Abstract

A new type of diffractive optical bar code (DOBC) is proposed. Rather than scanning directly, the DOBC is coherently illuminated, and the first diffraction order is sensed. The spacing between the bars is chosen so that the thresholded diffraction pattern yields a specified binary code. Two approaches are investigated for synthesis of the DOBC: phase shaping and a gradient-based, nonlinear, constrained optimization technique. The two design methods are compared based on numerical results, and the validity of the overall design approach is verified by optically sensing the diffraction patterns for a number of fabricated DOBC’s.

© 1992 Optical Society of America

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References

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  1. T. V. Sobczak, ed., Applying Industrial Bar Coding (Society of Manufacturing Engineers, Dearborn, Mich., 1985).
  2. H. Machida, J. Nitta, A. Seko, H. Kobayashi, “High-efficiency fiber grating for producing multiple beams of uniform intensity,” Appl. Opt. 23, 330–332 (1984).
    [CrossRef] [PubMed]
  3. J. Brandrup, E. H. Immergut, W. McDowell, eds., Polymer Handbook (Wiley, New York, 1975).
  4. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  5. P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (9November1971).
  6. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).
  7. N. C. Gallagher, B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 2328–2344 (1973).
    [CrossRef] [PubMed]
  8. M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2794 (1987).
    [CrossRef] [PubMed]
  9. B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
    [CrossRef]
  10. J. P. Allebach, B. Liu, “Minimax spectrum shaping with a bandwidth constraint,” Appl. Opt. 14, 3062–3072 (1975).
    [CrossRef] [PubMed]
  11. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  13. J. Bucklew, N. Gallagher, “Detour phase error in the Lohmann hologram,” Appl. Opt. 18, 575–580 (1979).
    [CrossRef] [PubMed]
  14. P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, Orlando, Fla., 1981).
  15. P. E. Gill, W. Murray, M. A. Saunders, M. H. Wright, User’s Guide for NPSOL (Version 4.0): A fortran Package for Nonlinear Programming, (Department of Operations Research, Stanford University, Stanford, Calif. 94305, 1986.
  16. Gyrex Model 1005 Pattern Generator, Gyrex Corporation, 400 East Gutierrez Street, Santa Barbara, Calif. 93101.

1989 (1)

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

1987 (1)

1984 (1)

1982 (1)

1979 (1)

1975 (1)

1973 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

1967 (1)

Allebach, J. P.

Bucklew, J.

Fienup, J. R.

Gallagher, N.

Gallagher, N. C.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Gill, P. E.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, Orlando, Fla., 1981).

P. E. Gill, W. Murray, M. A. Saunders, M. H. Wright, User’s Guide for NPSOL (Version 4.0): A fortran Package for Nonlinear Programming, (Department of Operations Research, Stanford University, Stanford, Calif. 94305, 1986.

Goodman, J. W.

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

Hirsch, P. M.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (9November1971).

Jennison, B. K.

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

Jordan, J. A.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (9November1971).

Kobayashi, H.

Lesem, L. B.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (9November1971).

Liu, B.

Lohmann, A. W.

Machida, H.

Murray, W.

P. E. Gill, W. Murray, M. A. Saunders, M. H. Wright, User’s Guide for NPSOL (Version 4.0): A fortran Package for Nonlinear Programming, (Department of Operations Research, Stanford University, Stanford, Calif. 94305, 1986.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, Orlando, Fla., 1981).

Nitta, J.

Paris, D. P.

Saunders, M. A.

P. E. Gill, W. Murray, M. A. Saunders, M. H. Wright, User’s Guide for NPSOL (Version 4.0): A fortran Package for Nonlinear Programming, (Department of Operations Research, Stanford University, Stanford, Calif. 94305, 1986.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Seko, A.

Seldowitz, M. A.

Sweeney, D. W.

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26, 2788–2794 (1987).
[CrossRef] [PubMed]

Wright, M. H.

P. E. Gill, W. Murray, M. A. Saunders, M. H. Wright, User’s Guide for NPSOL (Version 4.0): A fortran Package for Nonlinear Programming, (Department of Operations Research, Stanford University, Stanford, Calif. 94305, 1986.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, Orlando, Fla., 1981).

Appl. Opt. (7)

Opt. Eng. (1)

B. K. Jennison, J. P. Allebach, D. W. Sweeney, “Iterative approaches to computer-generated holography,” Opt. Eng. 28, 629–637 (1989).
[CrossRef]

Optik (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–250 (1972).

Other (7)

T. V. Sobczak, ed., Applying Industrial Bar Coding (Society of Manufacturing Engineers, Dearborn, Mich., 1985).

J. Brandrup, E. H. Immergut, W. McDowell, eds., Polymer Handbook (Wiley, New York, 1975).

P. M. Hirsch, J. A. Jordan, L. B. Lesem, “Method of making an object dependent diffuser,” U.S. Patent3,619,022 (9November1971).

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

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, Orlando, Fla., 1981).

P. E. Gill, W. Murray, M. A. Saunders, M. H. Wright, User’s Guide for NPSOL (Version 4.0): A fortran Package for Nonlinear Programming, (Department of Operations Research, Stanford University, Stanford, Calif. 94305, 1986.

