Abstract

A new method for designing holographic optical elements is presented. The method is based on matching the grating-spacing profile of the recording light interference pattern to the desired grating-spacing profile. We show that for designing near-field holograms, in which the optical images involved are close to the hologram aperture, the grating-matching technique is superior to the well-established aberration-balancing method introduced by Latta [Appl. Opt. 10, 609 (1971)].

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  4. C. B. Chen, R. G. Hegg, W. T. Johnson, W. B. King, D. F. Rock, R. Spande, “Visible-band testbed projector with a replicated diffractive optical element,” Appl. Opt. 38, 7105–7111 (1999).
    [CrossRef]
  5. K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
    [CrossRef]
  6. C. Maims, J. Hulme, P. R. Fielden, N. J. Goddard, “Grating coupled leaky waveguide microchannel sensor chips for optical analysis,” Sens. Actuators B 77, 671–678 (2001).
    [CrossRef]
  7. J. N. Latta, “Computer-based analysis imagery and aberrations. I. Hologram types and their nonchromatic aberrations,” Appl. Opt. 10, 599–608 (1971).
    [CrossRef] [PubMed]
  8. J. N. Latta, “Computer-based analysis imagery and aberrations. II. Aberrations induced by a wavelength shift,” Appl. Opt. 10, 609–618 (1971).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. L. H. Lin, E. T. Doherty, “Efficient and aberration-free wavefront reconstruction from holograms illuminated at wavelengths differing from the forming wavelength,” Appl. Opt. 10, 1314–1318 (1971).
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  13. K. Winick, “Designing efficient aberration-free holographic lenses in the presence of a construction-reconstruction wavelength shift,” J. Opt. Soc. Am. 72, 143–148 (1982).
    [CrossRef]
  14. H. P. Herzig, “Holographic optical elements (HOE) for semiconductor lasers,” Opt. Commun. 58, 144–148 (1986).
    [CrossRef]
  15. Y. Amitai, A. A. Friesem, V. Weiss, “Designing holographic lenses with different recording and readout wavelengths,” J. Opt. Soc. Am. A 7, 80–86 (1990).
    [CrossRef]
  16. J. Atencia, A. M. López, M. Quintanilla, “HOE recording with nonspherical waves,” J. Opt. A 3, 53–60 (2001).
    [CrossRef]

2001 (2)

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with nonspherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

C. Maims, J. Hulme, P. R. Fielden, N. J. Goddard, “Grating coupled leaky waveguide microchannel sensor chips for optical analysis,” Sens. Actuators B 77, 671–678 (2001).
[CrossRef]

2000 (1)

K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
[CrossRef]

1999 (1)

1997 (3)

1990 (1)

1986 (1)

H. P. Herzig, “Holographic optical elements (HOE) for semiconductor lasers,” Opt. Commun. 58, 144–148 (1986).
[CrossRef]

1982 (2)

1971 (4)

1967 (1)

Amitai, Y.

Atencia, J.

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with nonspherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

Billman, Å.

Bräuer, A.

Champagne, E. B.

Chen, C. B.

Dannberg, P.

Doherty, E. T.

Fielden, P. R.

C. Maims, J. Hulme, P. R. Fielden, N. J. Goddard, “Grating coupled leaky waveguide microchannel sensor chips for optical analysis,” Sens. Actuators B 77, 671–678 (2001).
[CrossRef]

Friesem, A. A.

Gale, M. T.

M. T. Gale, “Replication technology for holograms and diffractive optical elements,” J. Imaging Sci. Technol. 41, 211–220 (1997).

Goddard, N. J.

C. Maims, J. Hulme, P. R. Fielden, N. J. Goddard, “Grating coupled leaky waveguide microchannel sensor chips for optical analysis,” Sens. Actuators B 77, 671–678 (2001).
[CrossRef]

Hård, S.

Hegg, R. G.

Herzig, H. P.

H. P. Herzig, “Holographic optical elements (HOE) for semiconductor lasers,” Opt. Commun. 58, 144–148 (1986).
[CrossRef]

Hradaynath, R.

Hulme, J.

C. Maims, J. Hulme, P. R. Fielden, N. J. Goddard, “Grating coupled leaky waveguide microchannel sensor chips for optical analysis,” Sens. Actuators B 77, 671–678 (2001).
[CrossRef]

Jääskeläinen, T.

K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
[CrossRef]

Jacobsson, S.

Johnson, W. T.

Karthe, W.

Kettunen, V.

K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
[CrossRef]

King, W. B.

Kley, E.-B.

Latta, J. N.

Lautanen, J.

K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
[CrossRef]

Leppänen, V.-P.

K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
[CrossRef]

Lin, L. H.

