Abstract

A new type of multiple imaging and multiple Fourier transformation system under coherent illumination using microlens arrays has been developed. The optical system is based on geometrical optics instead of convolution or diffraction. As a result, it has the advantage of design flexibility especially in alignment of the duplicate images. The experimental results of the system, which are implemented using planar microlens arrays fabricated by an ion exchange technique, are also discussed.

© 1990 Optical Society of America

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References

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  1. I. Glaser, “Noncoherent Parallel Optical Processor for Discrete Two-Dimensional Linear Transformations,” Opt. Lett. 5, 449–451 (1980).
    [CrossRef] [PubMed]
  2. I. Glaser, L. Perelmutter, “Optical Interconnections for Digital Processing: a Noncoherent Method,” Opt. Lett. 11, 53–55 (1986).
    [CrossRef] [PubMed]
  3. K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array and its Applications to Imaging Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).
  4. A. Akiba, K. Iga, “Image Multiplexer (IMX) Using Planar Microlens Array,” in Technical Digest, MOC/GRIN ’89 (Publisher, Location, 1989), pp. 228–231.
  5. H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
    [CrossRef]
  6. F. B. McCormick, “Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings,” Opt. Eng. 28, 299–304 (1989).
    [CrossRef]
  7. L. P. Boivin, “Multiple Imaging Using Various Types of Simple Phase Gratings,” Appl. Opt. 11, 1782–1792 (1972).
    [CrossRef] [PubMed]
  8. H. Machida, J. Nitta, A. Seko, H. Kobayashi, “High-Efficiency Fiber Grating for Producing Multiple Beams of Uniform Intensity,” Appl. Opt. 23, 330–332 (1984).
    [CrossRef] [PubMed]
  9. A. S. Kumar, R. M. Vasu, “Multiple Imaging with an Aberration Optimized Hololens Array,” Opt. Eng. 28, 903–908 (1989).
    [CrossRef]
  10. L. K. Anderson, “Holographic Optical Memory for Bulk Data Storage,” Bell Lab. Rec.319–325 (Nov.1968).
  11. A. Kolodziejczyk, “Realization of Fourier Images Without Using a Lens by Sampling the Optical Object,” Opt. Acta 32, 741–746 (1985).
    [CrossRef]
  12. A. Kolodziejczyk, “Lensless Multiple Image Formation by Using a Sampling Filter,” Opt. Acta 59, 97–102 (1986).
  13. A. S. Kumar, R. M. Vasu, “Multiple Imaging and Multichannel Optical Processing with Split Lenses,” Appl. Opt. 26, 5345–5349 (1987).
    [CrossRef] [PubMed]
  14. J. C. Kirsch, D. A. Gregory, T. D. Hudson, D. J. Lanteigne, “Design of Photopolymer Holograms for Optical Interconnect Applications,” Opt. Eng. 27, 301–308 (1988).
    [CrossRef]
  15. D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4650–4570 (1984).
    [CrossRef]
  16. P. Asthana, A. Akiba, T. Yamaki, K. Nishizawa, M. Oikawa, “Gradient-Index Lens Array Matched Filtering,” Opt. Lett. 13, 84–86 (1988).
    [CrossRef] [PubMed]
  17. M. Agu, A. Akiba, S. Kamemaru, “A Parallel Processing Optical-Digital Recognition System as a Model of Biological Visual Perception,” Opt. Commun. 66, 69–73 (1988).
    [CrossRef]
  18. K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: an Application of the Planar Microlens,” Appl. Opt. 21, 3456–3460 (1982).
    [CrossRef] [PubMed]
  19. M. Oikawa, E. Okuda, K. Hamanaka, H. Nemoto, “Integrated Planar Microlens and its Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 898, 3–11 (1988).

1989

F. B. McCormick, “Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings,” Opt. Eng. 28, 299–304 (1989).
[CrossRef]

A. S. Kumar, R. M. Vasu, “Multiple Imaging with an Aberration Optimized Hololens Array,” Opt. Eng. 28, 903–908 (1989).
[CrossRef]

1988

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array and its Applications to Imaging Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).

