EPA-650/2-73-034


June 1974
Environmental  Protection  Technology Series



                                al
                                a

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                                        EPA-650/2-73-034
INTERFEROMETRIC  INSTRUMENTATION
     FOR  PARTICLE  SIZE  ANALYSIS
                         by

         D.W. Roberds, W.M. Farmer, andA.E. Lennert

              Arnold Research Organization, Inc.
           Arnold Air Force Station, Tennessee 37389
          Interagency Agreement No. EPA-IAG-0177 (D)
               Program Element No . 1AA010
                   ROAP No. 26AAM
              EPA Project Officer: John W. Davis

              Chemistry and Physics Laboratory
            National Environmental Research Center
          Research Triangle Park, North Carolina 27711
                     Prepared for

           OFFICE OF RESEARCH AND DEVELOPMENT
          U.S. ENVIRONMENTAL PROTECTION AGENCY
                WASHINGTON, D.C. 20460

                       June 1974

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This report has been reviewed by the Environmental Protection Agency and




approved for publication. Approval does not signify that the contents




necessarily reflect the views and policies of the Agency, nor does




mention of trade names or commercial products constitute endorsement




or recommendation for use.
                                 11

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                             ABSTRACT
    This report summarizes the results of a research program con-
ducted to determine the characteristics and potential capabilities of
particle size analysis using laser interferometer techniques.  Theo-
retical and experimental analyses are reported which indicate that a
range of particle sizes from submicron to millimeters in diameter
can be determined when the cross-sectional shape of the particle is
known.  It is shown that number density can be determined from the
interferometric measurements  in certain restricted applications.
The limitations and potentialities  of this method of determining parti-
cle size are discussed in detail.

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                             CONTENTS
1. 0   INTRODUCTION	7
2. 0   THEORETICAL INT ERFEROMETRIC PARTICLE
      SIZE ANALYSIS
      2. 1  General	8
      2. 2  Single Particle Visibility Determination	11
      2. 3  Determination of Number Density from Visibility
           Measurements	19
      2. 4  Error Analysis
           2. 4. 1  Error Analysis for Spherical Particles .... 20
           2. 4. 2  Error Analysis for Long Narrow Cylinders .  . 23
      2. 5  Visibility for Non-Paraxial Observations of Particles
           with Sizes Much Greater than a Wavelength  ..... 25
3. 0   EXPERIMENTAL OBSERVATIONS
      3. 1  Experimental Evaluation	27
      3. 2  Large Particle Error Analysis	30
      3. 3  Experimental Results of Large Particle Observations . 33
      3. 4  Experimental Results of Small Particle Observations . 43
4. 0   ELECTRONIC  INSTRUMENTATION
      4. 1  General	47
      4. 2  Visibility from Peak Values	47
      4. 3  Continuous Measurement of Signal Visibility	48
5. 0   SUMMARY AND CONCLUSIONS
      5. 1  Passage  Angles of the  Particle through the
           Interference Fringes	  . 49
      5. 2  Relative  Beam Intensities Used to Form the
           Interference Fringes	50
      5. 3  Relative  Coherence of  the Beams	50
      5. 4  Photon-Limited Signals	50
      5. 5  Radiation Pressure Effects on Very Small Particles  . 50
      5. 6  Light Absorption by the Particles	50
      5. 7  Index of  Refraction of Medium Surrounding the
           Particles	51
      5. 8  Limiting Particle Size (Maximum and Minimum) ... 51
      5.9. Particle  Shape  Effects	52
      5.10  Multiple  Particle Signals	53
6. 0   RECOMMENDATIONS	53
      REFERENCES	54

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                           ILLUSTRATIONS
Figure                                                         Page

   1.  Generation of Free Space Interference Fringes with a
       Laser Doppler Velocimeter System	9

   2.  Fringe. Intensity Distribution in y-z Piane	10

   3.  Signal Waveforms	13

   4.  Visibility Functions Near Geometric Center as a
       Function of D/6 and L sin ()3)/6 .  /	15

   5.  Range of the  Unambiguous Determination of Particle Size
       as a Function of Angle Between the Illumination Beams .  .17

   6.  Example of a Multi-Beam Interferometer Arrangement
       and the Different Observational Modes	18

   7.  Signal Visibility as a Function of Number of Observable
       Particles	21

   8.  Maximum Observable Particle Density as a Function of
       Particle Diameter for a Visibility of 0.01 and an
       Illuminating Wavelength of 0.5 £tm	22

   9.  Uncertainty Curve for a Spherical Particle with Size
       Determined by a Visibility Measurement	24

  10.  Uncertainty Curve for a Long Narrow Cylinder with Size
       Determined by a Visibility Measurement	25

  11. . Visibility for Non-Paraxial Observation of a Large
       Particle Compared to Illuminating Wavelength Xo	26

  12.  Schematic of the Optical Arrangement for the
       Experiment Observations	27

  13.  Photograph of Path Compensating Beam Splitting Blocks.  . 28

  14.  Schematic of the Two-Dimensional Bragg Cell
       Arrangement	28
  15.  Photograph of the  Overall Optical System	29

  16.  Photograph of the  Particle Holder and Traverse System .  .31

  17.  Schematic of the Data Reduction System	32

  18.  Experimental and  Theoretical Illuminating Intensity
       Distribution in the Probe  Volume	34

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Figure                                                         Page
  19.  Experimental and Theoretical Comparison for a Long
       Narrow Cylinder at Different Orientation Angles	35
  20.  Comparison of  Theoretical and Experimental Paraxial
       Visibility for a Spherical Particle	37
  21.  Average Signal Visibility as a Function of Particle
       Trajectory for  Different D/6	38
  22.  Variation of Visibility for Different D/6  and Solid
       Collection Angle	39
  23.  Comparison of  Number Density Measurements by Image
       Computer with  Those Made By an Interferometer	41
  24.  Photograph of Interferometer Signal versus Time as the
       Number of Particles Passing through the Probe
       Volume Changes	42
  25.  Experimental Arrangement for Small Particle
       Observation	44
  26.  Relative Particle Size Distribution of Laboratory
       Particles	45
  27.  Particle Visibility Histogram for Laboratory Air
       Particles	46
  28.  Electronics for Visibility Measurement from Peak Values .  47
  29.  Electronics for Continuous Measurement of Visibility ...  48

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                          1.0 INTRODUCTION
    Numerous techniques exist to determine the size of small particles
(Ref.  1).  Optical techniques which allow visible analysis of the particle
represent the most accurate means available for size determination.
These techniques range in diversity from simple microscope measure-
ments to the more sophisticated methods of size determination from
scattered light measurements.  Each optical technique has its own pe-
culiar limitation for the determination of particle size.   For example,
microscope analysis usually requires that the particles be stationary,
and that the size of the particles be greater than several wavelengths
of the light illuminating it.  On the other hand,  light scattering meas-
urements which can determine particle size less than a wavelength in
diameter require a priori knowledge of particle shape, index of refrac-
tion, and in some cases, the absolute values of the scattered light in-
tensity must be measured accurately.  Holographic techniques  have
been used extensively  in the measurement of particle sizes in a number
of different  applications (Refs. 2, 3,  and 4).  Holographic measure-
ments offer the advantage of extreme depths of field;  however, the
resolutions  are limited by the velocity of the dynamic particles (Refs.
2 and 3).  Furthermore,  since holography does not as yet provide on-
line measurements,  the analysis of particle hologram images is  some-
what tedious and time  consuming.  Thus, a need exists for a device that
can rapidly  determine particle sizes lower than the resolution limit of
standard microscope systems and that is not restricted to measuring
stationary particles.

    The purpose of this report is to  describe the research performed
to develop a technique and corresponding instrumentation to satisfy the
above needs.  The results of both the analytical and experimental work
indicate the feasibility of using interferometric techniques for measur-
ing particle sizes.  The characteristics and limitations of a prototype
instrument are summarized.  Predicted upon the results, recommen-
dations for continued effort are made to develop a viable instrument for
on-line particle size measurements.

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      2.0 THEORETICAL INTERFEROMETRIC PARTICLE SIZE ANALYSIS
2.1  GENERAL

    In this section,  a review of the theory and analysis of the inter-
ferometric particle  sizing technique will be discussed.  Figure  1 illus-
trates that when two coherent laser beams (assumed to be in the TEMOO
mode) are brought to a simultaneous cross-focus region by means of a
lens,  interference fringes are formed.  In the region of focus, the
wavefronts are planar and tilted relative to each other according to the
included angle,  a, between the beams.  Propagation vectors  are KQ and
K2.  The interference fringes generated are planes parallel to the bi-
sector between the beams and perpendicular to the plane of the beams.
The distance between successive fringes, 6, is given by


                                                                 (1)
                                 2?7 sin a/2

where T? is the index of refraction of the medium surrounding the parti-
cle and A0 is the wavelength of the interfering light.  A particle tra-
versing a set of interference fringes will receive varying amounts of
illumination as it passes alternately through the bright and dark regions.
If the light scattered by the moving particle is focused onto a photomul-
tiplier (PM) tube, as shown in Fig. 1, the velocity of the particle nor-
mal to the interference fringes may be determined from the time elapsed
between successive peaks in the collected light intensity (Refs.  5, 6, and
7).  Furthermore,  particle size  information is also inherent in the
collected scattered light signal (Refs. 8 and 9).

