Abstract

An image multiplexer (IMX) composed of a planar microlens array is proposed for an input device of an optical parallel processing system. Imaging properties were evaluated experimentally and numerically to find a design rule and the limitations of use of the IMX. As a result, it was found that a planar microlens has a relatively good distortion property and low MTF sensitivity for oblique imaging, even if an image height goes to as high as 60% of the lens radius. Furthermore, a compensation method for image shift nonlinearity is proposed. The effective lens number in an array is estimated.

© 1990 Optical Society of America

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References

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    [CrossRef]
  2. L. P. Boivin, “Multiple Imaging Using Various Types of Simple Phase Gratings,” Appl. Opt. 11, 1782–1792 (1972).
    [CrossRef] [PubMed]
  3. 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).
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  4. J. C. Kirsch, D. A. Gregory, T. D. Hudson, D. J. Lanteigne, “Design of Photopolymer Holograms for Optical Interconnect Application,” Opt. Eng. 27, 301–308 (1988).
    [CrossRef]
  5. K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).
  6. 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]
  7. M. Oikawa, E. Okuda, K. Hamanaka, H. Nemoto, “Integrated Planar Microlens and Its Applications,” Proc. Soc. Photo-Opt. Instrum. Eng. 898, 3–11 (1988).
  8. X. F. Zhu, K. Iga, “Index Profile of a Planar Microlens by Ion Exchange/Diffusion,” Appl. Opt. 25, 3397–3400 (1986).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  12. T. Izawa, H. Nakagome, “Optical Waveguide Formed by Electrically Induced Migration of Ions in Glass Plates,” Appl. Phys. Lett. 21, 584–586 (1972).
    [CrossRef]
  13. M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–454 (1981).
    [CrossRef]
  14. S. N. Houde-Walter, D. T. Moore, “Gradient-Index Profile Control by Filed-Assisted Ion Exchange in Glass,” Appl. Opt. 24, 4326–4333 (1985).
    [CrossRef] [PubMed]
  15. S. Misawa, K. Iga, “Estimation of a Planar Microlens by Oblique Ray Tracing,” Appl. Opt. 27, 480–485 (1988).
    [CrossRef] [PubMed]

1988

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

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

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]

A. Akiba, M. Agu, S. Kamemaru, T. Yamaki, “A Miniaturization of an Optical Matched Filter,” Kogaku 17, 306–308 (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).

S. Misawa, K. Iga, “Estimation of a Planar Microlens by Oblique Ray Tracing,” Appl. Opt. 27, 480–485 (1988).
[CrossRef] [PubMed]

1986

X. F. Zhu, K. Iga, “Index Profile of a Planar Microlens by Ion Exchange/Diffusion,” Appl. Opt. 25, 3397–3400 (1986).
[CrossRef] [PubMed]

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

1985

1984

1982

1981

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–454 (1981).
[CrossRef]

1972

L. P. Boivin, “Multiple Imaging Using Various Types of Simple Phase Gratings,” Appl. Opt. 11, 1782–1792 (1972).
[CrossRef] [PubMed]

T. Izawa, H. Nakagome, “Optical Waveguide Formed by Electrically Induced Migration of Ions in Glass Plates,” Appl. Phys. Lett. 21, 584–586 (1972).
[CrossRef]

Agu, M.

A. Akiba, M. Agu, S. Kamemaru, T. Yamaki, “A Miniaturization of an Optical Matched Filter,” Kogaku 17, 306–308 (1988).

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]

A. Akiba, M. Agu, S. Kamemaru, T. Yamaki, “A Miniaturization of an Optical Matched Filter,” Kogaku 17, 306–308 (1988).

Banno, J.

Boivin, L. P.

Glaser, I.

Gregory, D. A.

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

Hamanaka, K.

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).

Houde-Walter, S. N.

Hudson, T. D.

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

Iga, K.

Izawa, T.

