Abstract

We present what is to our knowledge a new type of diffractive optical element (DOE), the computer-generated stratified diffractive optical element (SDOE), a hybridization of thin computer-generated DOEs and volume holograms. A model and several algorithms for calculating computer-generated SDOEs are given. Simulations and experimental results are presented that exhibit the properties of computer-generated SDOEs: the strong angular and wavelength selectivity of SDOEs makes it possible to store multiple pages in a computer-generated SDOE, which can be read out separately (multiplexing). The reconstruction of an optimized SDOE has a higher quality than the reconstruction of optimized one-layer DOEs. SDOEs can be calculated to have only one diffraction order.

© 2003 Optical Society of America

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References

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  1. R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1972).
  2. F. Wyrowski, O. Bryngdhal, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
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  3. J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
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  4. J. Bengtsson, “Kinoform designed to produce different fan-out patterns for two wavelengths,” Appl. Opt. 37, 2011–2020 (1998).
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    [CrossRef]
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  12. D. Kermisch, “Image reconstruction from phase information only,” J. Opt. Soc. Am. 60, 15–17 (1970).
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    [CrossRef]

1999

1998

1997

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

R. S. Bennink, A. K. Powell, D. A. Fish, “An efficient method of implementing near-field diffraction in computer-generated hologram design,” Opt. Commun. 141, 194–202 (1997).
[CrossRef]

1991

F. Wyrowski, O. Bryngdhal, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

1986

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, “Bilayer holograms: theory and experiments,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

1982

1972

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

1970

Bengtsson, J.

Bennink, R. S.

R. S. Bennink, A. K. Powell, D. A. Fish, “An efficient method of implementing near-field diffraction in computer-generated hologram design,” Opt. Commun. 141, 194–202 (1997).
[CrossRef]

Bryngdhal, O.

F. Wyrowski, O. Bryngdhal, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Chambers, D. M.

Evtikhiev, N. N.

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, “Bilayer holograms: theory and experiments,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Fienup, J. R.

Fish, D. A.

R. S. Bennink, A. K. Powell, D. A. Fish, “An efficient method of implementing near-field diffraction in computer-generated hologram design,” Opt. Commun. 141, 194–202 (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 (Stuttgart) 35, 237–246 (1972).

Goodman, J. W.

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

Haist, T.

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

Ichikawa, H.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

Jannson, T.

K. Spariosu, T. Tengara, T. Jannson, “Stratified volume diffractive elements: modeling and applications,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 101–109 (1997).
[CrossRef]

Kermisch, D.

Miller, J. M.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

Mirovitskiy, D. I.

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, “Bilayer holograms: theory and experiments,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Noponen, E.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

Nordin, G. P.

Powell, A. K.

R. S. Bennink, A. K. Powell, D. A. Fish, “An efficient method of implementing near-field diffraction in computer-generated hologram design,” Opt. Commun. 141, 194–202 (1997).
[CrossRef]

Rostovtseva, N. V.

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, “Bilayer holograms: theory and experiments,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Saxton, W. O.

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

Schönleber, M.

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

Serov, O. B.

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, “Bilayer holograms: theory and experiments,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Spariosu, K.

K. Spariosu, T. Tengara, T. Jannson, “Stratified volume diffractive elements: modeling and applications,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 101–109 (1997).
[CrossRef]

Syms, R. R. A.

R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1972).

Taghizadeh, M. R.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

Tengara, T.

K. Spariosu, T. Tengara, T. Jannson, “Stratified volume diffractive elements: modeling and applications,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 101–109 (1997).
[CrossRef]

Tiziani, H. J.

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

Turunen, J.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

Vasara, A.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

Westerholm, J.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

Wyrowski, F.

F. Wyrowski, O. Bryngdhal, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Yakovleva, T. V.

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, “Bilayer holograms: theory and experiments,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Acta

N. N. Evtikhiev, D. I. Mirovitskiy, N. V. Rostovtseva, O. B. Serov, T. V. Yakovleva, “Bilayer holograms: theory and experiments,” Opt. Acta 33, 255–268 (1986).
[CrossRef]

Opt. Commun.

J. Turunen, A. Vasara, H. Ichikawa, E. Noponen, J. Westerholm, M. R. Taghizadeh, J. M. Miller, “Storage of multiple images in a thin synthetic Fourier hologram,” Opt. Commun. 84, 383–392 (1991).
[CrossRef]

R. S. Bennink, A. K. Powell, D. A. Fish, “An efficient method of implementing near-field diffraction in computer-generated hologram design,” Opt. Commun. 141, 194–202 (1997).
[CrossRef]

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

Optik (Stuttgart)

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

Rep. Prog. Phys.

F. Wyrowski, O. Bryngdhal, “Digital holography as part of diffractive optics,” Rep. Prog. Phys. 54, 1481–1571 (1991).
[CrossRef]

Other

R. R. A. Syms, Practical Volume Holography (Clarendon, Oxford, 1972).

K. Spariosu, T. Tengara, T. Jannson, “Stratified volume diffractive elements: modeling and applications,” in Optical Thin Films V: New Developments, R. L. Hall, ed., Proc. SPIE3133, 101–109 (1997).
[CrossRef]

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

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Figures (10)

Fig. 1
Fig. 1

Schematic illustration of the setup of a SDOE. The SDOE consists of two or more layers of separate DOEs. If the SDOE is illuminated by a laser beam, a reconstruction image arises in the reconstruction plane.

Fig. 2
Fig. 2

Schematic illustration of the propagation of light between two single DOEs, represented by a near-field transform.