J. C. Kirsch, D. A. Gregory, T. D. Hudson, D. J. Lanteigne, “Design of Photopolymer Holograms for Optical Interconnect Applications,” Opt. Eng. 27, 301–308 (1988).
[CrossRef]

P. Asthana, A. Akiba, T. Yamaki, K. Nishizawa, M. Oikawa, “Gradient-Index Lens Array Matched Filtering,” Opt. Lett. 13, 84–86 (1988).
[CrossRef] [PubMed]

M. Agu, A. Akiba, S. Kamemaru, “A Parallel Processing Optical-Digital Recognition System as a Model of Biological Visual Perception,” Opt. Commun. 66, 69–73 (1988).
[CrossRef]

M. Oikawa, E. Okuda, K. Hamanaka, H. Nemoto, “Integrated Planar Microlens and its Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 898, 3–11 (1988).

1987

1986

A. Kolodziejczyk, “Lensless Multiple Image Formation by Using a Sampling Filter,” Opt. Acta 59, 97–102 (1986).

I. Glaser, L. Perelmutter, “Optical Interconnections for Digital Processing: a Noncoherent Method,” Opt. Lett. 11, 53–55 (1986).
[CrossRef] [PubMed]

1985

A. Kolodziejczyk, “Realization of Fourier Images Without Using a Lens by Sampling the Optical Object,” Opt. Acta 32, 741–746 (1985).
[CrossRef]

1984

H. Machida, J. Nitta, A. Seko, H. Kobayashi, “High-Efficiency Fiber Grating for Producing Multiple Beams of Uniform Intensity,” Appl. Opt. 23, 330–332 (1984).
[CrossRef] [PubMed]

D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4650–4570 (1984).
[CrossRef]

1982

1980

1977

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

1972

1968

L. K. Anderson, “Holographic Optical Memory for Bulk Data Storage,” Bell Lab. Rec.319–325 (Nov.1968).

Agu, M.

M. Agu, A. Akiba, S. Kamemaru, “A Parallel Processing Optical-Digital Recognition System as a Model of Biological Visual Perception,” Opt. Commun. 66, 69–73 (1988).
[CrossRef]

Akiba, A.

M. Agu, A. Akiba, S. Kamemaru, “A Parallel Processing Optical-Digital Recognition System as a Model of Biological Visual Perception,” Opt. Commun. 66, 69–73 (1988).
[CrossRef]

P. Asthana, A. Akiba, T. Yamaki, K. Nishizawa, M. Oikawa, “Gradient-Index Lens Array Matched Filtering,” Opt. Lett. 13, 84–86 (1988).
[CrossRef] [PubMed]

A. Akiba, K. Iga, “Image Multiplexer (IMX) Using Planar Microlens Array,” in Technical Digest, MOC/GRIN ’89 (Publisher, Location, 1989), pp. 228–231.

Anderson, L. K.

L. K. Anderson, “Holographic Optical Memory for Bulk Data Storage,” Bell Lab. Rec.319–325 (Nov.1968).

Asthana, P.

Banno, J.

Boivin, L. P.

Dammann, H.

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Glaser, I.

Gregory, D. A.

J. C. Kirsch, D. A. Gregory, T. D. Hudson, D. J. Lanteigne, “Design of Photopolymer Holograms for Optical Interconnect Applications,” Opt. Eng. 27, 301–308 (1988).
[CrossRef]

D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4650–4570 (1984).
[CrossRef]

Hamanaka, K.

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array and its Applications to Imaging Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).

M. Oikawa, E. Okuda, K. Hamanaka, H. Nemoto, “Integrated Planar Microlens and its Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 898, 3–11 (1988).

Hudson, T. D.

J. C. Kirsch, D. A. Gregory, T. D. Hudson, D. J. Lanteigne, “Design of Photopolymer Holograms for Optical Interconnect Applications,” Opt. Eng. 27, 301–308 (1988).
[CrossRef]

Iga, K.