    Define a coordinate system  (Fig. 1) such that the z axis lies along
the bisector of the beams, x is the direction of polarization,  and y is
orthogonal to  both x and z.  Let  the electric field amplitudes EJ and
of the two laser beams be expressed as
                                    exp fiat — ikzi
                                       \

                                                                  (2)

                              xjj + yjj k
  ^2  ' f. 1    /
-	— I exp ficut - ikz
                                  8

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                                     Interference Fringes
                                     1/e Modulation Contour
                   Enlarged View of
                   Region of Cross-
                   Focus Point
          Self-Aligning
          Transmitting
          Optics
Scattered
Light Collecting
Optics
,^_X^ Aperture
        PH Tube
                                                             Signal
                                                             Processor
            Figure 1. Generation of free space interference fringes with a
                    laser doppler velocimeter system.
Each electric field is expressed in terms of  its own coordinate system
referred to its own direction of propagation:  z[ is  in the direction of
propagation of the ith beam,  x± is in the direction of polarization,  and
y£ is orthogonal  to the xj[Z[ plane.   The origin of both coordinate systems
is located at the cross-focus of the two beams.  In these equations,  Eo
is the field on the centerline of each beam, u is the optical frequency,
t is time,  k = 2ir/X,  where A is the laser  wavelength,  and  2 are
arbitrary phase  factors.   Since the beams are polarized in the same
direction,  xj = X2 = x and assume i = 02-  The variable bo  = 2fj_^A /tfdt,
is the radial distance at which the field amplitude of that beam has fallen
off to e~l times  its value on centerline;  the amplitude falls off in a
Gaussian manner with radial distance = (x^ + yf)"*"' ^•  The variable fj_,
is the focal length of the beam focusing lens  and d]-, is the diameter of
the input laser beam.

     The two plane wave radiations interfere to form a high contrast
fringe system.   By summing EI and £3 of Eq. (2)  and transforming
coordinates to the symmetrically located  coordinates xyz,  the  intensity
Io in the cross-over region can be  expressed as (Ref. 9)

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    2F     r*
»      o    1   2  / 9   ?   9 ct    9
I0 = —r exp  - — (x + y^ cos^ - + z^ sin'
     *-*     I  k^ *         ^
                                     in2 |)  cosh (-^V7 s'n «  + cos (^p-j
                     (3)
where z'  is the impedance of the surrounding medium.

     Equation (3) shows the only dependence on x is the factor exp
   x2/bQj; therefore,  the intensity distribution does not vary in the x
direction  except to decrease in a Gaussian manner.   Figure 2 is a
sketch of  Eq. (3) for the  plane x = 0  (y-z plane).   The fringes extend
parallel to the z axis.   For z = 0 the cosh term is unity for all y, and
the distribution consists  of alternate bright and dark fringes  decreasing
in intensity in a Gaussian manner in the y direction.   Farther out on the
z axis,  beyond the cross-over point  of the beams, the cosh term be-
comes significant before the Gaussian fall off causes the intensity to go
to zero.  One can visualize from Fig.  2 the two beams separating from
each other beyond the cross point.

     A "probe volume" can be defined from Eq.  (3) as that surface where
the Gaussian factor
                  [X
                  ^  o
                            x.  + y cos - + z sin  -
-,)]
has decreased to e~^.  Setting y = z = 0, the point where this surface
               Figure 2. Fringe intensity distribution in y-z plane.
                                  10

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intersects the x axis is found as

                           exp
Similarly,  the y and z axis intersections are

                             y = b0/cos (a/2)

                             z = b0/sin (a/2)

Note that for beam separation angle a small, the probe volume is cigar-
shaped,  extending considerably farther in the z direction than in either
the x or y directions.

    A  photomultiplier tube shown in Fig.  1 is used to detect the light
signal  scattered from a particle which passes through the fringe system.
It is important to note that the collected light intensity, even from a
point particle, may not be proportional to the illuminating intensity in
the probe volume.  This is because light from each beam is scattered
by the  particle in lobes independently of that from the other beam.  The
general case of the light scattered from a single  particle illuminated by
two beams has been reported (Ref.  9) using the relationships  of light
scattered from a spherical particle immersed in a dielectric  medium
scattering plane waves (Ref.  10).  It can be shown that where the two
illuminating beams are polarized in the same direction, there are two
different conditions under which the collected light scattered from a
point particle will in fact be proportional to the light  incident  on the
particle.  These conditions, either of which may be met, are:
     1.   The beam separation angle a is small,  and the light is
         collected from any point in the y-z plane.
     2.   The light is collected paraxially,  i.e., from a point
         near the z axis (regardless of the value  of a).  In the
         following development one of these conditions is assumed
         to be met.
2.2  SINGLE PARTICLE VISIBILITY DETERMINATION

    Suppose a particle whose dimensions are very small compared to
the fringe spacing passes through the probe volume.  The detected light
intensity will then trace out the illuminating intensity Io in the probe
                                  11

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volume.  For example, if a point particle moves along the y axis the
signal,  as viewed on an oscilloscope connected to the PM tube, will
trace out the center waveform depicted in Fig.  2 (similar also to Fig.
3b).   Here the signal alternately builds up as the scatterer crosses a
bright fringe then falls to zero as the scatterer passes through a dark
fringe.   The peak intensity crossing the bright fringes increases as the
particle approaches the center of the fringe set then decreases as the
particle leaves.

     Now suppose the particle is not very small  compared to a fringe
spacing.  The particle cannot be completely hidden in a dark fringe be-
cause its size will partially overlap the two adjoining bright fringes. A
larger particle following the same path as the point particle might  pro-
duce the signal shown in Fig. 3a.  Here the scattered intensity does not
fall  all the way to zero between bright fringes because the particle is
always intercepting some light.  A still larger particle,  overlapping
yet more of the adjoining fringes during its traversal, might produce a
signal similar to that of Fig.  3c.  These figures show that the magnitude
of oscillation of the signal decreases with increase in particle size.  In
fact, for certain particle dimensions comparable to the fringe spacing
the PM tube signal may display only a Gaussian form with no superim-
posed oscillation.  Theoretical analysis verifies this result.

     To show the dependence of the shape of the  signal on size, it is
assumed (Ref. 9) that a simple average of the illuminating intensity
over the cross-sectional area of the particle can be used to find the
mean incident intensity.  That is,  the scattered intensity Is is
assumed to be proportional to (again, with the light  collected paraxially)
                           l*~ T- //{odxdy                        (4)
                               AP Ap

where Ap is the cross-sectional particle area.  Actual measurements
of known particle sizes show good agreement with theory developed
from this assumption,  and it will be used in what follows.

     The integration of Io given by Eq.  (3) over a surface area is not
easily obtained.  However, if certain simplifying assumptions are made,
closed form solutions can be found for the cross-sectional areas of
spheres and cylinders.  Assume the maximum particle dimension is
small compared  to bo.  This allows one to assume that the slowly vary-
ing exponential and cosh terms remain constant over the  scatterer
                                  12

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                                             a. Visibility = 0.47
                                             b.  Visibility = 0.89
                                             c. Visibility = 0.17
Figure 3.  Signal waveforms.
              13

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            surface.  The condition that the dimension D be small compared to bo
            has been shown to be met if (Ref.  11)

                                            «  < 5 b0                            (5a)

                                            D  < 8                              (5b)

            Integration then gives, for the cross section of a sphere,
                                   --^(x2 + y2 cos2 | +  z2 sin2 |)
      f  ,r2    .1  r^jOrD/
      jcosh |-j yz ..„ aj + [-j^-
I  ~ exp
       L  br          -         -'j
                                                   (6)
                                                           .
                                                           cos
            Here x,  y,  and z refer to the coordinates of the center of the spherical
            scatterer,  D is the sphere diameter, and Ji is a first-order Bessel
            function of  the first kind.

                 Equation (6) is an expression for the scattered light collected par-
            axially from a spherical particle of diameter D located  at point x, y, z.
            It shows dependence of the signal shape on the diameter.  If a particle
            follows some trajectory through the fringe set and the signal is dis-
            played on an oscilloscope screen, the result might loo|c like any of those
            included in Fig. 3.  This type of signal will depend on the ratio of the
            particle diameter to the fringe spacing.  Note that there must be some
            component  of velocity in the y direction in order for the oscillating
            cosine term to be displayed.

                 Equation (6) may be considered as the sum of a Gaussian modulated
            cosh function, known as the "pedestal" or "d-c" component, and a
            Gaussian modulated cosine known as the "a-c" component of the signal.
            The ratio of the a-c magnitude to the pedestal is a.measure of how
            "visibile" the a-c component is and is called the "visibility", where
E
                                 ., A a-c magnitude     i_ ••—, - j                   . .
                                       pedestal   =    L /0—    ~v                  * '
                                                  cosh
            when either the plane z = 0 or y = 0, the cosh term is unity and the
            visibility reduces to the numerator of Eq.  (7).  In either of these
            planes, the visibility is then only & function of particle size,
            i.e.,
                                              14

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                      V =
                   2J1(7TD/8)

                    (irD/8)
(y  =  0  or  z = 0)
(8)
     A similar derivation for a cylindrical!;/ shaped particle gives for
the visibility in the y = 0 or z = 0 plane:
                     V =  sine (L/8 sin /S)   sine (D/8 cos /S)
                                                                (9)
where the function sine (u) is defined as sin(7ru)/7ru, L is the length of
the cylinder,  D its diameter,  and /3 is the angle the major axis of the
cylinder makes with the fringe planes.  The major axis is assumed to be
in a plane normal to the fringe planes.

