Abstract

We show that detour-phase encoding with a multilevel blaze structure as a carrier grating is especially suited to the implementation of diffractive elements with relatively high complexity in one axis. For our proposal the carrier grating is aligned perpendicularly to this axis. In this way the element can be encoded with a high space–bandwidth product and a high phase resolution by use of a moderate carrier frequency. Moreover, this frequency can be adjusted to isolate the reconstructed field from the noise resulting from high diffraction orders of the carrier grating or caused by etching errors during fabrication.

© 1998 Optical Society of America

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References

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  1. J. W. Goodmann, A. M. Silvestri, “Some effects of Fourier-domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
    [CrossRef]
  2. U. Krackhardt, “Optimum quantization rules for computer generated holograms,” in Diffractive Optics: Design, Fabrication and Applications, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 139–142.
  3. J. N. Mait, “Understanding diffractive optic design in the scalar domain,” J. Opt. Soc. Am. A 12, 2145–2158 (1995).
    [CrossRef]
  4. H. P. Herzig, D. Prongue, R. Dändlier, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, 1307–1309 (1990).
    [CrossRef]
  5. F. Wirowski, “Modulation schemes of phase gratings,” Opt. Eng. 31, 251–257 (1992).
    [CrossRef]
  6. J. Jahns, “Diffractive optical elements for optical computing,” in Optical Computing Hardware, J. Jahns, S. H. Lee, eds. (Academic, San Diego, Calif., 1994), pp. 137–167.
  7. V. Arrizón, M. Testorf, “Efficiency limit of spatially quantized Fourier array illuminators,” Opt. Lett. 22, 197–199 (1997).
    [CrossRef] [PubMed]
  8. V. Arrizón, S. Sinzinger, “Modified quantization schemes for Fourier-type array generators,” Opt. Commun. 140, 309–315 (1997).
    [CrossRef]
  9. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  10. J. Turunen, J. Fagerholm, A. Vasara, M. Taghizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
    [CrossRef]
  11. S. Sinzinger, V. Arrizón, “High-efficiency detour-phase holograms,” Opt. Lett. 22, 928–930 (1997).
    [CrossRef] [PubMed]
  12. J. Ojeda-Castañeda, V. Arrizón, “Syntheses of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
    [CrossRef]
  13. V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
    [CrossRef]
  14. J. Ojeda-Castañeda, A. W. Lohmann, “Youngs experiment in signal systhesis,” in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), Vol. 3, pp. 263–280.
    [CrossRef]
  15. S. Sinzinger, V. Arrizón, “The Detourphase as design freedom for kinoform diffractive optical elements,” Vol. 12 of EOS Technical Digest Series (European Space Agency, Noordwijk, The Netherlands, 1997), pp. 44–45.

1997

1995

1994

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

1992

F. Wirowski, “Modulation schemes of phase gratings,” Opt. Eng. 31, 251–257 (1992).
[CrossRef]

J. Ojeda-Castañeda, V. Arrizón, “Syntheses of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
[CrossRef]

1990

H. P. Herzig, D. Prongue, R. Dändlier, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, 1307–1309 (1990).
[CrossRef]

J. Turunen, J. Fagerholm, A. Vasara, M. Taghizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
[CrossRef]

1970

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

1967

Arrizón, V.

S. Sinzinger, V. Arrizón, “High-efficiency detour-phase holograms,” Opt. Lett. 22, 928–930 (1997).
[CrossRef] [PubMed]

V. Arrizón, M. Testorf, “Efficiency limit of spatially quantized Fourier array illuminators,” Opt. Lett. 22, 197–199 (1997).
[CrossRef] [PubMed]

V. Arrizón, S. Sinzinger, “Modified quantization schemes for Fourier-type array generators,” Opt. Commun. 140, 309–315 (1997).
[CrossRef]

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

J. Ojeda-Castañeda, V. Arrizón, “Syntheses of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
[CrossRef]

S. Sinzinger, V. Arrizón, “The Detourphase as design freedom for kinoform diffractive optical elements,” Vol. 12 of EOS Technical Digest Series (European Space Agency, Noordwijk, The Netherlands, 1997), pp. 44–45.

Dändlier, R.

H. P. Herzig, D. Prongue, R. Dändlier, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, 1307–1309 (1990).
[CrossRef]

Fagerholm, J.

Goodmann, J. W.

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

Herzig, H. P.

H. P. Herzig, D. Prongue, R. Dändlier, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, 1307–1309 (1990).
[CrossRef]

Ibarra, J. G.

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

Jahns, J.

J. Jahns, “Diffractive optical elements for optical computing,” in Optical Computing Hardware, J. Jahns, S. H. Lee, eds. (Academic, San Diego, Calif., 1994), pp. 137–167.

Krackhardt, U.

U. Krackhardt, “Optimum quantization rules for computer generated holograms,” in Diffractive Optics: Design, Fabrication and Applications, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 139–142.

Lohmann, A. W.

A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
[CrossRef] [PubMed]

J. Ojeda-Castañeda, A. W. Lohmann, “Youngs experiment in signal systhesis,” in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), Vol. 3, pp. 263–280.
[CrossRef]

Mait, J. N.