Lindell, C.

López, A. M.

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with nonspherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

Lundbladh, L.

Maims, C.

C. Maims, J. Hulme, P. R. Fielden, N. J. Goddard, “Grating coupled leaky waveguide microchannel sensor chips for optical analysis,” Sens. Actuators B 77, 671–678 (2001).
[CrossRef]

Metha, P. C.

Mönkkönen, K.

K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
[CrossRef]

Nikolajeff, F.

Pakkanen, T. T.

K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
[CrossRef]

Quintanilla, M.

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with nonspherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

Rao, S. S.

Rock, D. F.

Schnabel, B.

Spande, R.

Waldhäusl, R.

Weiss, V.

Winick, K.

Appl. Opt. (8)

J. Imaging Sci. Technol. (1)

M. T. Gale, “Replication technology for holograms and diffractive optical elements,” J. Imaging Sci. Technol. 41, 211–220 (1997).

J. Mater. Chem. (1)

K. Mönkkönen, J. Lautanen, V. Kettunen, V.-P. Leppänen, T. T. Pakkanen, T. Jääskeläinen, “Replication of an antireflecting element in COC plastics using a hot embossing technique,” J. Mater. Chem. 10, 2634–2636 (2000).
[CrossRef]

J. Opt. A (1)

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with nonspherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Commun. (1)

H. P. Herzig, “Holographic optical elements (HOE) for semiconductor lasers,” Opt. Commun. 58, 144–148 (1986).
[CrossRef]

Sens. Actuators B (1)

C. Maims, J. Hulme, P. R. Fielden, N. J. Goddard, “Grating coupled leaky waveguide microchannel sensor chips for optical analysis,” Sens. Actuators B 77, 671–678 (2001).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

General schemes for (a) recording and (b) reconstructing a hologram with spherical waves: O, object wave; R, reference wave; C, reconstruction wave; I, desired image wave; and I′, actual reconstructed image wave. The aperture of the hologram is 2h.

Fig. 2
Fig. 2

(a) Recording scheme and (b) reconstruction scheme, where the ray picture is used to describe the local grating spacing at point P.

Fig. 3
Fig. 3

Sign convention used in the grating-matching formalism for (a) light propagation in the z direction and (b) light propagation opposite the z direction.

Fig. 4
Fig. 4

Example of a desired reconstructed near-field hologram.

Fig. 5
Fig. 5

Grating-spacing profiles along the hologram aperture where aberration balancing is used: thin curve, desired profile; thick curve, profile obtained after O and R data from the aberration balancing procedure are used.

Fig. 6
Fig. 6

Ray trace of image reconstruction for near-field hologram designed with aberration balancing.

Fig. 7
Fig. 7

Ray deviation from the desired image focus at the image plane for the aberration-balanced hologram.

Fig. 8
Fig. 8

Holographic image of an aberration-balanced near-field hologram. The picture is taken 2.05 mm behind the hologram, i.e., at the image plane: (a) directly transmitted reconstruction beam; (b) holographic image.

Fig. 9
Fig. 9

Grating-spacing profiles along the hologram aperture for a grating-matched hologram: thin curve, desired profile; thick curve, profile obtained after O and R data obtained from the grating matching procedure are used.

Fig. 10
Fig. 10

Ray trace of image reconstruction for hologram designed with a grating matching.

Fig. 11
Fig. 11

Ray deviation from the desired image focus at the image plane for the grating-matched hologram.

Fig. 12
Fig. 12

Holographic image of grating-matched near-field hologram: (a) directly transmitted reconstruction beam; (b) holographic image.

Equations (16)

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EI=AI exp2iπrCλC-rO-rRλR,
EI=AI exp2iπ rIλC.
rC-rIλC=rO-rRλR.
rq=zq2+x-xq21/2.
|x2-2xxq|  Rq2,
rqRq+x2-2xxq2Rq-4xq2x2-4xqx3+x48Rq3,
A2x+B2x2+A3x2+B3x3+C3x4=0,
A2=0, B2=0, B3=0, A3h2+C3h4=0.
ΛRx=λR|sinθO-sinθR|,
ΛCx=λC|sinθI-sinθC|.
ΛRx=λRx-xOx-xO2+zO21/2-x-xRx-xR2+zR21/2,
ΛCx=λCx-xCx-xC2+zC21/2+x-xIx-xI2+zI21/2,
ΛRx-ΛCxB0+B1x+B2x2+B3x3,
B0=0, B1=0, B2=0, B3=0.
xO=6.694 mm, zO=4.127 mm xR=6.694 mm, zR=35.86 mm.
xO=6.924 mm, zO=1.769 mm, xR=4.460 m, zR=14.12 m.

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