Abstract

We demonstrate the planar integration of Talbot array illuminators designed to generate one-dimensional spot arrays. The array illuminator basically consists of a phase grating and a cylindrical diffractive lens integrated as a single diffractive optical element onto a transparent glass substrate. We discuss various design aspects, and we focus on problems typical for planar-integrated free-space optics like the tilted optical axis of the system. Experimental results and measurements, which were obtained from planar-integrated setups fabricated as surface-relief structures on a transparent glass substrate by use of standard photolithography, are included.

© 1998 Optical Society of America

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  1. N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
    [CrossRef]
  2. A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).
  3. H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  4. J. Mait, “Design of binary-phase and multiphase Fourier gratings for array generation,” J. Opt. Soc. Am. A 7, 1514–1528 (1990).
    [CrossRef]
  5. H. Machida, J. Nitta, A. Seko, H. Kobayashi, “High-efficiency fiber gratings for producing multiple beams of uniform intensity,” Appl. Opt. 23, 330–332 (1984).
    [CrossRef] [PubMed]
  6. N. Streibl, U. Nölscher, J. Jahns, S. Walker, “Array generation with lenslet arrays,” Appl. Opt. 30, 2739–2742 (1991).
    [CrossRef] [PubMed]
  7. A. W. Lohmann, J. Schwider, N. Streibl, J. Thomas, “Array illuminator based on phase contrast,” Appl. Opt. 27, 2915–2921 (1988).
    [CrossRef] [PubMed]
  8. L. Liu, “Talbot and Lau effects on incident beams of arbitrary wavefront, and their use,” Appl. Opt. 28, 4668–4677 (1989).
    [CrossRef] [PubMed]
  9. A. W. Lohmann, J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337–4340 (1990).
    [CrossRef] [PubMed]
  10. J. R. Leger, G. J. Swanson, “Efficient array illuminator using binary-optics phase plates at fractional Talbot planes,” Opt. Lett. 15, 288–290 (1990).
    [CrossRef] [PubMed]
  11. H. Hamam, “Talbot array illuminators: a general approach,” Appl. Opt. 36, 2319–2327 (1997).
    [CrossRef] [PubMed]
  12. V. Arrizón, J. Ojeda-Castañeda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994).
    [CrossRef] [PubMed]
  13. H. Hamam, J. L. de Bougrenet, “Multilayer array illuminators with binary phase plates at fractional Talbot distances,” Appl. Opt. 35, 1820–1826 (1996).
    [CrossRef] [PubMed]
  14. J. Jahns, A. Huang, “Planar integration of free space optical components,” Appl. Opt. 28, 1602–1605 (1989).
    [CrossRef] [PubMed]
  15. J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
    [CrossRef]
  16. M. Testorf, J. Jahns, “Paraxial theory of planar integrated systems,” J. Opt. Soc. Am. A 14, 1569–1575 (1997).
    [CrossRef]
  17. M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
    [CrossRef]
  18. G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
    [CrossRef]
  19. T. Shiono, H. Ogawa, “Diffraction-limited blazed reflection diffractive microlenses for oblique incidence fabricated by electron-beam lithography,” Appl. Opt. 30, 3643–3649 (1991).
    [CrossRef] [PubMed]
  20. J. Jahns, B. Acklin, “Integrated planar optical imaging system with high interconnection density,” Opt. Lett. 18, 1594–1596 (1993).
    [CrossRef] [PubMed]
  21. U. Krackhardt, “Optimum quantization rules for computer generated holograms,” in Diffractive Optical Elements: Design, Fabrication, and Testing, Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 139–142.
  22. J. T. Winthrop, C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373–381 (1965).
    [CrossRef]
  23. V. Arrizón, J. Ojeda-Castañeda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994).
    [CrossRef] [PubMed]
  24. V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
    [CrossRef]
  25. Further research investigates nonlinear numerical optimization methods to calculate optimized TAI structures. The optimization procedure can be understood mainly as a quantization algorithm for ideal TAI gratings.
  26. K. Patorski, “The self-imaging phenomenon and its applications,” Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. XXVII, pp. 1–108.
    [CrossRef]
  27. M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 132, 205–211 (1996).
    [CrossRef]

1997 (2)

1996 (3)

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

H. Hamam, J. L. de Bougrenet, “Multilayer array illuminators with binary phase plates at fractional Talbot distances,” Appl. Opt. 35, 1820–1826 (1996).
[CrossRef] [PubMed]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 132, 205–211 (1996).
[CrossRef]

1994 (4)

V. Arrizón, J. Ojeda-Castañeda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994).
[CrossRef] [PubMed]

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

V. Arrizón, J. Ojeda-Castañeda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994).
[CrossRef] [PubMed]

J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

1993 (1)

1991 (2)

1990 (3)

1989 (4)

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

L. Liu, “Talbot and Lau effects on incident beams of arbitrary wavefront, and their use,” Appl. Opt. 28, 4668–4677 (1989).
[CrossRef] [PubMed]

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

J. Jahns, A. Huang, “Planar integration of free space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

1988 (2)

A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).

A. W. Lohmann, J. Schwider, N. Streibl, J. Thomas, “Array illuminator based on phase contrast,” Appl. Opt. 27, 2915–2921 (1988).
[CrossRef] [PubMed]

1984 (1)

1971 (1)

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

1965 (1)

Acklin, B.

Arrizón, V.

Dammann, H.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

de Bougrenet, J. L.

Goncharenko, A. M.

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 132, 205–211 (1996).
[CrossRef]

Görtler, K.

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Hamam, H.

Huang, A.

Ibarra, J. G.

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

Jahns, J.

M. Testorf, J. Jahns, “Paraxial theory of planar integrated systems,” J. Opt. Soc. Am. A 14, 1569–1575 (1997).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 132, 205–211 (1996).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

J. Jahns, B. Acklin, “Integrated planar optical imaging system with high interconnection density,” Opt. Lett. 18, 1594–1596 (1993).
[CrossRef] [PubMed]

N. Streibl, U. Nölscher, J. Jahns, S. Walker, “Array generation with lenslet arrays,” Appl. Opt. 30, 2739–2742 (1991).
[CrossRef] [PubMed]

J. Jahns, A. Huang, “Planar integration of free space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

Khilo, N. A.

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 132, 205–211 (1996).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

Kobayashi, H.

Krackhardt, U.

U. Krackhardt, “Optimum quantization rules for computer generated holograms,” in Diffractive Optical Elements: Design, Fabrication, and Testing, Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 139–142.

Leger, J. R.

Liu, L.

Lohmann, A. W.

Machida, H.

Mait, J.

Nitta, J.

Nölscher, U.

Ogawa, H.

Ojeda-Castañeda, J.

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. XXVII, pp. 1–108.
[CrossRef]

Schwider, J.

Seko, A.

Shiono, T.

Streibl, N.

Swanson, G. J.

J. R. Leger, G. J. Swanson, “Efficient array illuminator using binary-optics phase plates at fractional Talbot planes,” Opt. Lett. 15, 288–290 (1990).
[CrossRef] [PubMed]

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Testorf, M.

M. Testorf, J. Jahns, “Paraxial theory of planar integrated systems,” J. Opt. Soc. Am. A 14, 1569–1575 (1997).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 132, 205–211 (1996).
[CrossRef]

Thomas, J.

Thomas, J. A.

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Walker, S.

Winthrop, J. T.

Worthington, C. R.

Appl. Opt. (11)

H. Machida, J. Nitta, A. Seko, H. Kobayashi, “High-efficiency fiber gratings for producing multiple beams of uniform intensity,” Appl. Opt. 23, 330–332 (1984).
[CrossRef] [PubMed]

N. Streibl, U. Nölscher, J. Jahns, S. Walker, “Array generation with lenslet arrays,” Appl. Opt. 30, 2739–2742 (1991).
[CrossRef] [PubMed]

A. W. Lohmann, J. Schwider, N. Streibl, J. Thomas, “Array illuminator based on phase contrast,” Appl. Opt. 27, 2915–2921 (1988).
[CrossRef] [PubMed]

L. Liu, “Talbot and Lau effects on incident beams of arbitrary wavefront, and their use,” Appl. Opt. 28, 4668–4677 (1989).
[CrossRef] [PubMed]

A. W. Lohmann, J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337–4340 (1990).
[CrossRef] [PubMed]

H. Hamam, “Talbot array illuminators: a general approach,” Appl. Opt. 36, 2319–2327 (1997).
[CrossRef] [PubMed]

V. Arrizón, J. Ojeda-Castañeda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994).
[CrossRef] [PubMed]

H. Hamam, J. L. de Bougrenet, “Multilayer array illuminators with binary phase plates at fractional Talbot distances,” