Abstract

We present a new technique for the design of diffractive optical elements (DOE’s) that is based on previous nonlinear least squares (NLS) and phase-shifting quantization methods [Appl. Opt. 36, 7297–7306 (1997)]. The technique uses a memory-matrix-based identification (MMBI) optimization procedure. We compare results from the MMBI method with those from iterative Fourier transform and NLS methods. In comparison, the MMBI DOE designs produce better-quality reconstructions for DOE’s with eight or more fabrication phase levels and generally have a higher signal-to-noise ratio and better uniformity.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Jahns, S. H. Lee, Optical Computing Hardware (Academic, San Diego, Calif., 1994).
  2. B. Hoanca, A. A. Sawchuk, “Cellular interconnects optimization algorithm for optoelectronic single-instruction multiple-data,” Appl. Opt. 37, 871–883 (1998).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  4. M. S. Kim, C. C. Guest, “Simulated annealing algorithm for binary phase only filters in pattern classification,” Appl. Opt. 29, 1203–1208 (1990).
    [CrossRef] [PubMed]
  5. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  6. C.-H. Chen, A. A. Sawchuk, “Nonlinear least-squares and phase-shifting quantization methods for diffractive optical element design,” Appl. Opt. 36, 7297–7306 (1997).
    [CrossRef]
  7. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990).
    [CrossRef]
  8. F. E. Udwadia, W. Proskurowski, “A memory-matrix-based identification methodology for structural and mechanical system,” Earthquake Eng. Struct. Dyn. 27, 1465–1481 (1998).
    [CrossRef]
  9. R. Kalaba, F. Udwadia, “An associative memory approach to the rapid identification of nonlinear structural and mechanical systems,” J. Optim. Theory Appl. 76, 207–223 (1993).
    [CrossRef]
  10. Routine leastsq has been replaced with lsqnonlin. Although leastsq currently works, it will be removed from the toolbox in the future.
  11. matlab software (Math Works, Inc., Natick, Mass., 1994).
  12. C.-H. Chen, B. Hoanca, C. B. Kuznia, A. A. Sawchuk, J.-M. Wu, “TRANslucent smart pixel array (TRANSPAR) chips for high throughput networks and SIMD signal processing,” IEEE J. Sel. Top. Quantum Electron. 5, 316–329 (1999).
    [CrossRef]
  13. C. B. Kuznia, “Cellular hypercube interconnections for optoelectronic smart pixel cellular arrays,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1994).
  14. J.-F. Lin, A. A. Sawchuk, “Optoelectronic communication speedup on mesh processors using reduced cellular hypercube interconnections,” in Optical Computing, Vol. 10 of 1995 OSA Technical Dig Series (Optical Society of America, Washington, D.C., 1995), pp. 269–271.

1999 (1)

C.-H. Chen, B. Hoanca, C. B. Kuznia, A. A. Sawchuk, J.-M. Wu, “TRANslucent smart pixel array (TRANSPAR) chips for high throughput networks and SIMD signal processing,” IEEE J. Sel. Top. Quantum Electron. 5, 316–329 (1999).
[CrossRef]

1998 (2)

F. E. Udwadia, W. Proskurowski, “A memory-matrix-based identification methodology for structural and mechanical system,” Earthquake Eng. Struct. Dyn. 27, 1465–1481 (1998).
[CrossRef]

B. Hoanca, A. A. Sawchuk, “Cellular interconnects optimization algorithm for optoelectronic single-instruction multiple-data,” Appl. Opt. 37, 871–883 (1998).
[CrossRef]

1997 (1)

1993 (1)

R. Kalaba, F. Udwadia, “An associative memory approach to the rapid identification of nonlinear structural and mechanical systems,” J. Optim. Theory Appl. 76, 207–223 (1993).
[CrossRef]

1990 (2)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Chen, C.-H.

