Abstract

The basic principles of applying hologram techniques to the problem of particle size determination have received considerable attention over the past year. In this paper the basic principles of the use of the Fraunhofer (far field) hologram are briefly reviewed. Techniques for making use of the method are described for both the recording of the hologram and the reconstruction of the particle distribution. Factors affecting the sample volume depth and particle size range are discussed. Typical results are shown.

© 1967 Optical Society of America

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References

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  1. B. J. Thompson, Japan. J. Appl. Phys. Suppl. 14, 302(1965).
  2. B. J. Thompson, Soc. Photo-Opt. Instr. Eng. 2, 43 (1964).
    [CrossRef]
  3. G. B. Parrent, B. J. Thompson, Opt. Acta 11, 183(1964).
    [CrossRef]
  4. J. B. DeVelis, G. B. Parrent, B. J. Thompson, J. Opt. Soc. Am. 56, 423 (1966).
    [CrossRef]
  5. B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
    [CrossRef]
  6. B. J. Thompson, G. B. Parrent, J. H. Ward, B. Justh, J. Appl. Met. 5, 343 (1966).
    [CrossRef]
  7. R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).
    [CrossRef]
  8. E. Leith, J. Upatnieks, K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).
    [CrossRef]
  9. D. Gabor, Proc. Roy. Soc. A 197, 483 (1949).
  10. G. O. Reynolds, J. B. DeVelis, Theory and Applications of Holography (Addison-Wesley Publishing Co., Reading, Massachusetts, 1967).
  11. G. O. Reynolds, J. B. DeVelis, IEEE Trans. AP-15, 41 (1967).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964).

1967 (1)

G. O. Reynolds, J. B. DeVelis, IEEE Trans. AP-15, 41 (1967).
[CrossRef]

1966 (2)

J. B. DeVelis, G. B. Parrent, B. J. Thompson, J. Opt. Soc. Am. 56, 423 (1966).
[CrossRef]

B. J. Thompson, G. B. Parrent, J. H. Ward, B. Justh, J. Appl. Met. 5, 343 (1966).
[CrossRef]

1965 (3)

1964 (3)

B. J. Thompson, Soc. Photo-Opt. Instr. Eng. 2, 43 (1964).
[CrossRef]

G. B. Parrent, B. J. Thompson, Opt. Acta 11, 183(1964).
[CrossRef]

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

1949 (1)

D. Gabor, Proc. Roy. Soc. A 197, 483 (1949).

Born, M.

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964).

DeVelis, J. B.

G. O. Reynolds, J. B. DeVelis, IEEE Trans. AP-15, 41 (1967).
[CrossRef]

J. B. DeVelis, G. B. Parrent, B. J. Thompson, J. Opt. Soc. Am. 56, 423 (1966).
[CrossRef]

G. O. Reynolds, J. B. DeVelis, Theory and Applications of Holography (Addison-Wesley Publishing Co., Reading, Massachusetts, 1967).

Gabor, D.

D. Gabor, Proc. Roy. Soc. A 197, 483 (1949).

Haines, K. A.

Justh, B.

B. J. Thompson, G. B. Parrent, J. H. Ward, B. Justh, J. Appl. Met. 5, 343 (1966).
[CrossRef]

Leith, E.

Meier, R. W.

Parrent, G. B.

B. J. Thompson, G. B. Parrent, J. H. Ward, B. Justh, J. Appl. Met. 5, 343 (1966).
[CrossRef]

J. B. DeVelis, G. B. Parrent, B. J. Thompson, J. Opt. Soc. Am. 56, 423 (1966).
[CrossRef]

G. B. Parrent, B. J. Thompson, Opt. Acta 11, 183(1964).
[CrossRef]

Reynolds, G. O.

G. O. Reynolds, J. B. DeVelis, IEEE Trans. AP-15, 41 (1967).
[CrossRef]

G. O. Reynolds, J. B. DeVelis, Theory and Applications of Holography (Addison-Wesley Publishing Co., Reading, Massachusetts, 1967).

Silverman, B. A.

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

Thompson, B. J.

J. B. DeVelis, G. B. Parrent, B. J. Thompson, J. Opt. Soc. Am. 56, 423 (1966).
[CrossRef]

B. J. Thompson, G. B. Parrent, J. H. Ward, B. Justh, J. Appl. Met. 5, 343 (1966).
[CrossRef]

B. J. Thompson, Japan. J. Appl. Phys. Suppl. 14, 302(1965).

B. J. Thompson, Soc. Photo-Opt. Instr. Eng. 2, 43 (1964).
[CrossRef]

G. B. Parrent, B. J. Thompson, Opt. Acta 11, 183(1964).
[CrossRef]

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

Upatnieks, J.

Ward, J. H.

B. J. Thompson, G. B. Parrent, J. H. Ward, B. Justh, J. Appl. Met. 5, 343 (1966).
[CrossRef]

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964).

