Abstract

The principle and experimental design of a real-time multichannel multiplexed optical pattern recognition system via use of a 25-focus dichromated gelatin holographic lens (hololens) are described. Each of the 25 foci of the hololens may have a storage and matched filtering capability approaching that of a single-lens correlator. If the space–bandwidth product of an input image is limited, as is true in most practical cases, the 25-focus hololens system has 25 times the capability of a single lens. Experimental results have shown that the interfilter noise is not serious. The system has already demonstrated the storage and recognition of over 70 matched filters—which is a larger capacity than any optical pattern recognition system reported to date.

© 1984 Optical Society of America

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References

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  1. A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [Crossref]
  2. A. VanderLugt, “Practical Considerations for the Use of Spatial Carrier Frequency Filters,” Appl. Opt. 5, 1760 (1966).
    [Crossref]
  3. A. VanderLugt, F. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. Tippet, Ed. (MIT Press, Cambridge, Mass., 1965), p. 125.
  4. D. Gabor, “Character Recognition by Holography,” Nature London, 208, 422 (1965).
    [Crossref]
  5. J. T. LaMacchia, D. L. White, “Coded Multiple Exposure Holograms,” Appl. Opt. 7, 91 (1968).
    [Crossref] [PubMed]
  6. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, N. Massay, “Holographic Data Storage in 3-D Media,” Appl. Opt., 5, 1303 (1966).
    [Crossref] [PubMed]
  7. G. Groh, “Optical Multiplex System for Pattern Recognition Utilizing Point Holograms,” Opt. Commun. 1, 454 (1970).
    [Crossref]
  8. M. I. Jones, J. F. Walkup, M. O. Hagler, “Multiplex Hologram Representations of Space-Invariant Optical Systems Using Ground-Glass Encoded Reference Beams,” Appl. Opt. 21, 1291 (1981).
    [Crossref]
  9. N. K. Shi, “Color-Sensitive Spatial Filters,” Opt. Lett. 3, 85 (1978).
    [Crossref] [PubMed]
  10. S. K. Case, “Pattern Recognition with Wavelength-Multiplexed Filters,” Appl. Opt. 18, 1890 (1979).
    [Crossref] [PubMed]
  11. J. R. Leger, S. H. Lee, “Hybrid Optical Processor for Pattern Recognition and Classification Using a Generalized Set of Pattern Functions,” Appl. Opt. 21, 274 (1982).
    [Crossref] [PubMed]
  12. H.-K. Liu, J. G. Duthie, “Real-Time Screen-Aided Multiple-Image Optical Holographic Matched-Filter Correlator,” Appl. Opt. 21, 3278 (1982).
    [Crossref] [PubMed]
  13. A. Grumet, “Automatic Target Recognition System,” U.S. Patent3,779,492 (1972).
  14. K. Leib, R. Bondurant, M. Wohlers, “Optical Matched Filter Correlator Memory Techniques and Storage Capacity,” Opt. Eng. 19, 414 (1980).
    [Crossref]
  15. J. Mendelsohn, M. Wohlers, K. Leib, “Digital Analysis of the Effects of Terrain Clutter on the Performance of Matched Filters for Target Identification and Location,” Proc. Soc. Photo-Opt. Instrum. Eng. 186, 190 (1979).
  16. B. J. Chang, C. D. Leonard, “Dichromated Gelatin for the Fabrication of Holographic Optical Elements,” Appl. Opt. 18, 2407 (1979).
    [Crossref] [PubMed]
  17. Y. Z. Liang, D. Z. Zhao, H. K. Liu, “Multifocus Dichromated Gelatin Hololens,” Appl. Opt. 22, 3451 (1983).
    [Crossref] [PubMed]
  18. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 86.
  19. H. K. Liu, “Halftone Screen with Cell Matrix,” U.S. Patent4,188, 255 (1980).
  20. A. VanderLugt, E. Leith, “Techniques in Optical Data Processing and Coherent Optics,” Ann. N.Y. Acad. Sci., 157, 99 (1969).
    [Crossref]
  21. D. Gregory, to be submitted to Appl. Opt.