C.-H. Chen, B. Hoanca, C. B. Kuznia, A. A. Sawchuk, J.-M. Wu, “TRANslucent smart pixel array (TRANSPAR) chips for high throughput networks and SIMD signal processing,” IEEE J. Sel. Top. Quantum Electron. 5, 316–329 (1999).
[CrossRef]

C.-H. Chen, A. A. Sawchuk, “Nonlinear least-squares and phase-shifting quantization methods for diffractive optical element design,” Appl. Opt. 36, 7297–7306 (1997).
[CrossRef]

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, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Guest, C. C.

Hoanca, B.

C.-H. Chen, B. Hoanca, C. B. Kuznia, A. A. Sawchuk, J.-M. Wu, “TRANslucent smart pixel array (TRANSPAR) chips for high throughput networks and SIMD signal processing,” IEEE J. Sel. Top. Quantum Electron. 5, 316–329 (1999).
[CrossRef]

B. Hoanca, A. A. Sawchuk, “Cellular interconnects optimization algorithm for optoelectronic single-instruction multiple-data,” Appl. Opt. 37, 871–883 (1998).
[CrossRef]

Jahns, J.

J. Jahns, S. H. Lee, Optical Computing Hardware (Academic, San Diego, Calif., 1994).

Kalaba, R.

R. Kalaba, F. Udwadia, “An associative memory approach to the rapid identification of nonlinear structural and mechanical systems,” J. Optim. Theory Appl. 76, 207–223 (1993).
[CrossRef]

Kim, M. S.

Kuznia, C. B.

C.-H. Chen, B. Hoanca, C. B. Kuznia, A. A. Sawchuk, J.-M. Wu, “TRANslucent smart pixel array (TRANSPAR) chips for high throughput networks and SIMD signal processing,” IEEE J. Sel. Top. Quantum Electron. 5, 316–329 (1999).
[CrossRef]

C. B. Kuznia, “Cellular hypercube interconnections for optoelectronic smart pixel cellular arrays,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1994).

Lee, S. H.

J. Jahns, S. H. Lee, Optical Computing Hardware (Academic, San Diego, Calif., 1994).

Lin, J.-F.

J.-F. Lin, A. A. Sawchuk, “Optoelectronic communication speedup on mesh processors using reduced cellular hypercube interconnections,” in Optical Computing, Vol. 10 of 1995 OSA Technical Dig Series (Optical Society of America, Washington, D.C., 1995), pp. 269–271.

Proskurowski, W.

F. E. Udwadia, W. Proskurowski, “A memory-matrix-based identification methodology for structural and mechanical system,” Earthquake Eng. Struct. Dyn. 27, 1465–1481 (1998).
[CrossRef]

Sawchuk, A. A.

C.-H. Chen, B. Hoanca, C. B. Kuznia, A. A. Sawchuk, J.-M. Wu, “TRANslucent smart pixel array (TRANSPAR) chips for high throughput networks and SIMD signal processing,” IEEE J. Sel. Top. Quantum Electron. 5, 316–329 (1999).
[CrossRef]

B. Hoanca, A. A. Sawchuk, “Cellular interconnects optimization algorithm for optoelectronic single-instruction multiple-data,” Appl. Opt. 37, 871–883 (1998).
[CrossRef]

C.-H. Chen, A. A. Sawchuk, “Nonlinear least-squares and phase-shifting quantization methods for diffractive optical element design,” Appl. Opt. 36, 7297–7306 (1997).
[CrossRef]

J.-F. Lin, A. A. Sawchuk, “Optoelectronic communication speedup on mesh processors using reduced cellular hypercube interconnections,” in Optical Computing, Vol. 10 of 1995 OSA Technical Dig Series (Optical Society of America, Washington, D.C., 1995), pp. 269–271.

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, 237–246 (1972).

Udwadia, F.

R. Kalaba, F. Udwadia, “An associative memory approach to the rapid identification of nonlinear structural and mechanical systems,” J. Optim. Theory Appl. 76, 207–223 (1993).
[CrossRef]

Udwadia, F. E.