IEEE Trans. (1)

G. O. Reynolds, J. B. DeVelis, IEEE Trans. AP-15, 41 (1967).
[CrossRef]

J. Appl. Met. (1)

B. J. Thompson, G. B. Parrent, J. H. Ward, B. Justh, J. Appl. Met. 5, 343 (1966).
[CrossRef]

J. Appl. Meteorol. (1)

B. A. Silverman, B. J. Thompson, J. H. Ward, J. Appl. Meteorol. 3, 792 (1964).
[CrossRef]

J. Opt. Soc. Am. (3)

Japan. J. Appl. Phys. Suppl. (1)

B. J. Thompson, Japan. J. Appl. Phys. Suppl. 14, 302(1965).

Opt. Acta (1)

G. B. Parrent, B. J. Thompson, Opt. Acta 11, 183(1964).
[CrossRef]

Proc. Roy. Soc. (1)

D. Gabor, Proc. Roy. Soc. A 197, 483 (1949).

Soc. Photo-Opt. Instr. Eng. (1)

B. J. Thompson, Soc. Photo-Opt. Instr. Eng. 2, 43 (1964).
[CrossRef]

Other (2)

G. O. Reynolds, J. B. DeVelis, Theory and Applications of Holography (Addison-Wesley Publishing Co., Reading, Massachusetts, 1967).

M. Born, E. Wolf, Principles of Optics (The Macmillan Company, New York, 1964).

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Figures (12)

Fig. 1
Fig. 1

Configuration for recording the hologram.

Fig. 2
Fig. 2

Configuration for reconstructing the hologram.

Fig. 3
Fig. 3

Schematic diagram of optical system for the fog hologram camera.

Fig. 4
Fig. 4

Photograph of the fog hologram camera at Otis Air Force Base.

Fig. 5
Fig. 5

Histogram of fog particle size distribution obtained at Otis Air Force Base 13 June 1965, between 06:54 and 07:05 hours. These results were provided by AFCRL Cloud Physics from data collected as part of Project Cat Feet.

Fig. 6
Fig. 6

Schematic diagram of readout system.

Fig. 7
Fig. 7

Hologram reconstructor and television monitor.

Fig. 8
Fig. 8

Reconstructed image on television monitor.

Fig. 9
Fig. 9

Schematic diagram of aerosol assessment camera. 1. Ruby laser, Lear Seigler, LS-100, 10 mW peak, pulse duration 20 × 10−9 sec. 2. Stop 2.2 mm, 31.75 cm from laser port. 3. Collimator lens—33 mm E.F.L. 4. Collimator objective 304 mm E.F.L. 5. Filter, neutral density 1.5. 6. Protective glass flat, 6 mm thick. 7. Light tube, 12.75 cm diam × 2.4 ml long (helium filled). 8. Protective flat, 6 mm thick. 9. Picture volume, 1.37 × 2.05 cm × 6 cm (for particles 22 μ and larger). 10. Flat 6 mm thick. 11. Camera lens, 5 cm E.F.L., f/1.6. 12. Shutter, Ilex No. 5 or Graflex Focal Plane. 13. Filter, Wratten No. 70. 14. Film, SO-243, 70 mm. 15. Shutter and magazine control.

Fig. 10
Fig. 10

Hologram camera and laser illuminator for aerosol assessment.

Fig. 11
Fig. 11

Image of an agglomeration of 10-μ particles generated in dynamic chamber test.

Fig. 12
Fig. 12

Coherence parameters.

Tables (2)

Tables Icon

Table I Laser Fog Hologram Camera Parameters

Tables Icon

Table II Illuminator and Fraunhofer Hologram Camera for Aerosol Assessment

Equations (16)

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A ( α , β ) = [ U B ( α , β ) + U O ( α , β ) ] .
I ( α , β ) = A ( α , β ) 2 = U B 2 + U B * U O + U B U O * + U O 2 .
D ( α , β ) = γ log [ I ( α , β ) t + c ] .
I ( α , β ) t > c .
T a = 1 + ( γ / 2 ) [ ( U O / U B ) + ( U O * / U B * ) + ( U O / U B ) 2 + ] .
m = [ R 1 / ( R 1 + z 1 ) - ( λ 2 z 1 / λ 1 R 2 ) ] - 1 .
z 2 = ( λ 1 / λ 2 ) z 1 .
I ( α , β ) = 1 - ( γ / 2 ) ( k 1 / 2 π z 1 ) D ˜ [ ( α / λ 1 z 1 ) , ( β / λ 1 z 1 ) ] × sin [ k 1 ( α 2 + β 2 ) / 2 z 1 + ( γ / 2 ) ( k 1 2 / 4 π 2 z 1 2 ) λ D ˜ [ ( α / λ 1 z 1 ) , ( β / λ 1 z 1 ) ] 2 ,
I ( x y ) = 1 + ( γ / 2 ) D ( x , y ) + ( γ 2 / 4 ) [ D ( x , y ) ] 2 .
z 2 = m 2 z 1 ( λ 1 / λ 2 ) .
I ( α ) = 1 - ( γ 2 ) k 2 π z 1 D ˜ ( α ¯ λ z 1 ) sin k α 2 2 z 1 + ( γ 2 ) k 2 4 π 2 z 1 2 D ˜ ( α ¯ λ z 1 ) 2 .
ω = α ¯ ( 2 π α ¯ 2 / 2 λ z 1 ) = 2 π α ¯ / λ z 1 .
r a = 1.22 / 2 l max .
coherence interval = α ¯ = ( 4 × 1.22 z λ ) / d .
coherence interval > 5 n d ,
coherence length > 12 λ n .

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