     Under the further assumption that the cylinder diameter D « 6, then
Eq.  (9)  reduces to
                             V ~ sine (L/S sin
                                                               (10)
     The visibility functions,  Eqs.  (8) and (10), are plotted in Fig.  4.
Examination of these equations and the curves of Fig.  4 show that the
     JO
     •H
     a
     o
     •¥>

i.o


0.9


0.8

0.7


0.6


0.5

0.4


0.3

0.2


0.1


  0
                             Spherical Particle
                             of Diameter D
                              Cylindrical Particle of
                              Length L, and Orientation p
                    3Tri.22T4     5     6:
                        irD/6: irL sin(p)/6
                                                    2.23TT
                                                               9     10
  Figure
                4.  Visibility functions near geometric center as a function
                   of D/8 and L sin
                                    15

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visibility has zeros; i.e., for certain particle dimensions, no a-c term
will appear.  In addition,  when the visibility function is less than about
0. 17 for spheres  and about 0.24 for cylinders, different particle sizes
can have the same value of visibility.  In addition, the visibility func-
tion changes sign as it passes through successive zeros.  Negative
visibility means that more light is scattered when the particle is
centered over a dark fringe (and overlapping  adjacent bright fringes)
than when it is centered over a bright fringe (and overlapping adjacent
dark fringes).  There is no way in practice to quickly determine if a
small measured visibility is positive or negative; therefore, only the
absolute value of  the visibility is plotted in Fig.  4.   If the visibility can
be determined within an accuracy of one per cent, Fig. 4 shows that
spherical  particle diameters can be determined  unambiguously over the
size range 0. 1 < D/6 < 1.0

     When  the particle passes through the probe volume the oscilloscope
signal may be photographed,  and the ratio of the ac to the pedestal may
be directly measured from the waveform.  Under the conditions that the
particle was moving in the "y" direction (to display the cosine term) and
that the fringe spacing is small compared to bo (such that a number of
cycles are included in the waveform) the visibility can be obtained using
the Michelson visibility definition (Ref.   12):

                            v _
                                 max   min
where Imax is the intensity of light scattered when the particle is cen-
tered in a bright fringe and Imin is the intensity scattered when the
particle is centered in the adjoining dark fringe.  Obviously, measuring
the fringe visibility using oscilloscope photographs and the above anal-
ysis is time consuming.

     As an alternative method of measuring the visibility,  the a-c com-
ponent may be separated from the lower frequency pedestal by electronic
filtering.  The two components can then be determined separately and
then combined in an analog divider to acquire the visibility.

    Visibility  measurements  should be made when the  particle is
either in the  y = 0  or z  = 0 plane (x-z plane or x-y plane). Particles
will generally be flowing in the "y" direction,  and one possible tech-
nique that can be used to ensure that the particles are near the z = 0
                                  16

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condition  when the measurement is made by optical  aperturing.
As will be shown  in a later section, for a particle moving within a re-
gion near  z  = 0 there is little variation in the visibility.  Optically aper-
turing the system so that particles outside the specified range are not
"seen" by the collection optics would ensure valid visibility measure-
ments.  It may also be possible to electronically aperture the  system,
as discussed in Section 4. 3.

     Consider the  size resolution of visibility measurements in
terms of  classical lens  resolution limits.   If two parallel beams
are separated by  0. 8 lens  diameters before they  are focused to
the probe  volume, the interference fringe  spacing is just equal to the
Rayleigh resolution limit of the lens (Ref.  10).  If the visibility meas-
urements  satisfy the above resolution limits then particle sizes may be
determined  that are approximately ten times  smaller than the  resolu-
tion limit  of the transmitting optics.   Figure  5 indicates :the particle
size range which  can be determined for the above criteria as a function
of the angle between the interfering beams.  The upper curve describes

                         Note:  Upper curve indicates largest
                         unambiguous particle size which can be
                         determined from the visibility.  Lower
                         curve indicates the smallest size which
                         can be determined for the same angle
                         between the illumination beams.  Dashed
                         lines are ranges of equivalent resolution-
                         limit F numbers covered by upper and
                         lower curves.
                   10
                   10J
                I  10'
                0
                o
                t lO'1
                  10'
                   ,-2

V
\


















\
s


















x





















F











K'50

>
1
j


>_
V
F











a
^1










s




s
•£
IT
m










if/
^v



|
?5










.5
F/0.















4




F/0,04
\Y ~1
ticle Si
Lt
ze



















                     0.1       1.0       10        100
                           Angle between Illuminating Beams, deg
                                                         1000
        Figure 5.  Range of the unambiguous determination of particle size as a
                 function of angle between the illumination beams.
                                    17

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the upper size limit, while the lower curve describes the lower size
limit.  The dashed vertical lines indicate the range of f numbers re-
quired for lenses to resolve a particle of the same size.  The largest
possible included angle between  the beams is 180°, which yields a fringe
spacing of X/2.  Thus, the smallest possible size that can be measured
by this technique is X/20.

    In Fig. 5 there is a vertical solid line labeled "probable self-
aligning limit. "  This limit arises because a single lens cannot accu-
rately focus and cross two beams for included  angles greater than ap-
proximately 12°, which corresponds to a transmitting lens f number of
approximately 4.  For angles greater than 12°  an optical arrangement
similar to that shown in Fig. 6 is required.  In this arrangement a lens
is used to focus the beams,  and  mirrors cross the beams at some
predetermined position.  Since the point of intersection is an independ-
ent variable,  with respect to the focusing lens, such systems are not
self-align ing.  Such optical systems are extremely sensitive to vibra-
tion and the precise alignment requirements for the beams to acquire
high quality interference fringes is difficult to  attain.
                           To Signal Processor
                       Dual Scatter
                       Observation Mode
                                                    Local Oscillator
                                                    Observation Mode
                                                             To Signal
                                                             Processor
         Figure 6.  Example of a multi-beam interferometer arrangement and
                 the different observational modes.
                                  18

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    In reviewing the important criteria for the determination of particle
sizes from visibility measurements it  is found that:

    1.   The two illuminating beams should be of the same center-
         line intensity and polarized in the same direction.

    2.   The observations should be made paraxially.

    3.   The particle trajectory should not depart greatly from
         the x-y plane (z = 0).
    4.   The maximum dimension of the particle should be rela-
         tively small compared with the probe volume width in
         order that the low frequency variation of the "pedestal"
         can be neglected when averaging the incident intensity
         over the surface of the particle.
2.3  DETERMINATION OF NUMBER DENSITY FROM VISIBILITY MEASUREMENTS

    The number density of particles, when many particles simultane-
ously occupy the probe volume, can also be determined from visibility
measurements.  The visibility may be written (Ref. 9) as

                                                                 (12)


where pg represents the a-c signal power for a single particle detected
by the collection optics and p^ represents the pedestal, or d-c signal
power for the same  particle,  and the time  average is taken over one
complete cycle of information.  The visibility function as defined by
Eq. (12) is independent of the absolute value of the scattering proper-
ties of the particle and is solely dependent upon relative values.   Thus,
particle sizing by this technique requires only a single measurement,
at a fixed angle,  of the relative scattering  intensity between dark and
bright fringes, and not a pair of measurements at different angles as
would be required by the usual process of determining sizes from
light intensity measurements and the Mie theory.

    Analogous to Eq.  (12), the visibility function for N particles in the
probe volume is defined as


                              „                              (13)
                                  19

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where Pg" and P^ are the respective a-c and d-c signal power collected
for N particles  in the focal volume.   It has been shown (Ref. 13) that
                                                                  (14)

                                                                  (15)

Combining Eqs.  (14), (15), and (12) the following is obtained:

                              YN =  -=                            <16)

where V is the ensemble average one particle visibility function for the
size distribution of N particles.  Thus, from Eq. (16) N can_be deter-
mined experimentally by adjusting the fringe spacing 6 until V is con-
stant, i. e.,  approximately unity for the size distribution.  Under this
condition, "le visibility measurement^ can reflect only the number of
particles contributing to the signal:  Vjg- <* l/-fN  (D « 6)  when a distri-
bution of sizes for the N particles exists then there is,  at present, no
straight-forward procedure to  determine the number of particles as a
function of size from the visibility measurement.  In Fig.  7 the visi-
bility is plotted as a function of the number of detectable particles.
Under the assumption that the visibility can  be  determined with an ac-
curacy of one percent, Fig. 8 shows the limiting number density as a
function of particle size that can be  determined from visibility measure-
ments, under the constraints that D < 6 < 5bo.  Figure 8 was  obtained
under the further condition that the diameter of the probe volume is de-
termined solely by the e~^ intensity contour.


2.4 ERROR ANALYSIS

     In this section a brief analysis is  performed to determine the type
of errors which can be expected in attempting to determine the particle
size from a visibility measurement.  Only errors associated with the
measurement of spherical and  cylindrical particle sizes will be discussed.

2.4.1  Error Analysis for Sphericel Particles

     Following a typical analysis (Ref. 17), the  deviation in the visibility,
AV, is
                                  20

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09

be
e
•H
O
&
    10
    10
      10
        -2

                                   \
1.0
                                 Signal  Visibility
     Figure 7.  Signal visibility as a function of number of observable particles.
                                      21

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10
  10
10
  9
10
10'
  8
I
0)
iH
O

S
&
10
10'
10'
10
1.0
                           \
                              \
                                                             \
                                                                   \
                                                                     \

   1.0                                10
                            Particle Diameter, \jja
   Figure 8.  Maximum observable particle density as a function of particle
             diameter for a visibility of 0.01 and an illuminating wave-
             length of 0.5 Mm-
                                                                            10
                                   22

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Using Eq.  (8) and standard Bessel function identities, Eq,  (17) can be
written as

                    AV = -2J2(^D/5)AD/D + 2J2(77D/S)AS/S                (18)

where 3% is a second-order Bessel function of the first kind.  On solving
Eq. (18) for AD/D,  the error estimate becomes
                                2J2(77-D/S)    5

Thus the standard deviation,  assuming no correlation between AV and
A 6, is
                                                                  (20)
In terms of the experimental parameter,  
                                  23

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                      1.0
2.0
  3.0
D/6
4.0
5.0
       Figure 9.  Uncertainty curve for a spherical particle with size determined
                by a visibility measurement.
Using Eq. (9) under the conditions imposed above gives the following
values for the derivatives:
                                        tsin^)- y]
                                     (23a)


                                     (23b)


                                     (23c)
Solving Eq.  (22) for AL/L by substituting Eqs. (23a), (23b), and (23c)
gives

               AL/L = ^ - A/8 cotjS + AV/[cos (^ sin /s)  - VJ            (24)
The standard deviation follows  immediately as
                 Av^
                                                                      (25)
                                    24

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Equation (25) is plotted in Fig. 10 under the assumptions that Aj3 and
A6 =* 0.  Trends in error propagation are seen that are similar to the
spherical particle uncertainty curve  (Fig. 9).  The most important
point to observe in the spherical particle case is that the least error
possible lies between V ~ 1  and the first zero (Fig. 4).   Thus, not only
does size determination become  ambiguous when the particle size is
greater than 6, but the uncertainty quickly increases.  On the other
hand, the uncertainty curve for the cylinder shows that regions exist
after the first zero which also give as good a minimum error as was
possible for L sin (/3)/6 < 1.
2.5 VISIBILITY FOR NON-PARAXIAL OBSERVATIONS OF PARTICLES WITH
    SIZES MUCH GREATER THAN A WAVELENGTH