1983 (1)

1982 (2)

1981 (1)

1980 (1)

K. Leib, R. Bondurant, M. Wohlers, “Optical Matched Filter Correlator Memory Techniques and Storage Capacity,” Opt. Eng. 19, 414 (1980).
[Crossref]

1979 (3)

J. Mendelsohn, M. Wohlers, K. Leib, “Digital Analysis of the Effects of Terrain Clutter on the Performance of Matched Filters for Target Identification and Location,” Proc. Soc. Photo-Opt. Instrum. Eng. 186, 190 (1979).

B. J. Chang, C. D. Leonard, “Dichromated Gelatin for the Fabrication of Holographic Optical Elements,” Appl. Opt. 18, 2407 (1979).
[Crossref] [PubMed]

S. K. Case, “Pattern Recognition with Wavelength-Multiplexed Filters,” Appl. Opt. 18, 1890 (1979).
[Crossref] [PubMed]

1978 (1)

1970 (1)

G. Groh, “Optical Multiplex System for Pattern Recognition Utilizing Point Holograms,” Opt. Commun. 1, 454 (1970).
[Crossref]

1969 (1)

A. VanderLugt, E. Leith, “Techniques in Optical Data Processing and Coherent Optics,” Ann. N.Y. Acad. Sci., 157, 99 (1969).
[Crossref]

1968 (1)

1966 (2)

1965 (1)

D. Gabor, “Character Recognition by Holography,” Nature London, 208, 422 (1965).
[Crossref]

1964 (1)

A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[Crossref]

Bondurant, R.

K. Leib, R. Bondurant, M. Wohlers, “Optical Matched Filter Correlator Memory Techniques and Storage Capacity,” Opt. Eng. 19, 414 (1980).
[Crossref]

Case, S. K.

Chang, B. J.

Duthie, J. G.

Gabor, D.

D. Gabor, “Character Recognition by Holography,” Nature London, 208, 422 (1965).
[Crossref]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 86.

Gregory, D.

D. Gregory, to be submitted to Appl. Opt.

Groh, G.

G. Groh, “Optical Multiplex System for Pattern Recognition Utilizing Point Holograms,” Opt. Commun. 1, 454 (1970).
[Crossref]

Grumet, A.

A. Grumet, “Automatic Target Recognition System,” U.S. Patent3,779,492 (1972).

Hagler, M. O.

Jones, M. I.

Klooster, A.

A. VanderLugt, F. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. Tippet, Ed. (MIT Press, Cambridge, Mass., 1965), p. 125.

Kozma, A.

LaMacchia, J. T.

Lee, S. H.

Leger, J. R.

Leib, K.

K. Leib, R. Bondurant, M. Wohlers, “Optical Matched Filter Correlator Memory Techniques and Storage Capacity,” Opt. Eng. 19, 414 (1980).
[Crossref]

J. Mendelsohn, M. Wohlers, K. Leib, “Digital Analysis of the Effects of Terrain Clutter on the Performance of Matched Filters for Target Identification and Location,” Proc. Soc. Photo-Opt. Instrum. Eng. 186, 190 (1979).

Leith, E.

A. VanderLugt, E. Leith, “Techniques in Optical Data Processing and Coherent Optics,” Ann. N.Y. Acad. Sci., 157, 99 (1969).
[Crossref]

Leith, E. N.

Leonard, C. D.

Liang, Y. Z.

Liu, H. K.

Liu, H.-K.

Marks, J.

Massay, N.

Mendelsohn, J.

J. Mendelsohn, M. Wohlers, K. Leib, “Digital Analysis of the Effects of Terrain Clutter on the Performance of Matched Filters for Target Identification and Location,” Proc. Soc. Photo-Opt. Instrum. Eng. 186, 190 (1979).

Rotz, F.

A. VanderLugt, F. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. Tippet, Ed. (MIT Press, Cambridge, Mass., 1965), p. 125.

Shi, N. K.

Upatnieks, J.

VanderLugt, A.

A. VanderLugt, E. Leith, “Techniques in Optical Data Processing and Coherent Optics,” Ann. N.Y. Acad. Sci., 157, 99 (1969).
[Crossref]

A. VanderLugt, “Practical Considerations for the Use of Spatial Carrier Frequency Filters,” Appl. Opt. 5, 1760 (1966).
[Crossref]

A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[Crossref]

A. VanderLugt, F. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. Tippet, Ed. (MIT Press, Cambridge, Mass., 1965), p. 125.