K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: an Application of the Planar Microlens,” Appl. Opt. 21, 3456–3460 (1982).
[CrossRef] [PubMed]

A. Akiba, K. Iga, “Image Multiplexer (IMX) Using Planar Microlens Array,” in Technical Digest, MOC/GRIN ’89 (Publisher, Location, 1989), pp. 228–231.

Kamemaru, S.

M. Agu, A. Akiba, S. Kamemaru, “A Parallel Processing Optical-Digital Recognition System as a Model of Biological Visual Perception,” Opt. Commun. 66, 69–73 (1988).
[CrossRef]

Kirsch, J. C.

J. C. Kirsch, D. A. Gregory, T. D. Hudson, D. J. Lanteigne, “Design of Photopolymer Holograms for Optical Interconnect Applications,” Opt. Eng. 27, 301–308 (1988).
[CrossRef]

Klotz, E.

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Kobayashi, H.

Kokubun, Y.

Kolodziejczyk, A.

A. Kolodziejczyk, “Lensless Multiple Image Formation by Using a Sampling Filter,” Opt. Acta 59, 97–102 (1986).

A. Kolodziejczyk, “Realization of Fourier Images Without Using a Lens by Sampling the Optical Object,” Opt. Acta 32, 741–746 (1985).
[CrossRef]

Kumar, A. S.

A. S. Kumar, R. M. Vasu, “Multiple Imaging with an Aberration Optimized Hololens Array,” Opt. Eng. 28, 903–908 (1989).
[CrossRef]

A. S. Kumar, R. M. Vasu, “Multiple Imaging and Multichannel Optical Processing with Split Lenses,” Appl. Opt. 26, 5345–5349 (1987).
[CrossRef] [PubMed]

Lanteigne, D. J.

J. C. Kirsch, D. A. Gregory, T. D. Hudson, D. J. Lanteigne, “Design of Photopolymer Holograms for Optical Interconnect Applications,” Opt. Eng. 27, 301–308 (1988).
[CrossRef]

Liu, H.-K.

D. A. Gregory, H.-K. Liu, “Large-Memory Real-Time Multichannel Multiplexed Pattern Recognition,” Appl. Opt. 23, 4650–4570 (1984).
[CrossRef]

Machida, H.

McCormick, F. B.

F. B. McCormick, “Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings,” Opt. Eng. 28, 299–304 (1989).
[CrossRef]

Misawa, S.

Nemoto, H.

M. Oikawa, E. Okuda, K. Hamanaka, H. Nemoto, “Integrated Planar Microlens and its Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 898, 3–11 (1988).

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array and its Applications to Imaging Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).

Nishizawa, K.

Nitta, J.

Oikawa, M.

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array and its Applications to Imaging Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).

P. Asthana, A. Akiba, T. Yamaki, K. Nishizawa, M. Oikawa, “Gradient-Index Lens Array Matched Filtering,” Opt. Lett. 13, 84–86 (1988).
[CrossRef] [PubMed]

M. Oikawa, E. Okuda, K. Hamanaka, H. Nemoto, “Integrated Planar Microlens and its Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 898, 3–11 (1988).

K. Iga, M. Oikawa, S. Misawa, J. Banno, Y. Kokubun, “Stacked Planar Optics: an Application of the Planar Microlens,” Appl. Opt. 21, 3456–3460 (1982).
[CrossRef] [PubMed]

Okuda, E.

M. Oikawa, E. Okuda, K. Hamanaka, H. Nemoto, “Integrated Planar Microlens and its Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 898, 3–11 (1988).

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array and its Applications to Imaging Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).

Perelmutter, L.

Seko, A.

Vasu, R. M.

A. S. Kumar, R. M. Vasu, “Multiple Imaging with an Aberration Optimized Hololens Array,” Opt. Eng. 28, 903–908 (1989).
[CrossRef]

A. S. Kumar, R. M. Vasu, “Multiple Imaging and Multichannel Optical Processing with Split Lenses,” Appl. Opt. 26, 5345–5349 (1987).
[CrossRef] [PubMed]

Yamaki, T.

