away from the center of the
beam than where a smaller particle can be detected. Thus it is inherent in
this type of measurement that larger particles can be seen more frequently
over a larger part of the beam and can be better detected and counted.
FIG. 7 shows the change in sample volume cross-section with particle size.
This approach offers a useful guide to the variation in sampling volume
cross section with particle diameter but cannot be relied upon completely
due to signal attenuations, beam distortion, etc. in practical flow
measurements. Thus, the method of the present invention includes a method
to measure the sampling cross section directly and correct the sample
volume measurement bias. The experimental data shown in FIG. 7 was
obtained using this method.
The sample volume measurement method of the present invention utilizes the
implicit fringe pattern formed by the intersecting beams as the
measurement scale. FIG. 8 illustrates a cross-section of the sample volume
16 showing the apparent interference fringe pattern with spacing
.delta.=.lambda./2sin (.gamma./2). Particles passing on random
trajectories through the sample volume 16 will produce signals with the
number of cycles corresponding to the number of fringes crossed. However,
particles having a certain diameter will travel at different trajectories.
Because of this, certain particles may cross more fringes if they travel
through the sample volume on a path closer to the center of the laser
beams. Thus for a size class, d (i.e., class of particles having diameters
within a narrow range), signals produced will reflect varying numbers of
fringes crossed. Well known electronics in circuit means 57 counts the
number of cycles in each burst signal, or equivalently, circuit means 57
measures the transit time of the beam and this information is used along
with the measured particle velocity to determine the beam diameter. For
each size class, a statistical distribution of fringe counts is acquired.
The maximum number of fringe counts, Nmax, (which is also the most
probable value) defines the effective beam diameter, D, and is given as
D=N.sub.7ax .delta.
where:
.delta.=.lambda./2 sin (.gamma./2) and .gamma. is the beam intersection
angle;
N.sub.max =maximum number of fringe counts
There is a minimum number of fringe counts, N.sub.min, required for
producing a signal reliable enough to process. Thus, the cross section of
sample volume 16, T, is given as
T=.delta..multidot.[N.sup.2.sub.max -N.sup.2.sub.min ].sup.1/2
The expression and procedure is used for each particle size class d. Thus
the cross section of a sample volume for a size class, T(d), may be
written as
T(d)=.delta.[N.sub.max (d).sup.2 -N.sub.min.sup.2 ].sup.1/2
where:
N.sub.max (d)=maximum number of fringe counts for a size class
N.sub.min =minimum number of fringe counts required for reliable signal
The measured size distribution is corrected for the nonuniform sampling
cross section by first determining the number of particles of a size class
measured, or n(d). This value is then multiplied by the ratio of sampling
cross-section (T(d.sub.max)/T(d)). That is,
n(d).sub.c =n(d)T(d.sub.max)/T(d)
where:
n(d)=number of particles measured in the size class d;
n(d).sub.c =corrected count for a particle of diameter d;
d.sub.max =maximum particle diameter measured in the distribution.
This procedure removes the bias due to nonuniform sampling cross section.
The method also serves to define the width of the measurement cross
section and with the length along the beam axis defined by the image of
the detector aperture, the sampling cross-sectional area is defined.
Accurate definition of the sample volume cross-sectional area is required
for measurements of particle number density and volume flux. The method
assumes that the mean particle angle of trajectory is orthogonal to the
interference fringe pattern or correspondingly, in the plane of the
intersecting beams. If this is not true, two components of the velocity
can be measured to determine the angle of trajectory for each particle
size class. FIGS. 9(a) and 9(b) illustrate a schematic of orthogonal
fringe patterns for measuring the sample volume. The relative fringe
counts or corrected fringe counts for a size class, N(d).sub.c, are
therefore adjusted as follows:
N(d).sub.c =N(d)/cos.theta.(d)
where:
.theta.(d)=mean angle of trajectory for particles of diameter, d;
N(d)=number of fringe counts for a size class
The cycle counts from both components may be used separately as
N.sub.R (d)=[N.sub.x.sup.2 (d)+N .sub.y.sup.2 (d)].sup.1/2
where:
N.sub.R (d)=number of resultant fringe counts for a si | | |