Walkup, J. F.

White, D. L.

Wohlers, M.

K. Leib, R. Bondurant, M. Wohlers, “Optical Matched Filter Correlator Memory Techniques and Storage Capacity,” Opt. Eng. 19, 414 (1980).
[Crossref]

J. Mendelsohn, M. Wohlers, K. Leib, “Digital Analysis of the Effects of Terrain Clutter on the Performance of Matched Filters for Target Identification and Location,” Proc. Soc. Photo-Opt. Instrum. Eng. 186, 190 (1979).

Zhao, D. Z.

Ann. N.Y. Acad. Sci. (1)

A. VanderLugt, E. Leith, “Techniques in Optical Data Processing and Coherent Optics,” Ann. N.Y. Acad. Sci., 157, 99 (1969).
[Crossref]

Appl. Opt. (9)

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal Detection by Complex Spatial Filtering,” IEEE Trans. Inf. Theory IT-10, 139 (1964).
[Crossref]

Nature London (1)

D. Gabor, “Character Recognition by Holography,” Nature London, 208, 422 (1965).
[Crossref]

Opt. Commun. (1)

G. Groh, “Optical Multiplex System for Pattern Recognition Utilizing Point Holograms,” Opt. Commun. 1, 454 (1970).
[Crossref]

Opt. Eng. (1)

K. Leib, R. Bondurant, M. Wohlers, “Optical Matched Filter Correlator Memory Techniques and Storage Capacity,” Opt. Eng. 19, 414 (1980).
[Crossref]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

J. Mendelsohn, M. Wohlers, K. Leib, “Digital Analysis of the Effects of Terrain Clutter on the Performance of Matched Filters for Target Identification and Location,” Proc. Soc. Photo-Opt. Instrum. Eng. 186, 190 (1979).

Other (5)

D. Gregory, to be submitted to Appl. Opt.

A. VanderLugt, F. Rotz, A. Klooster, in Optical and Electro-Optical Information Processing, J. Tippet, Ed. (MIT Press, Cambridge, Mass., 1965), p. 125.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 86.

H. K. Liu, “Halftone Screen with Cell Matrix,” U.S. Patent4,188, 255 (1980).

A. Grumet, “Automatic Target Recognition System,” U.S. Patent3,779,492 (1972).

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Figures (17)

Fig. 1
Fig. 1

Diagram of the Grumet multifocus holographic lens pattern recognition technique.

Fig. 2
Fig. 2

Schematic representation of a real-time multichannel multiple-image coherent optical correlator.

Fig. 3
Fig. 3

Optical system diagram for making a multifocus hololens.

Fig. 4
Fig. 4

Computer plot of the positive part of the transmittance T(x) of one unit cell of a 1-D contact screen vs x, where T(x) is given by Eq. (3).

Fig. 5
Fig. 5

Computer plot of the theoretically calculated Fourier transform of the positive part of the function T(x) of Fig. 4 vs spatial frequency.

Fig. 6
Fig. 6

Computer plot of the discrete-valued approximation of the positive part of the transmittance T(x) of one unit cell of a 1-D contact screen vs x, where T(x) is given by Eq. (3).

Fig. 7
Fig. 7

Computer plot of the theoretically calculated Fourier transform of the unit cell of Fig. 6 vs spatial frequency.

Fig. 8
Fig. 8

Few unit cells of the diffraction screen used in making the hololens (magnification = 100).

Fig. 9
Fig. 9

Photograph of the 5 × 5 array produced by the hololens (M = 5×).

Fig. 10
Fig. 10

Photograph of the 25 images of a tank produced by the hololens and liquid crystal light valve.

Fig. 11
Fig. 11

Photograph of the pattern produced using a 2.5-mm circular aperture as the input to the hololens (M = 200×).

Fig. 12
Fig. 12

Photograph of a matched filter of an aerial map of Huntsville (M = 100×).

Fig. 13
Fig. 13

Correlation intensity from all 25 elements vs the angular rotation of the input scene. The scene correlation and background correlation due to the hololens are superimposed.

Fig. 14
Fig. 14

Photograph of the TV screen displaying the separation of scene and hololens correlations.

