Abstract

Space-invariant, multilevel, diffractive phase elements are designed for large-scale pattern-formation tasks. The importance of the design algorithm and the phase-encoding geometry of the diffractive element is discussed with regard to the performance of both on- and off-axis reconstruction, notably for pixelated gratings. A new phase-encoding scheme is presented that results in an increase of the diffraction efficiency for the off-axis case.

© 1997 Optical Society of America

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References

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  1. L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitnonov, G. V. Uspleniev, “Focusators for laser-branding,” Opt. Lasers Eng. 15, 311–322 (1991).
    [CrossRef]
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    [CrossRef]
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  5. M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
    [CrossRef] [PubMed]
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  8. A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array, illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. J. R. Fienup, “Iterative method applied to image reconstructionand to computer generated holograms,” Opt. Eng. 19, 297–311 (1980).
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  13. N. C. Gallagher, B. Liu, “Method for computing kinoforms that reduces image reconstruction error,” Appl. Opt. 12, 2328–2335 (1973).
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    [CrossRef]
  15. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990).
    [CrossRef]
  16. J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
    [CrossRef]

1997 (1)

1995 (1)

1993 (2)

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1993).
[CrossRef] [PubMed]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

1992 (2)

M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

A. Vasara, M. R. Taghizadeh, J. Turunen, J. Westerholm, E. Noponen, H. Ichikawa, J. M. Miller, T. Jaakkola, S. Kuisma, “Binary surface-relief gratings for array, illumination in digital optics,” Appl. Opt. 31, 3320–3336 (1992).
[CrossRef] [PubMed]

1991 (1)

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitnonov, G. V. Uspleniev, “Focusators for laser-branding,” Opt. Lasers Eng. 15, 311–322 (1991).
[CrossRef]

1990 (1)

1989 (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Striebl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

1988 (1)

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstructionand to computer generated holograms,” Opt. Eng. 19, 297–311 (1980).
[CrossRef]

1973 (1)

1970 (1)

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Afshar-rad, T.

M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Bett, T. H.

D. M. Spriggs, T. H. Bett, “Laser damage studies of etched diffractive-optic components,” in SPIE Boulder Damage Symposia, Laser Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guether, B. E. Newman, M. J. Soileau, eds., Proc. SPIE2114, 136–144 (1994).

Blair, P.

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform and its Applications (Prentice-Hall International, London, 1988).

Bryngdahl, O.

Desselberger, M.

M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Doskolovich, L. L.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitnonov, G. V. Uspleniev, “Focusators for laser-branding,” Opt. Lasers Eng. 15, 311–322 (1991).
[CrossRef]

Downs, M. M.

J. Jahns, M. M. Downs, M. E. Prise, N. Striebl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstructionand to computer generated holograms,” Opt. Eng. 19, 297–311 (1980).
[CrossRef]

Gallagher, N. C.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, 1996).

Goodman, J. W.

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Ichikawa, H.

Jaakkola, T.

Jahns, J.

J. Jahns, M. M. Downs, M. E. Prise, N. Striebl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Kazanskiy, N. L.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitnonov, G. V. Uspleniev, “Focusators for laser-branding,” Opt. Lasers Eng. 15, 311–322 (1991).
[CrossRef]

Kharitnonov, S. I.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitnonov, G. V. Uspleniev, “Focusators for laser-branding,” Opt. Lasers Eng. 15, 311–322 (1991).
[CrossRef]

Khattak, F.

M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Kuisma, S.

Liu, B.

Luepken, H.

Miller, J. M.

Morrison, R. L.

Noponen, E.

Nuss, M. C.

Prise, M. E.

J. Jahns, M. M. Downs, M. E. Prise, N. Striebl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Ross, N.

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, “Multilevel-grating array generators: fabrication error analysis and experiments,” Appl. Opt. 32, 2519–2525 (1993).
[CrossRef] [PubMed]

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

Silvestri, A. M.

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Spriggs, D. M.

D. M. Spriggs, T. H. Bett, “Laser damage studies of etched diffractive-optic components,” in SPIE Boulder Damage Symposia, Laser Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guether, B. E. Newman, M. J. Soileau, eds., Proc. SPIE2114, 136–144 (1994).

Striebl, N.

J. Jahns, M. M. Downs, M. E. Prise, N. Striebl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Taghizadeh, M. R.

Turunen, J.