T. Izawa, H. Nakagome, “Optical Waveguide Formed by Electrically Induced Migration of Ions in Glass Plates,” Appl. Phys. Lett. 21, 584–586 (1972).
[CrossRef]

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]

A. Akiba, M. Agu, S. Kamemaru, T. Yamaki, “A Miniaturization of an Optical Matched Filter,” Kogaku 17, 306–308 (1988).

Kirsch, J. C.

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

Kobayashi, H.

Kokubun, Y.

Kolodziejczyk, A.

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

Lanteigne, D. J.

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

Machida, H.

Misawa, S.

Moore, D. T.

Nakagome, H.

T. Izawa, H. Nakagome, “Optical Waveguide Formed by Electrically Induced Migration of Ions in Glass Plates,” Appl. Phys. Lett. 21, 584–586 (1972).
[CrossRef]

Nemoto, H.

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array,” 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).

Nitta, J.

Oikawa, M.

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array,” 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).

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]

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–454 (1981).
[CrossRef]

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,” Proc. Soc. Photo-Opt. Instrum. Eng. 1014, 58–65 (1988).

Sanada, T.

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–454 (1981).
[CrossRef]

Seko, A.

Yamaki, T.

A. Akiba, M. Agu, S. Kamemaru, T. Yamaki, “A Miniaturization of an Optical Matched Filter,” Kogaku 17, 306–308 (1988).

Zhu, X. F.

Appl. Opt.

Appl. Phys. Lett.

T. Izawa, H. Nakagome, “Optical Waveguide Formed by Electrically Induced Migration of Ions in Glass Plates,” Appl. Phys. Lett. 21, 584–586 (1972).
[CrossRef]

Electron. Lett.

M. Oikawa, K. Iga, T. Sanada, “Distributed-Index Planar Microlens Array Prepared from Deep Electromigration,” Electron. Lett. 17, 452–454 (1981).
[CrossRef]

Kogaku

A. Akiba, M. Agu, S. Kamemaru, T. Yamaki, “A Miniaturization of an Optical Matched Filter,” Kogaku 17, 306–308 (1988).

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]

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

Opt. Eng.

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

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

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, “Aberration Properties of the Planar Microlens Array,” 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).

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the simple IMX that we considered. This IMX is composed of a planar microlens array: the input object must be illuminated incoherently.

Fig. 2
Fig. 2

Schematic chart of an imaging system used to record the image made by the planar microlens. A microscope was utilized as the imaging system.

Fig. 3
Fig. 3

Observed striped image made by the planar microlens. From this figure, we see that the planar microlens has good distortion property.

Fig. 4
Fig. 4

Relationship between the input object shift and the image shift. Each shift was measured as a spacing between stripes in object and image planes, respectively. Proportionality between the two shifts is well maintained when the object shift increases to 20 mm or the image height goes to 300 μm.

Fig. 5
Fig. 5

Schematic diagram of the ray tracing configuration. Incident angles are changed moving the point source on the y-axis.

Fig. 6
Fig. 6

Index distribution of the planar microlens used in the numerical analyses. The lens was made by the electromigration method, and the index distribution was measured experimentally. Parameter r is defined as r = ( x 2 + y 2 ), since axial symmetry of the lens is assumed.

Fig. 7
Fig. 7

Calculated ray trajectory when Δy = 0 and parameter r is the same as in Fig. 6.

Fig. 8
Fig. 8

Spot diagrams calculated for various incident angles. Coma aberration appears if the incident angle becomes large; however, intensity concentration is still well maintained.

Fig. 9
Fig. 9

MTFs calculated from spot diagrams. We see that the frequency response is not so sensitive to the imaging obliquity.

Fig. 10
Fig. 10

Image shift compensation method using a lens array having a nonuniform period. The period becomes wider as we go farther away from the center of the array; consequently decreasing the magnification is compensated.

Equations (2)

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A n c = π [ 0.4 ( mm ) × 100 ] 2             ( mm 2 ) ;
A c = π [ 0.665 ( mm ) × 100 ] 2             ( mm 2 ) .

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