Fig. 15
Fig. 15

Correlations of eight filters stored at one element of the hololens. The input scene was an aerial photograph of Huntsville.

Fig. 16
Fig. 16

Correlation of 18 different matched filters addressed in parallel through the hololens. The input scene was an aerial photograph of Huntsville.

Fig. 17
Fig. 17

Correlation of 75 filters addressed in parallel—tank input scene. Numbers represent the rotational position of the input scene (in degrees).

Tables (1)

Tables Icon

Table I Power Distribution (in microwatts) of Each of the 25 Foci of the Holographic Element with a Uniform LCLV Input; LCLV is Driven at f = 1400 Hz and V = 6.5 V

Equations (40)

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s ( x , y ) = [ T ( x , y ) * m , n = - δ ( x - m X ) δ ( y - n Y ) ] P s ( x , y ) ,
T ( x , y ) = T ( x ) T ( y ) .
T ( x ) = 0.2 + 0.4 cos ( 2 π x X ) + 0.4 cos ( 4 π x X ) ,
T ( y ) = 0.2 + 0.4 cos ( 2 π y Y ) + 0.4 cos ( 4 π y Y ) ,
T ( x , y ) = T ( x + X , y + Y ) .
P s ( x , y ) = 1 , ( x , y ) inside the aperture , = 0 , ( x , y ) outside the aperture .
S f 1 ( f x , f y ) = A j λ f 1 - s ( x , y ) exp [ - j 2 π ( f x s + f y y ) ] d x d y = A j λ f 1 F [ s ( x , y ) ] = A j λ f 1 F { [ T ( x ) T ( y ) * m n δ ( x - m X ) δ ( y - n Y ) ] p s ( x , y ) } = A j λ f 1 { F [ T ( x ) T ( y ) ] F [ m n δ ( x - m X ) δ ( y - n Y ) ] } * F [ p s ( x , y ) ] = 0.04 A j λ f 1 [ δ ( f x ) + δ ( f x - 1 X ) + δ ( f x + 1 X ) + δ ( f x - 2 X ) + δ ( f x 2 X ) ] · [ δ ( f y ) + δ ( f y - 1 Y ) + δ ( f y + 1 Y ) + δ ( f y - 2 Y ) + δ ( f y + 2 Y ) ] · { m n δ ( f x - m X ) δ ( f y - n Y ) * F [ p s ( x , y ) ] } = 0.04 A j λ f 1 [ m = - 2 2 n = - 2 2 δ ( f x - m X ) δ ( f y - n Y ) ] * F [ p s ( x , y ) ] ,
p s ( x , y ) = circ ( r s D s / 2 ) ;
F [ p s ( x , y ) ] = [ ( D s 2 ) 2 J 1 ( π D 1 r 1 λ f 1 ) ( D s r 1 ) / ( 2 λ f 1 ) ] · exp ( j π r 1 2 x f 1 ) ,
u 2 ( x 2 , y 2 ) = exp [ j k 2 f 2 ( 1 - d 20 f 2 ) ( x 1 2 + y 2 2 ) j λ f 2 - u 1 ( x 1 , y 1 ) · exp [ - j 2 π λ f 2 ( x 2 x 1 + y 2 y 1 ) ] d x 1 d y 1 ,
u 1 ( x 1 , y 1 ) = S f 1 ( x 1 λ f 1 , y 1 λ f 1 ) = A j λ f 1 F 1 [ s ( x , y ) ]
u 2 ( x 2 , y 2 ) = A exp [ j k 2 f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) ] - λ 2 f 1 f 2 F 1 F 2 [ s ( x , y ) ] = - A exp [ j k 2 f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) ] s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) .
U r ( x 2 , y 2 ) = R exp ( + j k sin θ x 2 ) ,
I 2 ( x 2 , y 2 ) = U r ( x 2 , y 2 ) + U 2 ( x 2 , y 2 ) 2 = U r ( x 2 , y 2 ) 2 + U 2 ( x 2 , y 2 ) 2 + U r * ( x 2 , y 2 ) U 2 ( x 2 , y 2 ) + U r ( x 2 , y 2 ) U 2 * ( x 2 , y 2 ) = R 2 + A 2 s 2 ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) + R A exp { - j [ k sin θ x 2 - k 2 f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) ] } · s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) + R A exp { j [ k sin θ x 2 - k 2 f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) ] } · s * ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) .
ϕ ( x 2 , y 2 ) = β I 2 ( x 2 , y 2 ) ,
t 2 ( x 2 , y 2 ) = exp [ j ϕ ( x 2 , y 2 ) ] = exp [ j β I 2 ( x 2 , y 2 ) ] .
t 2 ( x 2 , y 2 ) = 1 + ϕ ( x 2 , y 2 ) + ( negligible high order terms ) 1 + j ϕ ( x 2 , y 2 ) .
u i ( x 2 , y 2 ) = B exp ( j k sin θ x 2 ) ,
u ( x 2 , y 2 ) = u i ( x 2 , y 2 ) t 2 ( x 2 , y 2 ) ,
= B exp ( j k sin θ x 2 ) [ 1 + j β I 2 ( x 2 , y 2 ) ] = B exp ( j k sin θ x 2 ) + j β B exp ( j k sin θ x 2 ) I 2 ( x 2 , y 2 ) .
u ( x 2 , y 2 ) = B exp ( j k sin θ x 2 ) + j β B exp ( j k sin θ x 2 ) ( ( R 2 + A 2 S 2 ) + s R A exp { - j [ k sin θ x 2 - k 2 f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) ] } + s * R A exp { j [ k sin θ x 2 - k 2 f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) ] } ) = B exp ( j k sin θ x 2 ) + j β B exp ( j k sin θ x 2 ) ( R 2 + A 2 s 2 ) + j β B R A s exp [ j k 2 k f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) ] + j β B R A s * exp { j [ 2 k sin θ x 2 - k 2 f 2 × ( 1 - d 20 2 f 2 ) ( x 2 2 + y 2 2 ) ] } .
s s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 )
u l ( x 2 , y 2 ) = j β B R A exp [ j k 2 f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) × s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) ] .
exp [ j k 2 f 2 ( 1 - d 20 f 2 ) ( x 2 2 + y 2 2 ) ]
exp [ - j k ( x 2 2 + y 2 2 ) 2 f 2 ( d 20 f 2 - 1 ) - 1 ] = exp [ - j k 2 f H ( x 2 2 + y 2 2 ) ] ,
f H f 2 / ( d 20 f 2 - 1 ) .
u l ( x 2 , y 2 ) = j β B R A exp [ - j k 2 f H ( x 2 2 + y 2 2 ) ] × s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) .
s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) .
u l ( f x , f y ) = 0.04 β R B A λ f H [ m = - 2 2 n = - 2 2 δ ( f x - m X ) δ ( f y - n Y ) ] * F [ P s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) ] ,
f x = - f 1 f 2 x 3 λ f H ,             f y = - f 1 f 2 y 3 λ f H .
f 2 / ( d 20 f 2 - 1 ) f H = d 2 i - f 2 ,
f 1 [ 1 + ( d 20 f 2 - 1 ) - 1 ] = d 2 i .
1 d 20 + 1 d 2 i = 1 f 2 .
u 0 ( x 2 , y 2 ) = B h i ( x 2 , y 2 ) .
u r = r 0 exp ( - j k x 3 sin ψ ) .
u l ( x 2 , y 2 ) = j β B R A exp [ - j k 2 f H ( x 2 2 + y 2 2 ) ] h i ( x 2 , y 2 ) · s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) .
U l ( f x , f y ) = 0.04 β R B A λ f H H i ( x x , f y ) * [ m ; n = - 2 2 δ ( f x - m y , f y - n y ) ] * F { P s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) } ,
I ( x 3 , y 3 ) = u r + U l ( f x , f y ) 2 = r 0 exp ( - j k x 3 sin ψ ) + U l ( f x , f y ) 2 .
t c ( x 3 , y 3 ) = α r 0 exp ( - j k x 3 sin ψ ) U l * ( f x , f y )
U l ( f x , f y ) = 0.04 β R B A λ f H G ( f x , f y ) * [ m ; n = - 2 2 δ ( f x - m X · f y - n Y ) ] * F [ p s ( - f 1 f 2 x 2 , - f 1 f 2 y 2 ) ] .

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