    In evaluating the visibility for spheres,  it was tacitly assumed that
the observation of the scattered light would depend on the total flux in-
cident on the particle.  This should be a reasonable assumption as long
as the observations are not biased by reflection and refraction effects
(i.e.,  when the particle sizes are less than 4 to 5 X0) and the observa-
tions  are made paraxially.  However,  when  sizes are greater than 4 to
5 X0,  then effects related to Snell's law (i.e., reflection and refraction)
          10.0
          9.0
          8.0
          7.0
          6.0
           5.0
           4.0
          3.0
           2.0
           1.0
                     1.0      2.0       3.0
                                L sin (p)/5
                                              4.0
                                                       5.0
         Figure 10.  Uncertainty curve for a long narrow cylinder with size
                  determined by a visibility measurement.
                                  25

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can play a significant role in determining observation limits imposed
by the scattered light viewing system.  It has been shown (Ref.  11)
that for large particles observed non-paraxially,  evaluation of Eq. (4)
requires that the limits of integration be changed to include only a por-
tion,  rather than all, of the particle's cross-sectional area.  Figure 11
plots  an example of the visibility calculated for a particle, large com-
pared to X0, for an observation angle 10° off axis.  For comparison, the
paraxial visibility is also plotted as a dashed line.  The figure shows
that for such large particles, observed non-paraxially, the visibility
can give only ambiguous values of particle size.  This complication
can be avoided by  making all observations paraxially.
    •H
    0)
    •H
    O
    CO
Curves Calculated for 10
Illuminating Fringes
                                                Paraxial Observation
                                                10-deg Off Axis
                                                 Observation
                                                           5.0
         Figure 11. Visibility for non-paraxial observation of a large particle
                  compared to illuminating wavelength A0.
                    3.0 EXPERIMENTAL OBSERVATIONS
     In this section the results of an experimental program to determine
the feasibility of dynamic particle  size analysis from the interferomet-
ric visibility techniques are described and discussed.  The  experiments
were conducted on particles in the size range 1. 0 to 120 ^m.  It
                                  26

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was not surprising to find that the large particles required an entirely
different set of experimental observations and methods than  did the
small (less than 4 to 5 Xo in diameter) particles.  Thus, a natural point
of division in discussing the experiments is  in the large and  small par-
ticle observations.
3.1  EXPERIMENTAL EVALUATION
                    \
    A schematic of the optical arrangement for the experiments is
shown in Fig.  12.  Light from a 15-mw He-Ne  laser has its polariza-
tion vector rotated until it is perpendicular to the plane of the beams
defining the probe volume.   Collimating lenses  then cross the beams
and focus them simultaneously.  Two types of beam splitters were used
in these experiments.  The first type is a set of properly coated glass
blocks, shown in the photograph in Fig. 13,  which produce two beams
that (1) traverse equal path lengths, (2) are  of equal intensity,  and (3)
have centerlines parallel within a  tolerance  of a few arc-seconds (Ref.
15).  The second type of beam splitter  is a two-dimensional, ultrasonic
modulator operated in  a traveling  wave Bragg mode (Refs. 5 and  16).
This device can produce four  equally intense frequency shifted beams
(the frequency shifts are identical to the modulator frequency).  If both
acoustic modulators are referenced to  a common oscillator, stationary
interference fringes can be generated in the probe volume by two of the
beams.  When the modulators are referenced to two different oscillators,
the interference fringes move at a rate which is the difference frequency
between the two oscillators.   Such a device gives the capability of po-
sitioning stationary particles  in the probe volume and moving the fringes
past the particle.   This is most desirable when the particles are small
(<5A0) and not easily located.  A schematic  of a two-dimensional  Bragg
cell (TDBC) particle-observation system is  shown in Fig.  14.
                                          Variable Lense Aperture
       Collimating
       Lenses
                        Beam    Probe Volume
                        Splitter
^Polarization
 Rotator
                                                           Removable
                                                           Detector
nr—>-,
          Detector
          Aperture
      Scattered Light
      Collection Lenses
             Figure 12. Schematic of the optical arrangement for the
                      experimental observations.
                                  27

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      Figure 13.  Photograph of path compensating beam splitting blocks.
To Electronics
                         Input Polarization Vector
                                     Two-Dimensional
                                     Bragg Cell
                                                             Direction of
                                                             Measured Velocity
                                                             Components
                                                            Probe Volume
                                   •Scattered Light
                                    Collection Optics
    Figure 14.  Schematic of the two-dimensional  Bragg cell arrangement.
                                     28

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    After the beams are split,  a set of lenses positions the probe vol-
ume to the desired observation region.  The scattered light collection
optics are  designed and  mounted such that almost any desired set-of
observation angles can be obtained while observing the  same  portion of
the probe volume.  When the collection aperture  is fully open, an f/5
solid  collection angle is  subtended.   A variable aperture is also  placed
in front of  the detector to control stray light and  to determine the size
of the observable probe  volume. The beam stops and detector are re-
movable in order to allow visual observation of the interference  fringes
by paraxial projection through the scattered light collection telescope.
Figure 15 shows a  photograph  of the  overall optical system.

    The large spherical particles used in these experiments  were glass
and aluminum spheres.  Tungsten wires of varying lengths having a diam-
eter of 11.6 Mm were also used in the experiments. To  control the posi-
tion of the  particle as it  traversed the  probe volume,  a  traverse  system
was used which had a positional accuracy of ±1. 0  urn  along the z  axis and
±5.0 Mm along the y axis.  The spheres were mounted by electrostatic
                                                            A E D c
                                                            5170-72
              Figure 15.  Photograph of the overall optical system.
                                 29

-------
attraction (van der Waals forces) on coated optical flats.  The flats were
then mounted vertically with micropositioners on the traverse system.
The particles  were visually positioned as desired in the probe volume
by observing the projected image either through the scattered light col-
lection telescope or through a microscope with a calibrated reticle.
Thus, fringe spacing and particle diameters could be  measured directly
for comparison against the visibility measurements.  The y axis portion
of the traverse could be released from the mechanical crank drive and
pushed by hand smoothly on ball bearing rollers. Hence,  particle tra-
jectory relative to the geometric center could be precisely controlled.
Presumably, the velocity of the particle could be assumed constant dur-
ing the short time interval the particle was in the probe volume.  The
11.6-jum wire was mounted in a  similar fashion, except no glass plate
was used (the  wire was stretched across an aperture).  A micro-
positioner could vary the angular orientation  of the wire (0) about the z
axis with an angular precision of ±30.0 arc-seconds.  The wire served
two purposes in these experiments. First, for a large fringe spacing
and j3 = 0, the wire served as an integrating probe (in the  sense that the
wire averaged the entire light distribution along the major axis of the
interference fringe) through which +he illuminating intensity distribution
could be studied.  Secondly,  by suitably imaging the fringes at the de-
tector, various orientations of the wire  provided straightforward ex-
perimental verification of Eq. (9).   The particle-holding jig and tra-
verse system  are shown in the photograph in  Fig.  16.

    Scattered light signals detected with a photomultiplier tube were
filtered and amplified with a variable bandpass differential amplifier
and were recorded on a  storage oscilloscope.   From the oscilloscope,
the signals were photographed for measurement analysis using Eq. (11).

    For stationary particles with interference fringes moving past them,
a continuous wave signal of constant amplitude was generated.  Thus,
the a-c signal values could be measured directly with an RMS voltmeter
while the d-c level of the signal could be measured either with an  elec-
trometer or with the oscilloscope set for a zero width frequency band-
pass.  With this arrangement an average over many cycles of informa-
tion could be obtained for one particle position in a short time interval.
3.2  LARGE PARTICLE ERROR ANALYSIS

    The accuracy of this technique in determining particle sizes de-
pends in large measure on how well the interference fringe spacing is
                                 30

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                                                   A E D C
                                                   5173-72
         Figure 16. Photograph of the particle holder and traverse system.
known.  For these experiments, the fringe spacing was measured by
two independent techniques.   In the first method, the fringe spacing was
determined by measurements of an image projected through a micro-
scope which also projected the  image of a calibrated reticle.  Compari-
son of the reticle  period with the interference fringe period provided a
measure of the fringe spacing.   In the second technique,  use is made of
the fact that the fringe spacing,  6, for a « 1, can be written as
                               8 =< A0'a
(26)
                                  31

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a in these experiments was typically between 0. 5 to 3. 0° and could be
measured with an uncertainty of about ±2 percent.  Xo is known to at
least six significant figures.   Thus, fringe spacing could be measured
by this technique with an uncertainty of ±2 percent.  Generally, the two
separate determinations of the fringe spacing agreed within ±3 percent,
which was considered sufficient for these experiments.