Uspleniev, G. V.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitnonov, G. V. Uspleniev, “Focusators for laser-branding,” Opt. Lasers Eng. 15, 311–322 (1991).
[CrossRef]

Vasara, A.

Viana, S.

M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Walker, S. J.

J. Jahns, M. M. Downs, M. E. Prise, N. Striebl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Westerholm, J.

Willi, O.

M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Wyrowski, F.

Appl. Opt. (4)

IBM J. Res. Dev. (1)

J. W. Goodman, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

J. Mod. Opt. (1)

J. M. Miller, M. R. Taghizadeh, J. Turunen, N. Ross, E. Noponen, A. Vasara, “Kinoform array illuminators in fused silica,” J. Mod. Opt. 40, 723–732 (1993).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

J. R. Fienup, “Iterative method applied to image reconstructionand to computer generated holograms,” Opt. Eng. 19, 297–311 (1980).
[CrossRef]

J. Jahns, M. M. Downs, M. E. Prise, N. Striebl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Opt. Lasers Eng. (1)

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitnonov, G. V. Uspleniev, “Focusators for laser-branding,” Opt. Lasers Eng. 15, 311–322 (1991).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

M. Desselberger, T. Afshar-rad, F. Khattak, S. Viana, O. Willi, “Nonuniformity imprint on the ablation surface of laser-irradiated targets,” Phys. Rev. Lett. 68, 1539–1542 (1992).
[CrossRef] [PubMed]

Other (3)

J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, 1996).

E. O. Brigham, The Fast Fourier Transform and its Applications (Prentice-Hall International, London, 1988).

D. M. Spriggs, T. H. Bett, “Laser damage studies of etched diffractive-optic components,” in SPIE Boulder Damage Symposia, Laser Induced Damage in Optical Materials, H. E. Bennett, L. L. Chase, A. H. Guether, B. E. Newman, M. J. Soileau, eds., Proc. SPIE2114, 136–144 (1994).

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Figures (9)

Fig. 1
Fig. 1

Profile of the modulation function d mn arising from the pixelated encoding geometry.

Fig. 2
Fig. 2

Maximum efficiency of an on-axis, pixelated DPE as a function of the pattern window size.

Fig. 3
Fig. 3

Maximum efficiency of the off-axis, pixelated DPE as a function of the displacement of the pattern window from the optical axis.

Fig. 4
Fig. 4

(a) Detail of one structure for the phase-encoding geometry of trapezoids in evenly spaced stripes. (b) Detail of one stripe for the angled-pixels phase-encoding geometry.

Fig. 5
Fig. 5

Profile of the altered modulation function d mn a for the angled-pixels encoding scheme (δ = -1/N).

Fig. 6
Fig. 6

Binary pattern of 128 × 128 pixels used in the design process.

Fig. 7
Fig. 7

Photograph showing an on-axis cross-pattern output. The cross structure is formed from lines composed of 127 × 11 diffraction orders.

Fig. 8
Fig. 8

Photograph showing an on-axis grid pattern output. The grid structure is formed from lines composed of 127 × 3–5 diffraction orders.

Fig. 9
Fig. 9

Photograph showing the reconstructed pattern from Fig. 6, positioned diagonally off axis by 4 diffraction orders.

Tables (2)

Tables Icon

Table 1 Comparison of Design Algorithms for On-Axis Pattern Formation

Tables Icon

Table 2 Comparison of the Design Algorithms for Off-Axis Pattern Formation

Equations (10)

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

Um, n=-expiθx, y-i2πmx+nydxdy,
Pmn=dmnθx, yFTexpiθx, y2,
dmnp=sinc2m/Msinc2n/N,
Pmn=12πmN2r=1Nj=1Mexpiθjr-2πnrN×exp-iπmajr+bjr×sincmbjr-ajr+n/N-exp-iπmaj+1r+bj+1r×sincmbj+1r-aj+1r+n/N.
Pmnsinc2mδ+n/N2πmN2r=1Nj=1Mexpiθjr-2πnrN×exp-iπmajr+bjr-exp-iπmaj+1r+bj+1r2,
δ+bjr-ajr.
Pmnsinc2mδ+n/Nsinc2m/MMN2×r=1Nj=1Mexpiθjr-2πnrN-2πmjM2.
dmna=sinc2mδ+n/Nsinc2m/M.
η=m,nεWPmn,
ΔR=Pmax-PminPmax+Pmin,

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