F. E. Udwadia, W. Proskurowski, “A memory-matrix-based identification methodology for structural and mechanical system,” Earthquake Eng. Struct. Dyn. 27, 1465–1481 (1998).
[CrossRef]

Wu, J.-M.

C.-H. Chen, B. Hoanca, C. B. Kuznia, A. A. Sawchuk, J.-M. Wu, “TRANslucent smart pixel array (TRANSPAR) chips for high throughput networks and SIMD signal processing,” IEEE J. Sel. Top. Quantum Electron. 5, 316–329 (1999).
[CrossRef]

Wyrowski, F.

Appl. Opt. (3)

Earthquake Eng. Struct. Dyn. (1)

F. E. Udwadia, W. Proskurowski, “A memory-matrix-based identification methodology for structural and mechanical system,” Earthquake Eng. Struct. Dyn. 27, 1465–1481 (1998).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C.-H. Chen, B. Hoanca, C. B. Kuznia, A. A. Sawchuk, J.-M. Wu, “TRANslucent smart pixel array (TRANSPAR) chips for high throughput networks and SIMD signal processing,” IEEE J. Sel. Top. Quantum Electron. 5, 316–329 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Optim. Theory Appl. (1)

R. Kalaba, F. Udwadia, “An associative memory approach to the rapid identification of nonlinear structural and mechanical systems,” J. Optim. Theory Appl. 76, 207–223 (1993).
[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, 237–246 (1972).

Other (6)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Routine leastsq has been replaced with lsqnonlin. Although leastsq currently works, it will be removed from the toolbox in the future.

matlab software (Math Works, Inc., Natick, Mass., 1994).

C. B. Kuznia, “Cellular hypercube interconnections for optoelectronic smart pixel cellular arrays,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1994).

J.-F. Lin, A. A. Sawchuk, “Optoelectronic communication speedup on mesh processors using reduced cellular hypercube interconnections,” in Optical Computing, Vol. 10 of 1995 OSA Technical Dig Series (Optical Society of America, Washington, D.C., 1995), pp. 269–271.

J. Jahns, S. H. Lee, Optical Computing Hardware (Academic, San Diego, Calif., 1994).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Flow diagram of the MMBI method.

Fig. 2
Fig. 2

Diagram of the 3 × 3 uniform spot-array pattern.

Fig. 3
Fig. 3

Diagram of the [4, 8] reduced cellular hypercube pattern.

Fig. 4
Fig. 4

Diagram of the off-axis letter X pattern.

Tables (3)

Tables Icon

Table 1 Simulation Results of Different Methods for 3 × 3 Uniform Spot-Array Pattern

Tables Icon

Table 2 Simulation Results of Different Methods for [4, 8] Reduced Cellular Hypercube Pattern

Tables Icon

Table 3 Simulation Results of Different Methods for Off-Axis Letter X Pattern

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

Id=|FT-1G×W|2=|FT-1expiΘ×W|2,
I=|FT-1Gˆ×W|2=|FT-1expiΘˆ×W|2,
A0=Φ0P0TP0P0T+αE-1.
β1=ΔI¯0/I¯d=I¯d-I¯ˆ0/I¯d.
θ¯i,jk=1+μi,jβkθˆ¯ik-1 for i=1, 2,, MN and j=1, 2,.
I¯d-I¯jk<δΔI¯k-1,
Ak=ΦkPkTPkPkT+αE-1.
θˆ¯k=AkI¯d.
ΔI¯k=I¯d-I¯ˆk
βk+1=ΔI¯k/I¯d.
NU=Smax-Smin/Smax+Smin×100.
ηw=m,n Srm, nm,n Irm, n×100.
ηg=m,n Srm, n×100.
SNR=10 log10Smin/Nmax.
QF=w1100-NU+w2ηw+w3ηg+w4SNR,
ηo=m,nR Idm, nm,n Idm, n,

Metrics