     The largest source of error in the experiments was in the analysis
of the photographs.  Since the oscilloscope traces were measurably
wide  relative to the magnitude of the signal, some uncertainty in the
values of the signal was automatically introduced.  The amount of data
to be reduced was  voluminous, and therefore the data reduction system
shown in Fig.  17 was used to analyze the photographs and  to perform
various  manipulations with the recorded data.  X-Y positions of points
                     X-Y Recorder
                     E
      Voltage Divider
      Position'Box
                             Digital
                             Volt-
                             meter
                                                o o
                                         • 2
Analog
Scanner
                                 HP 2100A
                                 Computer
                                 Teletype
     Paper
    Tape Punch
               Figure 17.  Schematic of the data reduction system.
                                  32

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on the photographs were proportional to a particular voltage as deter-
mined by the X-Y recorder and a voltage divider box.  The  value of the
voltage for a particular measurement point was read by a digital volt-
meter and the value stored in the computer, memory for recording on
punched paper tape.  Additional uncertainty was, therefore, introduced
into the measurement by any uncertainty in the voltage measurement.
Furthermore, error enters into the measurement due to slight dis-
tortions introduced into the image in the photographic process.  In
order to determine the magnitude of the uncertainty in these measure-
ments, the data reduction  system was used to scan a photograph of the
grid face present on the oscilloscope.  The result showed that the mea-
sured visibility was uncertain by ±3 percent.
3.3  EXPERIMENTAL RESULTS OF LARGE PARTICLE OBSERVATIONS

    The geometric center of the probe volume and the relative illumi-
nating intensity distribution are fundamental parameters which must be
known if accurate particle sizes  are to be obtained from visibility meas-
urements.  Knowledge of the spatial position of the geometric center is
required if accurate fringe spacing measurements are to be made from
the measurement of angles technique.  Equation (3)  and subsequent analy-
sis show that contrast variations in the illuminating intensity distribu-
tion can be expected as the distance from the geometric center increases.
Furthermore,  Eq.  (3) is for an ideal focusing condition; thus,  some de-
viation from the ideal focus case might be expected for the lenses used
in the  experiment.  The mounted wire discussed previously was used to
probe the intensity distribution for a fringe set  with a spatial period
much greater that the wire diameter.  The observed signal scattered
from the probe represented an average intensity along the major axis
of the fringe.   Since the intensity distribution is Gaussian along the
major fringe axis,  the averaged  intensity distribution was representa-
tive of the y-z plane intensity distribution.  Figure  18  contains a theo-
retical plot (x = 0,  6.=* A/a) of the y-z plane intensity distribution for
different values of z where z is written in terms of a dimensionless
depth of field parameter (Ref.  8) m:
                            m = zsin(a/2)/bo                       (27)
(Thus m = 1.0 where the edge of the defined probe volume crosses the
x axis.)  The corresponding experimental scans with the small wire are
also shown for qualitative comparison.  To keep the diagram from being
too cluttered,  theoretical plots are shown for six cycles of information
                                 33

-------
                                                  -0.2
                                                1/e Intensity
                                                Modulation Contour
                            m -0.8^-1/e^ Intensity Modulation Contour
                     m • 1.0
           Figure 18.  Experimental and theoretical illuminating intensity
                     distribution in the probe volume.
               e\
between the e~" relative intensity points along the y axis passing through
the geometric center.   The experimental scans are for approximately
ten cycles of  information;  quantitative comparison in this case is  cir-
cuitous.  However, when a comparison is made with identical numbers
of interference fringes in both theory and experiment,  calculated  and
measured visibility for random checks  of different fringe points agree
within a few percent.  The observed fringe visibility at m = 0 is about
0. 95.  This is attributable to an intensity mismatch of the illuminating
beams.  This mismatch was not attributable to the beam splitter but
rather to the  complex  phase variations  introduced into the beams  by
the transmitting lenses.  This effect is also reflected in the slight
skewness of the Gaussian envelopes and in the apparent phase changes
of the fringe position as m varies.  These effects could be controlled
through the use of diffraction limited lenses  or carefully controlling
the orientation of lenses of inferior quality relative to  the incident
beams.

                                  34

-------
     An experiment was performed to determine the validity of Eq.  (9).
A  slit aperture placed in front of the signal detector was oriented normal
to the projected image of the interference fringes.  The fringe spacing
was chosen to be 109 yum.  The width of the slit was set to 500 /urn.
Hence, as the wire was rotated through the angle /3, a very narrow
cylinder of length L and orientation ]3,  was observed.  L was related to
the magnified width of the slit w" and orientation angle through the re-
lationship
      L = wYcos(/3)
                                                                      (28)
Substitution of Eq. (28) into Eq.  (9)  shows that the visibility is then
given by (paraxial or small angle approximation)
                     V =
sin [TTW' tan (/3)/5] sin [nD cos (/3)/S]
   [ffw'tan (|8)/S][77D cos (/3)/S]
(29)
Figure 19 contains a graph of Eq.  (29) as a solid line between one and
the first zero in V for the parametric values of w1, D,  6, and |3.
                   l.Oi
                  0.9
                  0.8
                  0.7
                  0.6
                S 0.5
                  0.4
                  0.3
                  0.2
                  0.1
             D irv'/S - 1.067
             O irw'/6 - 4.85
             A irw'/6 - 3.77
             Note: Dashed Curve Is
             Theoretical Correction
            .for Diameter of the
             Cylinder
                             1.0       2.0
                                 irw' tan (p)/6
                                               3.0
                                                        4.0
        Figure 19. Experimental and theoretical comparison for a long narrow
                 cylinder at different orientation angles
                                    35

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Experimental points are indicated with circles,  squares, and triangles
for three values of 7rw'/6.  As can be seen in Fig. 19, reasonable agree-
ment exists between theory and experiment.  The primary cause of the
deviation from theory are uncontrollable variables in this particular
observation technique. The measurements were carried beyond the
first zero in V.  However, systematic error was found to be compar-
able to the measured visibility.  Therefore, these results  are not in-
cluded for any valid comparison with theory.

    Observations of large, single spherical particles have also been
made.  For particle sizes greater than 90 /um,  spheres of  aluminum
and glass  were examined.  When the diameter was less than 90 /urn,
only glass  spheres were available.  Observations for different solid
collection angles were made to determine any visibility dependence in
terms of observation angle resolution.  Front scatter measurements
were made for different angles of observation with respect to.the bi-
sector between the beams in order to determine visibility dependence
on these parameters.  Signals attributable to different trajectories of
the particle traveling  in the y-z plane and normal to the z axis were
also observed  in order to determine practical depths of field for those
observations.

     Figures 20 through 22 summarize the  results.   The solid curve in
Fig. 20 indicates the theoretical visibility  for a particle at the geometric
center of the probe volume.  Data points for both glass and aluminum
spheres are plotted as circles and squares, respectively.  The  data
show that reasonable agreement  with theory is obtained for both types
of particles when D/6  is less than or approximately equal to unity.
Large deviations are observed when the particle diameter  is compar-
able to the diameter of the probe volume, even when D/6 is about the
right magnitude (note  the data  points inside the dashed square).  This
should be expected on the basis of the assumptions expressed by Eq.
(5).  Some deviation can also be  attributed to reflection and refraction
biasing the signal and contributing significantly to the signal when the
particle is not fully illuminated.   Some systematic error is also appar-
ent for D ^ 0.5 6 and is believed to be attributable to calibration errors
in measuring particle size for comparison with the visibility measure-
ments.

     Figure 21  shows how the average visibility varies as a function of
the depth of field.  It shows that  there is little variation in visibility
when the particle size is  of the order of a fringe spacing and the tra-
jectory is within m = ±0.2 (Eq.  (27).  This is consistent with numerical
                                 36

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      1.0
                                   D oi b  for These Data
                                              O Glass Sphere
                                              D Aluminum Sphere
      10
                                                       5.0
                                                                 6.0
          Figure 20. Comparison of theoretical and experimental paraxial
                   visibility for a spherical particle.

evaluations of Eq.  (4).  Also plotted in Fig. 21 is the average visibility
for a point particle passing through ten interference fringes.  It is seen
that the m = ±0.2 criterion defines  a relatively error-free region in both
cases (for experimentally large particles and for a theoretical point
particle) wherein size can be determined from Eq.  (8) or Eq. (9).

     Figure 22 indicates the results of making observations for  different
solid collection angles to determine any visibility dependence.  The plots
show the visibility independent of solid collection angle over more than
three decades of variation.

     To test the validity of Eq.  (16) which predicts the variation in the
visibility as a function of number of illuminated particles, the following
experiments were performed.  The interference fringes were adjusted
for 120-jum separation distance.  Glass  spheres 10 to  15 /urn in  diameter
were randomly spread over the glass plate formerly used to hold the
single large particles.  The glass plate was then mounted vertically on
the holding jig such that it could be moved through any probe volume
position.  The TDBC was  first arranged to provide moving interference
fringes.   The glass plate was randomly  searched for .regions where the
scattered light intensity was high or relatively low, which indicated high
or low concentrations of particles.
                                  37

-------
1.0
0.01
                           Theoretical Decrease in Average
                           Visibility for a  Point Particle
                         O  D/6 =  5.86 Aluminum Sphere
                         d  D/6 =  5.61 Glass Sphere
                         A  D/6 =  2.36 Glass Sphere
            0.2     0.4     0.6     0.8    1.0     1.2
                 Probe Volume Depth of Field,  m
1.4
       Figure 21. Average signal visibility as a function of particle
                trajectory for different D/6.
                              38

-------
    1.0
    0.1
•H
.0
•H
09
•H
    0.01

    1.0
>»
•p
2   o.i
f^
XI
•H
CO
•H
>
    0.01
1(













*

J































































All
D
0
^m^m




T
1
— ,
y













_,



pr ±
11 J~




r ^


»



p
j




uininuin Spheres
D/6 = 5.86
D/6 = 2.46
— Average Visibili



^
.



ty
r4 io~3 io~z









































































Glass
D D/
















I i
15

T





X
— §


Spheres
'6 = 5.61
5




O D/6 = 2.36
— Average Visibility



























10"




















        10
          -4
    10 •*                10 '
Solid Collection Angle,
10
  -1
    Figure 22. Variation of visibility for different D/6 and solid collection angle.
                                     39

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    Once a particular plate position was selected,  an image videcon
tube was mounted in the position formerly held by the PM tube in the
light collection system.  The scattered light collection system was used
to image the particles illuminated on the glass plate onto the image vide-
con tube which in turn displayed the image on a TV monitor.  Thus, the
number of particles being illuminated and their relative positions could
be determined either by visually counting the particle images or by using
an electronic  computer system which was available.  The computer and
associated electronics could be set to automatically count the number of
images having an intensity level greater than a preset value.  The num-
ber of images as determined by the computer was then displayed on the
TV monitor along with the  images observed by the videcon tube.  The
computer system also caused the TV display to indicate which images
had been counted in order to allow the preset image intensity to be con-
sistent with the  experimental requirements (in this case, those images
which  could be observed to exist within the probe volume cross section
of illumination).