Appl. Opt.

Bell Lab. Rec.

L. K. Anderson, “Holographic Optical Memory for Bulk Data Storage,” Bell Lab. Rec.319–325 (Nov.1968).

Opt. Acta

A. Kolodziejczyk, “Realization of Fourier Images Without Using a Lens by Sampling the Optical Object,” Opt. Acta 32, 741–746 (1985).
[CrossRef]

A. Kolodziejczyk, “Lensless Multiple Image Formation by Using a Sampling Filter,” Opt. Acta 59, 97–102 (1986).

H. Dammann, E. Klotz, “Coherent Optical Generation and Inspection of Two-Dimensional Periodic Structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Commun.

M. Agu, A. Akiba, S. Kamemaru, “A Parallel Processing Optical-Digital Recognition System as a Model of Biological Visual Perception,” Opt. Commun. 66, 69–73 (1988).
[CrossRef]

Opt. Eng.

F. B. McCormick, “Generation of Large Spot Arrays from a Single Laser Beam by Multiple Imaging with Binary Phase Gratings,” Opt. Eng. 28, 299–304 (1989).
[CrossRef]

A. S. Kumar, R. M. Vasu, “Multiple Imaging with an Aberration Optimized Hololens Array,” Opt. Eng. 28, 903–908 (1989).
[CrossRef]

J. C. Kirsch, D. A. Gregory, T. D. Hudson, D. J. Lanteigne, “Design of Photopolymer Holograms for Optical Interconnect Applications,” Opt. Eng. 27, 301–308 (1988).
[CrossRef]

Opt. Lett.

Proc. Soc. Photo-Opt. Instrum. Eng.

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array and its Applications to Imaging Optics,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).

M. Oikawa, E. Okuda, K. Hamanaka, H. Nemoto, “Integrated Planar Microlens and its Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 898, 3–11 (1988).

Other

A. Akiba, K. Iga, “Image Multiplexer (IMX) Using Planar Microlens Array,” in Technical Digest, MOC/GRIN ’89 (Publisher, Location, 1989), pp. 228–231.

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Figures (12)

Fig. 1
Fig. 1

Parallel processing with multiple images.

Fig. 2
Fig. 2

Optical setup for multiple imaging and multiple Fourier transformation under coherent illumination using a microlens array.

Fig. 3
Fig. 3

Alternative technologies: (a) 2-D phase grating; (b) holographic optical element.

Fig. 4
Fig. 4

Examples of the alignment of multiple images: closest alignment, segmentation, and specific alignment.

Fig. 5
Fig. 5

Optical setup for obtaining both multiple Fourier transforms and multiple images in the output plane simultaneously.

Fig. 6
Fig. 6

Interferograms of one of the microlenses used in the experiments: (a) on-axis; (b) at the off-axis angle of 13°.

Fig. 7
Fig. 7

Off-axis aberration properties of the PML: (a) third-order coma; (b) third-order astigmatism.

Fig. 8
Fig. 8

Experimental result of the multiple Fourier transformation: (a) photograph of the Fourier plane; (b) input pattern; (c) magnified images; (d) light intensity profile along a line.

Fig. 9
Fig. 9

Point spread functions on the Fourier plane.

Fig. 10
Fig. 10

Experimental result of multiple imaging: (a) multiple images; (b) light intensity profile along a line.

Fig. 11
Fig. 11

Coherent transfer function measured by the multiple images of a resolution test chart.

Fig. 12
Fig. 12

Example of the possible applications: multichannel matched filtering.

Tables (1)

Tables Icon

Table I Specifications of the Lenses Used In the Experiments

Equations (6)

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

p = p 1 β ,
2 r = 2 a 1 ( f 2 / f 1 ) ,
2 r = 2 a 1 ( f 2 / f 1 ) .
β = - f 4 / f 3 ;
p 4 = p 1 β .
ν c = N . A . 4 / λ .

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