Ojeda-Castañeda, J.

J. Ojeda-Castañeda, V. Arrizón, “Syntheses of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
[CrossRef]

J. Ojeda-Castañeda, A. W. Lohmann, “Youngs experiment in signal systhesis,” in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), Vol. 3, pp. 263–280.
[CrossRef]

Paris, D. P.

Prongue, D.

H. P. Herzig, D. Prongue, R. Dändlier, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, 1307–1309 (1990).
[CrossRef]

Silvestri, A. M.

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

Sinzinger, S.

S. Sinzinger, V. Arrizón, “High-efficiency detour-phase holograms,” Opt. Lett. 22, 928–930 (1997).
[CrossRef] [PubMed]

V. Arrizón, S. Sinzinger, “Modified quantization schemes for Fourier-type array generators,” Opt. Commun. 140, 309–315 (1997).
[CrossRef]

S. Sinzinger, V. Arrizón, “The Detourphase as design freedom for kinoform diffractive optical elements,” Vol. 12 of EOS Technical Digest Series (European Space Agency, Noordwijk, The Netherlands, 1997), pp. 44–45.

Taghizadeh, M.

Testorf, M.

Turunen, J.

Vasara, A.

Wirowski, F.

F. Wirowski, “Modulation schemes of phase gratings,” Opt. Eng. 31, 251–257 (1992).
[CrossRef]

Appl. Opt.

IBM J. Res. Dev.

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

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

H. P. Herzig, D. Prongue, R. Dändlier, “Design and fabrication of highly efficient fan-out elements,” Jpn. J. Appl. Phys. 29, 1307–1309 (1990).
[CrossRef]

Microwave Opt. Technol. Lett.

J. Ojeda-Castañeda, V. Arrizón, “Syntheses of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
[CrossRef]

Opt. Commun.

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

V. Arrizón, S. Sinzinger, “Modified quantization schemes for Fourier-type array generators,” Opt. Commun. 140, 309–315 (1997).
[CrossRef]

Opt. Eng.

F. Wirowski, “Modulation schemes of phase gratings,” Opt. Eng. 31, 251–257 (1992).
[CrossRef]

Opt. Lett.

Other

J. Jahns, “Diffractive optical elements for optical computing,” in Optical Computing Hardware, J. Jahns, S. H. Lee, eds. (Academic, San Diego, Calif., 1994), pp. 137–167.

U. Krackhardt, “Optimum quantization rules for computer generated holograms,” in Diffractive Optics: Design, Fabrication and Applications, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 139–142.

J. Ojeda-Castañeda, A. W. Lohmann, “Youngs experiment in signal systhesis,” in Trends in Optics, A. Consortini, ed. (Academic, San Diego, Calif., 1996), Vol. 3, pp. 263–280.
[CrossRef]

S. Sinzinger, V. Arrizón, “The Detourphase as design freedom for kinoform diffractive optical elements,” Vol. 12 of EOS Technical Digest Series (European Space Agency, Noordwijk, The Netherlands, 1997), pp. 44–45.

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Figures (4)

Fig. 1
Fig. 1

Schematic representation of a quantized 1-D phase DE.

Fig. 2
Fig. 2

Two periods of the phase profile of the blaze carrier grating B(y), quantized with eight phase levels.

Fig. 3
Fig. 3

FAI for the generation of a 1 × 480 spot array: (a) Central portion in the basic cell of the FAI’s phase profile. (b) Computed intensity distribution in the reconstruction plane. The normalized intensity (≈0.02) occurs for diffraction orders from -239 to +240.

Fig. 4
Fig. 4

Detour-phase encoding of the 1 × 480 spot-array generator in Fig. 3: (a) Density plot of a section in the KDPH’s basic cell. (b) CCD image of the experimentally generated spot array. (c) Close-up with 58 spots of the reconstructed image.

Equations (14)

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D x ,   y = rect y / L n = 1 N exp i ϕ n rect x - na / a ,
D ˜ u ,   v = L   sinc Lv W u ;   ϕ n ,
W u ;   ϕ n = a   sinc au n = 1 N exp i ϕ n exp - i 2 π nau .
H x ,   y = rect y / L n = 1 N   B y - Δ n rect x - na / a .
H ˜ u ,   v = L δ u sinc Lv     B ˜ v W u ;   - 2 π v Δ n ,
B 0 y = n = 0 7 exp in π / 4 rect y - nb / b ,
A p = sinc p / 8 ,
B ˜ v = m = -   A 8 m + 1 δ v - 8 m + 1 / d B .
H ˜ u ,   v = L   m =   A 8 m + 1   sinc L v - 8 m + 1 / d B × W u ;   8 m + 1 ϕ n .
H ˜ 0 u ,   v = A 1 L   sinc L v - 1 / d B W u ;   ϕ n = A 1 D ˜ u ,   v - 1 / d B .
L = K 1 d B / 8
d B = M d a d , L = Na , a d = a ,
K 1 = 8 N / M d .
K 2 = N / M d .

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