    The TV monitor image was photographed as was the computer-
measured image.  The image videcon tube was then removed and a PM
tube put in its place.  Only the scattered light was allowed to enter the
PM tube.  The particle positions and optical system were otherwise
undisturbed from that observed with the image videcon tube.  The
scattered light signal from the interference fringes moving past the
particle array observed with the image videcon was displayed on an
oscilloscope and photographed.  Ten different particle  arrays were ob-
served in this fashion.  Figure 23 presents the photographs obtained
from these observations.   Each row represents a single set of obser-
vations.   The  photographs are (reading left to right) the TV monitor
image of the array,  the computer-counted image of the array,  and the
scattered light signal.  To the left and right of the photographs is the
computer-counted number of particles and the number  determined from
the visibility measurement.  Agreement is seen to exist between the
values determined from the two separate measurements in only a few
cases.  Variations between the two are to be expected on the basis of
size variations in the number of particles observed at any one time.

    In order to  examine the changes  in the visibility as the number of
particles in the probe volume kinematically changes, the following ex-
periments were performed.  Diametrical scans of about 6 cm in length
were made across the face of the glass plate containing the glass parti-
cles.   The scans were always across the same diameter and were made
for stationary interference fringes of the same period as in the previous
                                 40

-------
multiple particle experiments.  Thus, as the plate,  which contained
varying numbers of particles  across  the  scanned  diameter,  traveled
through the cross section of the probe volume, the kinematic  evolution
of the signal attributable to varying numbers of particles could be
                 Photographs of Image                    No.  of Particles
 No.  of  Computer  Videcon and Particle   Interferometer        from the
 Counted Images   Image Computer Display      Signal     Visibility Measurement
       128 ±  25
        88 ±  18
        86  ±  17
        85 ±  17
        73  ±  15
        72 ±  14
        65 ±  13
        62 ±  12
        58 ± 12
        49 ± 10
                                           •••»•-••
                                           • •••••••
••••••tfMd
 !•••••••••
 •••••••d
                              r-^^M       fJI"
                                                     46 ± 20
                                                    308 ± 148
                                                     43 ± 20
          Signal Too
          Erratic for
          Measurement
                                                     112 ± 56
                                                     191 ± 83
          ,,n  .  _4
           5  *
     Figure 23. Comparison of number density measurements by image computer
              with those made by an interferometer.
                                    41

-------
observed.  Since the signal lasted about twice as long as the sweep time
of the oscilloscope, two oscilloscopes triggered in sequence were used
to record the signal.  The respective signals were then photographed
and then matched in sequence to provide a complete time history of the
particle scan.  To determine the number of particles in the probe vol-
ume,  for a comparison with instantaneous visibility measurements,  the
PM tube was replaced with the  image videcon tube and the entire parti-
cle distribution across the plate diameter photographed and number of
images sampled and counted  by the computer.   Figure 24 is an example
of ;he observed scattered light  signal as determined by the oscilloscope
recordings.  The scattered light  signal was observed for different light
collection solid angles and for  different angles of observation in the y-z
plane.  The results revealed the  following:
     1.   The visibility for N  particles is not a function of solid
         collection angle.
     2.   The visibility for N  particles is a function of observa-
         tion angle when the particles are large; the dependence
         seems to be a reflection mechanism that is similar to
         that observed for single large particles.
     3.   Number density can be determined for size distributions
         when the distribution is  sufficiently narrow (this suffici-
         ency condition has not been determined analytically).
     4.   There appear to be phase reversals in the signal for
         certain spatial combinations and numbers of particles.
         The conditions for the reversal to occur have not been
         determined.
   o
   •a
   3
                                 Time
      Figure 24. Photograph of interferometer signal versus time as the number
               of particles passing through the probe volume changes.
                                  42

-------
The results from the experiments show (at least for particle sizes
greater than about 10 Mm) that with additional development the number
density can be determined from visibility measurements.
3.4  EXPERIMENTAL RESULTS OF SMALL PARTICLE OBSERVATIONS


    Experiments involving small particles (diameters less than about
2 Mm for visible light) required several different approaches than those
involved in the large particle observations.   The transition from self-
aligning to non-self-aligning optical systems must be made in order to
obtain small fringe periods.  The result is an optical system which is
subject  to alignment errors and is vibration sensitive.  When non-self-
aligning systems are used, the interference fringe period can no longer
be measured with a microscope projection system.  The fringe period
must then be determined from a measurement of the included angle
between the beams.  The most difficult practical limitations to such
experiments,  however,  were in (1)  the generation of consistent par-
ticle sizes,  (2)  the realization of a well controlled trajectory, and
(3)  the  use  of some other method to measure the particle size for
comparison with the visibility measurement.  Therefore, by compar-
ison with the large particle measurements,  those of the small particles
were crude  and the associated errors disproportionately large.


    The non-self-aligning optical arrangement shown in Fig. 25 was
used to  examine particle sizes less than 2 Mm.  Lenses LI and L2
focus the two beams and mirrors MI and MS simultaneously cross  the
beams.   The probe volume location is  determined by the beam splitter
and mirrors MI, M2, and MS. The scattered light is detected par-
axLally by lens LS and the photometer system.  Since the system is
non-self-aligning, the quality  of the interference fringes depended on
manual  adjustments of MI and M2.   Such adjustments did not present
any undue difficulty.


    Two approaches  were taken to resolve the particle  control
problem.  Polystyrene  latex spheres  of less than 2.0-Mm  diam-
eter,  manufactured  by  the  Dow Chemical Corporation, were
used.  These particles are sized  with  an electron microscope and
were  specified to have a standard deviation  of 0. 0027 Mm  and
were  specified spherical.   They were measured by the. interfer-
ometer  in a water solution.  The  water base for the particles
                                 43

-------
                                          Probe Volume
                                                         Photometer
                                                         Signal
        Figure 25. Experimental arrangement for small particle observation.
was initially filtered to remove all extraneous particles with sizes
•greater than the 0.2 yum.  The second approach involved statistical infer-
ence and has much less control than the latex sphere experiments.  In
this approach,  particles present in laboratory air were examined.  A
large circular  window was cleaned and placed on  edge in the proximity
of the probe volume for seven days.  At the end of this period the win-
dow was examined with a 400X microscope. The overwhelming number
of observable dust particles collected on the window were either spheres
or "fat" cylinders of aspect ratio (length/diameter) 2:1 and approximately
2.5 Mm in diameter.  Particles larger than 2.5 jum were generally found
to be highly irregular in shape, although shapes tended to cylindrical
symmetry with aspect ratios varying between 1.5 to. 4.   Large numbers
of particles present in the laboratory air were examined with the inter-
ferometer and  the visibility and signal magnitude recorded;   These
measurements were then compared with the microscope observations.

    Two different fringe period settings were used in these experiments.
The fringe periods for the particle measurements in air were 3.5 nm
and 1.22 /urn.  Probe volumes in air were computed to be 2.75 x 10"^ cc
and 9.63 x 10~6 cc, respectively. In water, these values are reduced
by a factor of 2. 35 due to the index'of refraction. Approximately 100
interference fringes for the large probe volume and 200 for the small
one were  observed.

    Measurements of the latex spheres in the water suspension were
difficult because of index of refraction variations and low frequency
                                 44

-------
vibrations.  Visibility measurements gave an indication of particle
diameters between 0. 50 jum and 0. 65 jum.  However, the data were of
insufficient quality to be valid.


    The number of   particle signals from laboratory air per unit
time  as a function  of signal amplitude  was determined.  Under the
assumption that the signal amplitude is proportional to the cross-
sectional area  of the particles,  an estimate of the relative particle
size distribution can be obtained.   A plot of the  normalized number
density versus  relative  size (relative to the smallest size observed)
based on the above assumption is  given in Fig. 26.   For example, from
Fig. 26,  1. 0 particle per  second was observed with  a  diameter in
the range  from 1.00 to 1.22.  For a given amplitude range,  ap-
proximately ten signals were observed and signal visibility measured.
                 1.0 r4
               1
               • o.i
                 0.01
                   1.0
                             3.0        3.0
                             Relative Particle Dlauter
                                                 4.0
        Figure 26.  Relative particle size distribution of laboratory particles.
                                  45

-------
Fringe spacing 6 was 3. 4 Mm.  Histograms of number versus visibility
for these observations are shown in Pig.  27.  Without knowing particle
shape,  little quantitative information about particle size can be verified
from the histograms.  For the larger particles (as determined from
the signal amplitudes), the large variations in the visibility suggest
irregularly shaped particles.  If the smallest particles are spheres,
the size range described (visibility between 0.2 and 0. 5) lies between
2.4 Mm and 3.4 Mm which is  in good agreement with the microscope
observations of the window-collected dust particles.
                            3.46 - 3.87*
                                                    3.16 - 3.46
           I
           a
           •H

           •O
           e
           o
           e
           a.
           e
           •H
           8
           1-1


           I
           44
           O
           o
4
3
2
1
5
4
3
2
1
5
4
3
2
1
5
4
3
2
1
C
MMM







2.44 - 2.82
-
-
1 	 1
1




1.73 - :
- I— 1
-
-



MHH



n


— 1

1.0



1.22 - 1.41
-
-
I 	
'





MMH





1 0.2 0.4 0.6
Signal Visibility




1 •
0.8








iii i iii
2.0 - 2.44






n n




1




i
0








~i
iii ii
1.41 - 1.73







MMM


n
1 1 1 1
1.0 - 1.22
MMH













n
0.2 0.4 0.6 0.8
Signal Visibility
                    *Note:  Nuabers in upper right-hand corners correspond
                          to relative particle size diameter.

