Abstract

A cosine-approximated binary Gabor zone plate is proposed. The zone plate is fabricated by standard photographic techniques. It was evaluated by simulation and by experiment to match the focusing behavior of an ideal Gabor zone plate, but it has a focusing efficiency at least 23% higher than that of a binary Gabor zone plate. Duplication of an alphabetic character to form a 4 × 4 array of images with little astigmatism by the proposed zone-plate array is demonstrated.

© 1994 Optical Society of America

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  1. H. H. Barratt, F. A. Horrigan, “Fesnel zone plate imaging of gamma rays: theory,” Appl. Opt. 12, 2686–2702 (1973).
    [CrossRef]
  2. H.H. Barratt Swindell, Radiological Imaging, (Academic, New York, 1981), Vol. 2, pp. 490–515.
  3. O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a Fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
    [CrossRef] [PubMed]
  4. P. D. Kearney, A. G. Klein, G. I. Opat, R. Gahler, “Imaging and focusing of neutrons by a zone plate,” Nature (London) 287, 313–314 (1980).
    [CrossRef]
  5. K. Kodate, E. Tokunaga, Y. Tatuno, J. Chen, T. Kamiya, “Efficient zone plate array accessor for optoelectronic integrated circuits: design and fabrication,” Appl. Opt. 29, 5115–5119 (1990).
    [CrossRef] [PubMed]
  6. Y. Okada, K. Kodate, H. Kamiyama, T. Kamiya, “Fiber-optic pulse delay using composite zone plates for very fast optoelectronics,” Jpn. J. Appl. Phys. 27, 1440–1444 (1988).
    [CrossRef]
  7. J. L. Chen, K. Kodate, T. Kamiya, “Multiple beam elements using linear zone plate array suitable for parallel optoelectronic computing,” Jpn. J. Appl. Phys. 29, 1539–1541 (1990).
    [CrossRef]
  8. R. Tatchyn, P. L. Csonka, I. Lindau, “Symmetry-restricted profiles for maximizing the output diffraction efficiencies of zone plates in the soft-x-ray range,” J. Opt. Soc. Am. B 2, 1287–1293 (1985).
    [CrossRef]
  9. B. E. Patt, A. Meyyappan, A. Cai, G. Wade, “Gabor zone-plate apertures for imaging with the mercuric iodide gamma-ray camera,” Nucl. Instrum. Methods A 299, 554–558 (1990).
    [CrossRef]
  10. T. D. Beynon, I. Kirk, T. R. Mathews, “Gabor zone plate with binary transmittance values,” Opt. Lett. 17, 544–546 (1992).
    [CrossRef] [PubMed]
  11. T. Shiono, K. Setsune, O. Yamazaki, K. Wasa, “Rectangular-apertured micro-Fresnel lens arrays fabricated by electron-beam lithography,” Appl. Opt. 26, 587–591 (1987).
    [CrossRef] [PubMed]
  12. H. Ming, Y. Wu, J. Xie, T. Nakajima, “Fabrication of holographic microlens using deep UV lithographed zone plate,” Appl. Opt. 29, 5111–5114 (1990).
    [CrossRef] [PubMed]
  13. H. Fujisaki, N. Nakagiri, H. Kihara, N. Watanabe, M. Taniguchi, “Focusing efficiency and resolution of a nickel phase zone plate for soft x-rays,” Jpn. J. Appl. Phys. 30, 2943–2946 (1991).
    [CrossRef]
  14. K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, T. Kishimoto, “Multiple imaging and multiple Fourier transformation using planar microlens arrays,” Appl. Opt. 29, 4064–4070 (1990).
    [CrossRef] [PubMed]
  15. A. Akiba, K. Iga, “Image multiplexer using a planar microlens array,” Appl. Opt. 29, 4092–4097 (1990).
    [CrossRef] [PubMed]
  16. K. W. Wong, L. M. Cheng, “Optical cosine transform using microlens array and phase conjugate mirror,” Jpn. J. Appl. Phys. 31, 1672–1676 (1992).
    [CrossRef]

1992 (2)

T. D. Beynon, I. Kirk, T. R. Mathews, “Gabor zone plate with binary transmittance values,” Opt. Lett. 17, 544–546 (1992).
[CrossRef] [PubMed]

K. W. Wong, L. M. Cheng, “Optical cosine transform using microlens array and phase conjugate mirror,” Jpn. J. Appl. Phys. 31, 1672–1676 (1992).
[CrossRef]

1991 (2)

H. Fujisaki, N. Nakagiri, H. Kihara, N. Watanabe, M. Taniguchi, “Focusing efficiency and resolution of a nickel phase zone plate for soft x-rays,” Jpn. J. Appl. Phys. 30, 2943–2946 (1991).
[CrossRef]

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a Fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

1990 (6)

1988 (1)

Y. Okada, K. Kodate, H. Kamiyama, T. Kamiya, “Fiber-optic pulse delay using composite zone plates for very fast optoelectronics,” Jpn. J. Appl. Phys. 27, 1440–1444 (1988).
[CrossRef]

1987 (1)

1985 (1)

1980 (1)

P. D. Kearney, A. G. Klein, G. I. Opat, R. Gahler, “Imaging and focusing of neutrons by a zone plate,” Nature (London) 287, 313–314 (1980).
[CrossRef]

1973 (1)

Akiba, A.

Barratt, H. H.

Barratt Swindell, H.H.

H.H. Barratt Swindell, Radiological Imaging, (Academic, New York, 1981), Vol. 2, pp. 490–515.

Beynon, T. D.

Cai, A.

B. E. Patt, A. Meyyappan, A. Cai, G. Wade, “Gabor zone-plate apertures for imaging with the mercuric iodide gamma-ray camera,” Nucl. Instrum. Methods A 299, 554–558 (1990).
[CrossRef]

Carnal, O.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a Fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Chen, J.

Chen, J. L.

J. L. Chen, K. Kodate, T. Kamiya, “Multiple beam elements using linear zone plate array suitable for parallel optoelectronic computing,” Jpn. J. Appl. Phys. 29, 1539–1541 (1990).
[CrossRef]

Cheng, L. M.

K. W. Wong, L. M. Cheng, “Optical cosine transform using microlens array and phase conjugate mirror,” Jpn. J. Appl. Phys. 31, 1672–1676 (1992).
[CrossRef]

Csonka, P. L.

Fujisaki, H.

H. Fujisaki, N. Nakagiri, H. Kihara, N. Watanabe, M. Taniguchi, “Focusing efficiency and resolution of a nickel phase zone plate for soft x-rays,” Jpn. J. Appl. Phys. 30, 2943–2946 (1991).
[CrossRef]

Gahler, R.

P. D. Kearney, A. G. Klein, G. I. Opat, R. Gahler, “Imaging and focusing of neutrons by a zone plate,” Nature (London) 287, 313–314 (1980).
[CrossRef]

Hamanaka, K.

Horrigan, F. A.

Iga, K.

Kamiya, T.

K. Kodate, E. Tokunaga, Y. Tatuno, J. Chen, T. Kamiya, “Efficient zone plate array accessor for optoelectronic integrated circuits: design and fabrication,” Appl. Opt. 29, 5115–5119 (1990).
[CrossRef] [PubMed]

J. L. Chen, K. Kodate, T. Kamiya, “Multiple beam elements using linear zone plate array suitable for parallel optoelectronic computing,” Jpn. J. Appl. Phys. 29, 1539–1541 (1990).
[CrossRef]

Y. Okada, K. Kodate, H. Kamiyama, T. Kamiya, “Fiber-optic pulse delay using composite zone plates for very fast optoelectronics,” Jpn. J. Appl. Phys. 27, 1440–1444 (1988).
[CrossRef]

Kamiyama, H.

Y. Okada, K. Kodate, H. Kamiyama, T. Kamiya, “Fiber-optic pulse delay using composite zone plates for very fast optoelectronics,” Jpn. J. Appl. Phys. 27, 1440–1444 (1988).
[CrossRef]

Kearney, P. D.

P. D. Kearney, A. G. Klein, G. I. Opat, R. Gahler, “Imaging and focusing of neutrons by a zone plate,” Nature (London) 287, 313–314 (1980).
[CrossRef]

Kihara, H.

H. Fujisaki, N. Nakagiri, H. Kihara, N. Watanabe, M. Taniguchi, “Focusing efficiency and resolution of a nickel phase zone plate for soft x-rays,” Jpn. J. Appl. Phys. 30, 2943–2946 (1991).
[CrossRef]

Kirk, I.

Kishimoto, T.

Klein, A. G.

P. D. Kearney, A. G. Klein, G. I. Opat, R. Gahler, “Imaging and focusing of neutrons by a zone plate,” Nature (London) 287, 313–314 (1980).
[CrossRef]

Kodate, K.

J. L. Chen, K. Kodate, T. Kamiya, “Multiple beam elements using linear zone plate array suitable for parallel optoelectronic computing,” Jpn. J. Appl. Phys. 29, 1539–1541 (1990).
[CrossRef]

K. Kodate, E. Tokunaga, Y. Tatuno, J. Chen, T. Kamiya, “Efficient zone plate array accessor for optoelectronic integrated circuits: design and fabrication,” Appl. Opt. 29, 5115–5119 (1990).
[CrossRef] [PubMed]

Y. Okada, K. Kodate, H. Kamiyama, T. Kamiya, “Fiber-optic pulse delay using composite zone plates for very fast optoelectronics,” Jpn. J. Appl. Phys. 27, 1440–1444 (1988).
[CrossRef]

Lindau, I.

Mathews, T. R.

Meyyappan, A.

B. E. Patt, A. Meyyappan, A. Cai, G. Wade, “Gabor zone-plate apertures for imaging with the mercuric iodide gamma-ray camera,” Nucl. Instrum. Methods A 299, 554–558 (1990).
[CrossRef]

Ming, H.

Mlynek, J.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a Fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Nakagiri, N.

H. Fujisaki, N. Nakagiri, H. Kihara, N. Watanabe, M. Taniguchi, “Focusing efficiency and resolution of a nickel phase zone plate for soft x-rays,” Jpn. J. Appl. Phys. 30, 2943–2946 (1991).
[CrossRef]

Nakajima, T.

Nemoto, H.

Oikawa, M.

Okada, Y.

Y. Okada, K. Kodate, H. Kamiyama, T. Kamiya, “Fiber-optic pulse delay using composite zone plates for very fast optoelectronics,” Jpn. J. Appl. Phys. 27, 1440–1444 (1988).
[CrossRef]

Okuda, E.

Opat, G. I.

P. D. Kearney, A. G. Klein, G. I. Opat, R. Gahler, “Imaging and focusing of neutrons by a zone plate,” Nature (London) 287, 313–314 (1980).
[CrossRef]

Patt, B. E.

B. E. Patt, A. Meyyappan, A. Cai, G. Wade, “Gabor zone-plate apertures for imaging with the mercuric iodide gamma-ray camera,” Nucl. Instrum. Methods A 299, 554–558 (1990).
[CrossRef]

Setsune, K.

Shiono, T.

Sigel, M.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a Fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Sleator, T.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a Fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Takuma, H.

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a Fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Taniguchi, M.

H. Fujisaki, N. Nakagiri, H. Kihara, N. Watanabe, M. Taniguchi, “Focusing efficiency and resolution of a nickel phase zone plate for soft x-rays,” Jpn. J. Appl. Phys. 30, 2943–2946 (1991).
[CrossRef]

Tatchyn, R.

Tatuno, Y.

Tokunaga, E.

Wade, G.

B. E. Patt, A. Meyyappan, A. Cai, G. Wade, “Gabor zone-plate apertures for imaging with the mercuric iodide gamma-ray camera,” Nucl. Instrum. Methods A 299, 554–558 (1990).
[CrossRef]

Wasa, K.

Watanabe, N.

H. Fujisaki, N. Nakagiri, H. Kihara, N. Watanabe, M. Taniguchi, “Focusing efficiency and resolution of a nickel phase zone plate for soft x-rays,” Jpn. J. Appl. Phys. 30, 2943–2946 (1991).
[CrossRef]

Wong, K. W.

K. W. Wong, L. M. Cheng, “Optical cosine transform using microlens array and phase conjugate mirror,” Jpn. J. Appl. Phys. 31, 1672–1676 (1992).
[CrossRef]

Wu, Y.

Xie, J.

Yamazaki, O.

Appl. Opt. (6)

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

Jpn. J. Appl. Phys. (4)

Y. Okada, K. Kodate, H. Kamiyama, T. Kamiya, “Fiber-optic pulse delay using composite zone plates for very fast optoelectronics,” Jpn. J. Appl. Phys. 27, 1440–1444 (1988).
[CrossRef]

J. L. Chen, K. Kodate, T. Kamiya, “Multiple beam elements using linear zone plate array suitable for parallel optoelectronic computing,” Jpn. J. Appl. Phys. 29, 1539–1541 (1990).
[CrossRef]

K. W. Wong, L. M. Cheng, “Optical cosine transform using microlens array and phase conjugate mirror,” Jpn. J. Appl. Phys. 31, 1672–1676 (1992).
[CrossRef]

H. Fujisaki, N. Nakagiri, H. Kihara, N. Watanabe, M. Taniguchi, “Focusing efficiency and resolution of a nickel phase zone plate for soft x-rays,” Jpn. J. Appl. Phys. 30, 2943–2946 (1991).
[CrossRef]

Nature (London) (1)

P. D. Kearney, A. G. Klein, G. I. Opat, R. Gahler, “Imaging and focusing of neutrons by a zone plate,” Nature (London) 287, 313–314 (1980).
[CrossRef]

Nucl. Instrum. Methods A (1)

B. E. Patt, A. Meyyappan, A. Cai, G. Wade, “Gabor zone-plate apertures for imaging with the mercuric iodide gamma-ray camera,” Nucl. Instrum. Methods A 299, 554–558 (1990).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

O. Carnal, M. Sigel, T. Sleator, H. Takuma, J. Mlynek, “Imaging and focusing of atoms by a Fresnel zone plate,” Phys. Rev. Lett. 67, 3231–3234 (1991).
[CrossRef] [PubMed]

Other (1)

H.H. Barratt Swindell, Radiological Imaging, (Academic, New York, 1981), Vol. 2, pp. 490–515.

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Figures (11)

Fig. 1
Fig. 1

Binary Gabor zone plate proposed by Beynon et al.10

Fig. 2
Fig. 2

Geometrical arrangement and construction of the proposed cosine-approximated binary Gabor zone plate.

Fig. 3
Fig. 3

Pattern of the cosine-approximated Gabor zone plate without an offset to the center (opaque center).

Fig. 4
Fig. 4

Pattern of the cosine-approximated binary Gabor zone plate with an offset changing the position of r0 to 1/2r1 (transparent center).

Fig. 5
Fig. 5

Optical setup for measuring the focal spot power of two types of binary Gabor zone plate under coherent illumination.

Fig. 6
Fig. 6

Focusing efficiencies of the two types of binary Gabor zone plate versus the different sizes of spatial filter. Solid curves denote the cosine-approximated binary Gabor zone plate. Dashed curves denote the Beynon-type binary Gabor zone plate. The numbers in the legend represent the numbers of zones.

Fig. 7
Fig. 7

Log intensity plotting of a 2048 × 2048 cosine approximated binary Gabor zone-plate image.

Fig. 8
Fig. 8

Log intensity plotting of a 2048 × 2048 Beynon-type binary Gabor zone-plate image.

Fig. 9
Fig. 9

Cumulative intensity of the first 100 pixels from the center of a 2048 × 2048 fast-Fourier-transform image: cosine-approximated binary Gabor zone-plate image (solid curve), Beynon-type binary Gabor zone-plate image (dashed curve).

Fig. 10
Fig. 10

Percentage of intensity improvement of the first 100 pixels from the center of a 2048 × 2048 fast-Fournier-transform image.

Fig. 11
Fig. 11

Multiple images formed by the proposed 4 × 4 zone-plate array.

Tables (1)

Tables Icon

Table 1 Proportion of Absorption Area of the Proposed Zone Plate with Different Numbers of Zones

Equations (21)

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g ( r ) = 1 2 [ 1 - cos ( 2 π r 2 r 1 2 ) ] .
r = i N n r 1 ,
g ( i ) = 1 2 [ 1 - cos ( 2 π i 2 n N 2 ) ] .
A ( x j ) = 1 2 { 1 + cos 2 π [ 2 x j - ( r j + r j - 1 ) 2 ( r j - r j - 1 ) ] } ,
r j + r j - 1 = ( j + j - 1 ) r 1 = j [ 1 + ( 1 - 1 / j ) 1 / 2 ] r 1 .
r j + r j - 1 [ 2 j - 1 / ( 2 j ) ] r 1 .
r j - r j - 1 1 / ( 2 j ) r 1             for j 1.
A ( x j ) = 1 2 ( 1 + cos 2 π { 2 x j - [ 2 j - 1 ( 2 j ) r 1 ] 1 / ( j ) r 1 } ) = 1 2 [ 1 + cos 2 π ( 2 x j j r 1 - 2 j + 1 2 ) ] .
A ( x j ) = 1 2 [ 1 - cos 2 π ( 2 x j j r 1 ) ] .
x j k = ( j - j - 1 ) r 1 ( k N / n ) ,
x j k k n r 1 / 2 j N             for 1.
A ( k ) = 1 / 2 [ 1 - cos ( 2 π n k / N ) ] .
k = i 2 / N ,
B j = r j - 1 r j h A ( x j ) d x ,
B j = r j - 1 r j 1 4 ( r j + r j - 1 ) × tan θ { 1 + cos 2 π [ 2 x j - ( r j + r j - 1 ) 2 ( r j - r j - 1 ) ] } d x ,
B j = ¼ ( r j 2 - r j - 1 2 ) tan θ .
B j = ( r 1 2 ) 2 tan θ .
B 1 = 3 4 ( r 1 2 ) 2 tan θ .
2 [ ( r 1 / 2 ) 2 ( N - 1 ) tan θ + ( 3 / 4 ) ( r 1 / 2 ) 2 tan θ ] N s ,
2 [ ( r 1 / 2 ) 2 ( N - 1 ) tan θ + ( 3 / 4 ) ( r 1 / 2 ) 2 tan θ ] N s π N r 1 2
1 2 π ( N s N ) ( N - 1 4 ) tan θ .

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