Fig. 3
Fig. 3

Capital letter A in a signal window off center.

Fig. 4
Fig. 4

(a) Simulated reconstruction of a two-layer binary diffractive optical element with a binary random distribution in the second layer, calculated with the phase levels 0 and π/2. (b) Fourier transform of the first layer of Fig. 6(a). (c) Same as Fig. 6(a) calculated with the phase levels 0 and π. (d) Fourier transform of the first layer of Fig. 6(c).

Fig. 5
Fig. 5

Simulated reconstruction of a two-layer binary diffractive optical element calculated with the phase levels 0 and π, with a binary kinoform (F) in the second layer, reconstructed with the phase levels 0 and π/2.

Fig. 6
Fig. 6

(a) Angular selectivity of a two-layer binary phase element: diffraction efficiency η (solid curve) and MSE (dashed curve). (b) Wavelength selectivity of a two-layer binary phase element: diffraction efficiency η (solid curve) and MSE (dashed curve). (c) Phaseshift insensitivity of a two-layer binary phase element: diffraction efficiency η (solid curve) and MSE (dashed curve).

Fig. 7
Fig. 7

(a) Angular multiplexed two-layer binary phase element: diffraction efficiency η A (solid curve), MSE A (dashed curve), diffraction efficiency η F (dashed and dotted curve), MSE F (dotted curve). (b) Wavelength multiplexed two-layer binary phase element: diffraction efficiency η A (solid curve), MSE A (dashed curve), diffraction efficiency η F (dashed and dotted curve), MSE F (dotted curve).

Fig. 8
Fig. 8

Experimental reconstructions of two-layer binary diffractive optical elements with a binary random distribution in the second layer. (a) Only one diffraction order appears. (b) The whole reconstruction plane can be used.

Fig. 9
Fig. 9

Experimental reconstructions of two-layer binary diffractive optical elements with a kinoform in the second layer. (a) When illuminated under 0 degree the reconstruction consists of the reconstruction of the kinoform (2D barcode) and the coded signal (letters O.K.). (b) When illuminated under a slightly different angle of incidence the letters O.K. disappear.

Fig. 10
Fig. 10

Experimental reconstruction of a angular multiplexed two-layer binary diffractive optical element with page b for 0 degree and page 6 for 1 degree: (a) 0 degree, (b) 0.5 degrees, (c) 1 degree.

Tables (1)

Tables Icon

Table 1 Mean Squared Error (MSE) and Diffraction Efficiency ηa

Equations (26)

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

hkx, y=|hkx, y|expiΦkx, y, k=1K.
Ax, y, z=|Ax, y, z|expiΦAx, y, z,
Ax, y, zk+=hkx, yAx, y, zk-=|hkx, yAx, y, zk-|expiΦkx, y+ΦAx, y, zk-,
Ax, y, zk+1-=NFTzk+1-zkAx, y, zk+,
Ax, y, z=NFTΔzAx, y, z-Δz=FT-1FTAx, y, z-Δzexp-ikzΔz=00FTAx, y, z-Δzνx, νy×exp-i2πνxx+νyy×exp-ikzΔzdνxdνy,
Aoutx, y=hΚNFTzΚ-zΚ-1h3×NFTz3-z2h2NFTz2-z1h1Ainx, y,
Ainx, y=1h1NFTz2-z1-1 1hK-2×NFTzK-1-zK-2-11hK-1×NFTzK-zK-1-11hK Aoutx, y.
Rx, y=TAoutx, y.
Ãoutx, y=T-1R˜x, y.
Ax, y, zr-=NFTzr-zr-1h3×NFTz3-z2h2NFTz2-z1h1Ainx, y,
Ãx, y, zr+=NFTzr+1-zr1 1hK-2×NFTzK-1-zK-2-11hK-1×NFTzK-zK-1-11hK Ãoutx, y.
h˜rx, y=Ãx, y, zr+Ax, y, zr-.
hrx, y=Ch˜rx, y,
Rx, y=ThKNFTzK-zK-1hr+1×NFTzr+1-zrhrAx, y, zr-.
hrx, y=C1Jj=1J h˜rjx, y.
h1x, y=expiβΦ1x, y
h2x, y=expiβΦ2x, y
Rx, y=FTh2x, yNFTΔzh1x, y,
h1x, y=expiβΦ1x, y=1+eiβ-1Φ1x, y; Φ1x, y=01.
NFTΔzh1x, y=NFTΔz1+eiβ-1Φ1x, y =FT-1FT1+eiβ-1Φ1x, yexp-ikzΔz =exp-ikΔz+eiβ-1NFTΔzΦ1x, y,
Rx, y=FTh2NFTΔzh1=FT1+eiβ-1Φ2x, y×exp-ikΔz+eiβ-1NFTΔzΦ1x, y=δx, yexp-ikΔz+eiβ-1×FTΦ2x, yexp-ikΔz+FTNFTΔzΦ1x, y +eiβ-12×FTΦ2x, yNFTΔzΦ1x, y,
h1x, y=CNFTΔz-1FT-1R˜x, yh2x, y
h2x, y=CFT-1R˜x, yNFTΔzh1x, y.
MSE=1x1-x0y1-y0x0x1y0y1|R˜x, y|-a|Rx, y|2dxdy,
a=x0x1y0y1 |R˜x, yRx, ydxdyx0x1y0y1 |Rx, y|2dxdy.
η=x0x1y0y1 |Rx, y|2dxdy |Rx, y|2dxdy.

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