          Figure 27. Particle visibility histogram for laboratory air particles.
                                   46

-------
                  4.0 ELECTRONIC INSTRUMENTATION
4.1  GENERAL

    A primary result of this research is the graphic demonstration of
the need for an electronic device which can automatically determine the
visibility from the input signal.  Without the  development of such an in-
strument, the utility of this method of particle size analysis is greatly
limited.  Therefore, preliminary work was initiated to determine design
concepts which would be most appropriate for the scattered light  signals.
Two design approaches have been taken.  The first separately measures
the peak values reached by the a-c component and the pedestal;  the ratio
of these two peak values is then taken to form the visibility.   The second
approach continuously measures both the a-c and pedestal magnitudes
and ratios these values, providing a continuous visibility measurement
over the signal waveform.
4.2  VISIBILITY FROM PEAK VALUES

    Peak values separately reached by the a-c and pedestal components
may be used to measure the visibility.  This assumes optical aperturing
is used so that the light collection optics see only particles whose tra-
jectories  lie close to the x-y (z = 0) plane which passes through the cen-
ter of the probe volume.  In this region,  visibility remains fairly con-
stant and  is a  function of particle size alone.  The ac and pedestal rise
and peak at  the same time, and signal waveforms look like those shown
in Fig. 3.  In  this method, filters are used to separate the ac from the
pedestal as  shown in Fig. 28.  Peak detectors are used to measure the
peak values reached.  The a-c peak is then divided by the pedestal peak
.WlA/Wvu

PH
Tube




-rf* A A A A .
High
Pass
Filter

Low
Pass
Filter



Peak
Detector

Peak
Detector


•viv v w vuv-
~l
1 	
1 —
J1
Divider




A-D
Converter

                                                         i Visibility
        Figure 28. Electronics for visibility measurement from peak values.
                                 47

-------
in an analog divider to form the visibility.  The visibility is converted
to digital form for storage until it is ready for output.  The method of
using peak values has some inherent disadvantages as follows:
     1.
     2.
     3.
Optical aperturing must be used but is difficult to
achieve.
There is no way to know if a noise spike raises a peak
value, giving an erroneous visibility.
Frequency response of peak  detectors has been found
to be limited to about 5  MHz.  If higher frequencies
are to be used, frequency down-conversion must be
used prior to the detector, which introduces additional
non-linearities and extraneous signals to be dealt with.
4.3 CONTINUOUS MEASUREMENT OF SIGNAL VISIBILITY

     Because of the disadvantages encountered in the first method de-
scribed above,  a second method is now being developed.   This approach
is designed to take advantage of the fact that the visibility remains
fairly constant in the region of the x-y plane, where it is desired to
measure the visibility.   In this  method, shown in  Fig.  29,  the a-c and
pedestal components are again  separated by filters.  An envelope de-
tector is used in the a-c channel to extract the envelope of the ac, i.e.,
a signal proportional everywhere to the magnitude of the ac.   The a-c
magnitude is divided by the pedestal in an analog divider,  and the visi-
bility is continuously output from the divider throughout the particle's
                                            Commands to Begin
                                            and End Comparison
                                               i    j


1"
Tube



n*









High
Pass
Filter

Low
Filter

Envelope
- Detector "I
Divider
r
1
^\



Track-
hold
1
J

1


Comparison
Circuit

A-D
Converter
                                                        Signal to Accept
                                                        >or Reject
                                                        Measurement
                                                        jVisibility
                                       Command to Hold
                                       and Convert When
                                       Pedestal Peaks
          Figure 29.  Electronics for continuous measurement of visibility.
                                   48

-------
traversal of the probe volume.  At some point on the trajectory (e.g.,
when the pedestal reaches a peak) the visibility  is recorded by a track/
hold module (sample/hold) and converted to digital form.  This re-
corded value is then compared with the visibility subsequently output
from the divider as the particle proceeds along  its trajectory.  Com-
parison is continued for a period  of time,  e.g.,  until the pedestal has
fallen to some preselected value.


    If the visibility does not vary more than some preselected amount
while the comparison is being made, the particle probably passed
sufficiently close to the  x-y plane for the visibility measured  to be
valid.   If the visibility varies more than the amount selected, either
noise perturbed the signal or the particle passed top far from center,
and the measured values are rejected.  Aperturing is thus achieved
electronically and noise-perturbed signals are rejected.  Further,
the envelope detector has a higher frequency response than the peak
detector and frequency down-conversion is not necessary.

    The electronic instrument for visibility measurement is  still under
development, and extensive testing will be required to confirm the best
method to be used.
                    5.0 SUMMARY AND CONCLUSIONS
     The results of the research described in this report are best sum-
marized in terms of parameters which were examined during the course
of the analytical and experimental work.
5.1  PASSAGE ANGLES OF THE PARTICLE THROUGH THE INTERFERENCE FRINGES

     In order to use the expressions for the visibility developed in this
report, it is necessary that the visibility be measured in a specified
region sufficiently near the plane z = 0 (x-y plane);  this  plane passes
through the center of the probe volume.  Optical aperturing may be
used to detect only light that originates near the x-y plane, or  alter-
natively, as described in Section 4.3,  electronics may be used to se-
lect only signals originating in this region.  There is no other  limita-
tion on the particle's trajectory except that for systems  without moving
fringes the particle must move across the fringes in order for the  sig-
nal to be adequately displayed on the pedestal waveform.
                                 49

-------
5.2 RELATIVE BEAM INTENSITIES USED TO FORM THE INTERFERENCE FRINGES

    The condition for least possible error in a visibility measurement
occurs when the beam intensities are equal.  However, it may be shown
that for observations that satisfy Eqs. (5a and b) and for paraxial ob-
servations,  the beams may be mismatched in intensity by 30 percent
and still produce visibility errors of 1 percent or less.
5.3 RELATIVE COHERENCE OF THE BEAMS

    With currently available lasers and path-matched beam splitting
techniques this parameter does not appear to present any significant
problem.
5.4  PHOTON-LIMITED SIGNALS

     Photon-limited signals will occur when insufficient light is scat-
tered to the detector.  This condition exists when the signal-to-noise
ratio becomes less than a specified value which is determined by ac-
ceptable error limitations  in the measurement process.   Generally
speaking, photon limited signals can be minimized by carefully de-
signing the interferometer system.
5.5 RADIATION PRESSURE EFFECTS ON VERY SMALL PARTICLES

    Gaussian laser beams may be used to contain small particles and
to levitate them through a true radiation pressure phenomenon. Such
effects have been demonstrated on nearly stationary spheres.  How-
ever, for moving particles, a momentum calculation will show that a
0. 1-jum-diam particle moving 1 cm/sec,  illuminated by a 1-mw beam
100 Mm in diameter, will be deviated off a straight trajectory normal
to the beam by less than 0. 3°.  Therefore, the probability of the laser
beam measurably affecting the particles would appear to be exceptionally
small.
5.6 LIGHT ABSORPTION BY THE PARTICLES

    These phenomena can be fitted into the general category of particle
index of refraction effects.   For paraxial observations these effects
                                 50

-------
 have been shown to be negligible,  both analytically and experimentally.
 When the particle is highly absorbing and large, then reflection effects
 discussed elsewhere can radically change the value of the visibility ob-
 served nonparaxially and, therefore, the particle size cannot be deter-
 mined from the visibility without additional information such as a signal
 magnitude.
 5.7  INDEX OF REFRACTION OF MEDIUM SURROUNDING THE PARTICLES

     The index of refraction of the medium affects the position of the
 probe volume and the value of the fringe period.  Equation (1) indi-
 cates that as the index of refraction varies, the value of the fringe
 period changes.  Index of refraction values for gases are unity out to
 four or five decimal places so that the magnitude of the change over a
 short path is usually insignificant.  However, changes in index of re-
 fraction also affect the relative phases of the wavefronts in the probe
 volume-and thereby shift the spatial position of the interference fringes
 while leaving the value of the fringe period unchanged. Thus, attempts
 to associate phase of the signal with particle size appears impractical
 since the visibility can produce ambiguous values of D/6.

     A vast body of literature exists on the effects of a medium with
 random  inhomogeneities in the density (which is  related directly to the
 index of refraction for dielectric media) on electromagnetic wave propa-
 gation.  This literature shows that when the light must propagate through
 a highly turbulent medium the above effects plus scintillation of the in-
 tensity and beam wander occur.   These effects diminish with increasing
 optical wavelengths.  Furthermore, these effects occur as time average
jphenomena over time scales which are long compared to the times
 usually associated with a visibility and velocity measurement.  Investi-
 gators have shown that in these cases good quality data can be taken.
 However,  the circumstances under which .the data will be limited for
 essentially instantaneous measurements is not known.  Considerable
 further study is required in this area.
 5.8 LIMITING PARTICLE SIZE (MAXIMUM AND MINIMUM)

     This parameter is a function of the shape of the particle,  and only
 spherical particles will be considered.  Extension to other shapes re-
 quires additional analysis along similar lines.   For a constant fringe
 spacing,  6, the particle size limit determined by an accuracy limit of
                                  51

-------
±1 percent places a lower size limit of 0. 1 6 on the particle diameter
while the upper limit is restricted by the fact that small values of the
visibility can be associated with many values of D/6.  The anomaly is
removed by restricting the upper particle size to be less than or equal
to one fringe period.   With these restrictions,  the theoretical lower
limit in particle size measurement is about 0. 05 wavelengths of the
illuminating laser line.  The upper size limit is dictated by practical
limitations,  such as beam splitting techniques, to about a millimeter.
A further size restriction is placed by the optical system.  If the opti-
cal system must be self-aligning,  then a lower limit on particle size
determination is about 0. 5 wavelengths of the illumination.

     Extreme difficulties were encountered when attempting to make
visibility measurements of particles whose  sizes were below 5. 0 jum
(see Section  3.4).  Additional refinements in the control of the experi-
ments are required.   Nevertheless, it has been established that parti-
cle sizes on  the order of 0. 5 A*m can be measured utilizing this tech-
nique.  Unfortunately, time did not permit further experiments to be
performed to substantiate the lower limit (0. 05 XQ).  Additional work
is required to determine the threshold of particle size  detection,
particularly  under dynamic operating conditions.
5.9 PARTICLE SHAPE EFFECTS

     The visibility is a direct function of particle shape, and the shape
must be known or assumed in order to determine size from a one-
component visibility measurement.  This is not an uncommon feature
for all object size determinations from scattered light measurements.
The problem of determining the size of odd shaped particles appears
to be a universal one since there is no commonly accepted size param-
eter.  Until  a suitable  size standard can be set for odd shaped particles
it would seem that the  most straightforward solution to the dilemma is
to use a two-dimensional set of interference fringes (i. e., two inde-
pendent fringe sets sharing a common probe volume with the respec-
tive fringe planes orthogonal to each other) to determine relative
symmetry properties of the particle.  For example, if both measured
visibilities are identical, then the particle shape is assumed to be
square or circular.  Since square shapes do not occur frequently  in
most natural processes,  the particle presumably was  spherical in
shape.  On the other hand, when the visibility is not the same for each
signal, cylindrical or ellipsoidal symmetry could be assumed and the
major and minor dimensions of the particle specified.
                                   52

-------
5.10 MULTIPLE PARTICLE SIGNALS

    In order to analyze multiple particle signals,  at least 80 particles
should exist in the probe volume at any instant in time in order for
Eq. (16) to be a valid approximation.  Fewer than 30 particles can lead
to significant deviations from those predicted  by this equation,  and even
for this number certain rare spatial positions of the particles can lead
to surprisingly large deviations.  No straightforward means has yet
been developed to determine non-mono-disperse size distributions
from visibility measurements.  For practical applications, multiple
particle considerations will be an academic exercise.  Experimental
experience has shown that when a medium containing the particles is
optically thin, the probability of observing more than one particle dur-
ing a signal cycle is very small.  Thus, particle size distributions can
be determined by measurement of individual particles  and forming
histograms of number versus size as determined by visibility measure-
ments .
                        6.0  RECOMMENDATIONS
    From the analysis that has been reported here, one conclusion is
that the fringe visibility technique can be incorporated into a viable
instrument for the real time analysis of particle sizes simultaneously
with velocity measurements.   Particle sizes to 1. 0 Mm can be deter-
mined; however, the threshold of detection has not  been established.
For self-aligning optics, 0. 5 wavelengths of the illuminating beam
appears Oto be the limit,  e. g., in the case of the He-Cd laser,  operating
at 4416 A, approximately 0. 22 jurn.   With the laser operating  at 3250 A,
then the threshold would be further lowered to approximately  0. 17 Aim..
Additional experimental effort is required to substantiate these con-
clusions.

    One-dimensional particle sizing experiments leave much to be de-
sired. Two-dimensional particle sizing is a minimum  condition for
realizing  reliable measurements.  Thus, additional experiments with
a two-dimensional fringe technique are recommended to be performed.
The experiments should be designed  to focus on particle sizes below
1. 0 jum.   After preliminary static measurements are made and micro-
scopic photographs are obtained for the particle size, then dynamic
measurements should be made to' ascertain the validity of the theoretical
predictions made during this  phase of the study.
                                  53

-------
    A newly developed telescope system (Ref. 17),  where it will be
possible to acquire not only two-dimensional fringe visibilities but
where two wavelengths, e. g., 4416 A and 3250 A can be used simul-
taneously, is recommended for further studies.  In this manner,  a
correlation between the two sets  of data on the same particulates
being measured can be performed to  verify the accuracy of the tech-
nique.

    An electronic device  to automatically determine signal visibility
is an absolute necessity for on-line particle sizing measurements.
Preliminary studies conducted during this effort indicate the feasibility
of developing such an instrument.

    Upon completion of the prototype subsystems the instrumentation
system should be checked out initially in a controlled environment and
then used in established,  practical, test systems to determine (1)  the
quality, accuracy,  and data acquisition rate as a function of signal-to-
noise relationships, (2)  additional refinements to be incorporated into
the system to make it an  operational  tool,  and (3)  determination of
operational details, e.g., sampling methods, data analysis and evalua-
tion,  correlation with sampling probes or other measuring techniques.
                             REFERENCES
1.  Davies,  R.  "Rapid Response Instrumentation for Particle Size
         Analyses. "  A Series of Review Articles in American
         Laboratory, Vol. 5, No. 12, December 1973; Vol.  6,
         No. 1, January 1974; and Vol.  6, No.  2,  February 1974.

2.  Trollinger, J. D. and Belz, R. A.  "Holography in Dust Erosion
         Facilities." AEDC-TR-73-160 (AD766420), September 1973.

3.  Belz,  R. A. and Dougherty, N. S.  "In-Line Holography of Re-
         acting Liquid Sprays. "  Proceedings of the Symposium on
         Engineering Methods of Holography.  Sponsored by ARPA,
         Conducted by TRW Systems,  Los Angeles, California,
         February 1972.

4.  Wuerker,  R.  F. "Applications of Pulsed Laser Holography. "
         Published in Laser Technology in Aerodynamic Measure-
         ments, AGARD-LS-49, p.  8. 1, 1972.
                                  54

-------
 5.   Lennert, A.  E.,  Hornkohl,  J. O. ,  and Kalb, H.  T.   "The Appli-
          cation of Laser Velocimeters for Flow Measurements. "
          Published in The Air Breathing Propulsion Conference Pro-
          ceedings, Monterey,  California,  September  19-21, 1972.
 6.   Brayton, D.  B.,  Kalb,  H.  T. ,  and Crosswy, F.  L.   "Two-
          Component,  Dual-Scatter,  Laser Doppler Velocimeter with
          Frequency Burst Signal Readout. "  Applied Optics, Vol. 12,
          No.  6, June  1973.
 7.   Kalb, H. T., Brayton,  D.  B. ,  and McClure, J.  A.  "Laser
          Velocimetry Data Processing. " AEDC-TR-73-116
          (AD766418),  September 1973.
 8.   Rudd,  M. J.  "A New Theoretical Model for the Laser Doppler
          Meter. " Journal of Scientific Instruments (Journal of Physics
          E), Series 2, Vol.  2, 1969.

 9.   Farmer, W.  M.  "Measurement of Particle Size,  Number Density
          and Velocity Using  a Laser Interferometer. "  Applied Optics,
          Vol. 11, No.  11, November 1972.
10.   Kerker,  M.  The Scattering of Light.  Academic  Press,  New York,
          1969.
11.   Farmer, W.  M.  "The Interferometric Observation of Dynamic
          Particle Size, Velocity, and  Number Density. "  Ph. D.
          Thesis,  College of  Liberal Arts, Department of Physics,
          The University of Tennessee, Knoxville, Tennessee,  March
          1973.
12.   Born,  M. and Wolf,  E.   Principles of Optics. Third Edition,
          Pergamon Press, New York, 1965.
13.   Farmer, W.  M. and Brayton,  D.  B.  "Analysis  of Atmospheric
          Laser Doppler Velocimeters. "  Applied Optics,  Vol.  10,
          No.  10,  October  1971.
14.   Beers, Y.  Introduction to the Theory of Error.   Addison-Wesley
          Publishing Company, Inc., Reading, Massachusetts,  1957.

15.   Brayton, D.  B. and Goethert,  W. H.   "A New Dual-Scatter Laser
          Doppler-Shift Velocity Measuring Technique. " ISA Trans-
          actions,  Vol.  10, No.  1, January  1971.
                                55

-------
16.   Farmer, W. M.  and Hornkohl, J. O.  "Two-Component Self-
         Aligning Laser Vector Velocimeter. "  Applied Optics, Vol. 12,
         No. 11, November 1973.

17.   Lennert, A. E., Crosswy,  F. L., Kalb, H. T.,  et al.  "Appli-
         cation of the Laser Velocimeter for Trailing Vortex Mea-
          surements."  AEDC-TR-74-26 (ADA002151), December
          1974.
                                 56

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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
^($0/2,73-034:
LE AND SUBTITLE
nterferometric Instrumentation for Particle
tze Analysis
THORNO.
5. REPOflT-DAT-e-
June-1974 *
6. PERFORMING OflGANJZATJON CODE
8. PERFORMING-ORGANIZATIOf^REPOflT NO.

10. PROGRAM ELEMENT NO.
1AA010
11. CONTRACT/GRANT NO.
EPA-IAG-0177(d)
• *
13. TYPE OF REPORT AND PERIOD COVERED
Final Report
14. SPONSORING AGENCY CODE
«
   . SUPPLEMENTARY NOTES
  >. ABSTRACT
   This  report summarizes-the results-of^a ^research..program, conducted todetermine.„
   the character! stics and potenticrKcapatfH ities of ^particle s*ze analysis -with ~
   laser interferometer techniques.   Theorettcal and-experimentcul. analyses are^
   reported which indicate -thatra-ranga=of,rparticle^sizes:-fronpmicr-om,to=imil.l-Tmeters
   in-d-fameter can be-determi*ed^hefi^tlTe-cross^sec^on                                -
   known^   It is^shown-that number density carNae detenninecHfromM:he-interferoTnetric-
   measurements ,1 n .certain- -restcl cted-^ppi-i-cat4oBs^  The 1 imi tations^and;potentiaid ties
   of^this  method.of^ determining par-tide size=-are discussed  in'detarhr
17.
                                KEY1WOROS AND-DOCUMEMT ANALYSIS
a.
                  DESCRIPTORS
b.lDEN-TIF4€flSA3PEN ENDED-TERMS"
  COSATI Field/Group
   Parti cle _Si ze Analysis
   Instrumental Size  Analysis
   Particulate Analysis-
   Stack Emission- Sfze -Analysis
   Optical Size Analysis
  Interferometric
"Instrumentation:
  Laser
  Laser 'Veloe3'metry
-Stack Monitoring
 B.-DISTRIBUTION STATEMENT

   Release-Unl imited-
19. SECURJTY. CLASS (This Reportf

 llnr.Ta«;«;i-FipH	
21. NO. OF.PAGES
        59 v
                                              20;SECURITY CLASS (Thispage)
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                           22..PRICE-
EPA-F-orm-2220-1 (9-73)
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