Gyrex Model 1005 Pattern Generator, Gyrex Corporation, 400 East Gutierrez Street, Santa Barbara, Calif. 93101.

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Figures (8)

Fig. 1
Fig. 1

Diffractive optical bar code consisting of transparent bars on an opaque background.

Fig. 2
Fig. 2

Modulated ribbon grating, which could also be used as a DOBC.

Fig. 3
Fig. 3

Diffractive optical bar code illuminated by a coherent plane wave and geometry for detecting the resulting intensity pattern in the first diffraction order.

Fig. 4
Fig. 4

Field distributions (a) at the detector plane and (b) in the first diffraction order for a DOBC consisting of N = 8 bars.

Fig. 5
Fig. 5

Diffraction pattern intensity and detector outputs for the diffractive bar codes corresponding to two 8-bit binary codes. The bar codes were designed with the phase-shaping method and containing eight replications.

Fig. 6
Fig. 6

Diffraction pattern intensity and detector outputs for the diffractive bar codes corresponding to two 8-bit binary codes. The bar codes were designed with the SQM method and contain eight replications.

Fig. 7
Fig. 7

Observed rms error ∊obs and diffraction efficiency η for (a) 64 and (b) 180 solutions generated by the SQM method for the specified 8-bit binary codes. The solutions tend to cluster at a relatively small number of points. The brightness of the plotted points is proportional to the number of solutions clustered there.

Fig. 8
Fig. 8

Photographs of the video monitor for the DOBC’s listed in Table II.

Tables (2)

Tables Icon

Table I Performance of Phase-Shaping and Sequential Quadratic Minimization Methods in the Design of DOBC’s for 25 Random 8-Bit Codes

Tables Icon

Table II DOBC’s Designed by SQM for Eight Different Binary Codes and Written with the Gyrex Pattern Generator

Equations (23)

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f 0 ( x , y ) = n = 0 N 1 rect [ x ( n + Δ n ) R W ] rect [ y L ] ,
f M ( x , y ) = m = ( M 1 ) / 2 ( M 1 ) / 2 f 0 ( x m X , y ) ,
F M ( u , υ ) = f M ( x , y ) exp [ i 2 π ( u x + υ y ) ] d x dy .
F M ( u , υ ) = F 0 ( u , υ ) S M ( u , υ ) ,
F 0 ( u , υ ) = W L sinc ( W u ) sinc ( L υ ) n = 0 N 1 exp { i 2 π [ ( n + Δ n ) R u ] } ,
S M ( u , υ ) = m = ( M 1 ) / 2 ( M 1 ) / 2 exp ( i 2 π m X u ) .
D k = H / 2 H / 2 k / X S / 2 k / X + S / 2 | F M ( u , υ ) | 2 d u d υ .
D k = 2 L π Φ ( π L H ) × [ n = 0 N 1 p = 0 N 1 m = ( M 1 ) / 2 ( M 1 ) / 2 1 = ( M 1 ) / 2 ( M 1 ) / 2 W 2 u sin 2 ( π W u ) × cos [ 2 π ( C n m C p l ) u ] ( C n m C p l ) π Φ [ 2 π ( C n m C p l ) u ] ( C n m C p l + W ) 2 π Φ [ 2 π ( C n m C p l + W ) u ] + ( C n m C p l W ) 2 π Φ [ 2 π ( C n m C p l W ) u | u = k / X + S / 2 u = k / X S / 2 ] ,
Φ [ ξ ] = q = 0 ( 1 ) q ( ξ ) 2 q + 1 ( 2 q + 1 ) ( 2 q + 1 ) ! ,
S M ( u , υ ) = M m = sinc [ M X ( u m / X ) ] ,
F M ( u , υ ) M m = F 0 ( m / X , υ ) sinc [ M X ( u m / X ) ] .
D k = A μ 2 sinc 2 ( μ k / N ) | B k | 2 , k = N / 2 , , 3 N / 2 1 ,
B k = 1 N n = 0 N 1 exp { i 2 π [ ( n + Δ n ) k / N ] } ,
D max = max N / 2 k 3 N / 2 1 { D k } ,
G ˆ k = { 1 D k / D max 0 . 5 0 otherwise .
obs = [ 1 N k = N / 2 3 N / 2 1 ( G k D k / D max ) 2 ] 1 / 2 .
η = k = N / 2 3 N / 2 1 μ 2 sinc 2 ( μ k / N ) | B k | 2 × 100 %
B k = B k + N , k = N / 2 , , N / 2 1 , = 1 N n = 0 N 1 exp ( i 2 π Δ n ) exp ( i 2 π Δ n k / N ) exp ( i 2 π n k / N ) .
k = 0 N 1 | B k | 2 = 1 ,
syn = [ 1 N k = N / 2 3 N / 2 1 ( G k γ s y n D k ) 2 ] 1 / 2 .
minimize x R n F ( x ) subject to l { x A L x } u
W / 2 x 0 , W x n + 1 x n , n = 0 , , N 2 , x N 1 X W / 2
γ syn γ max .

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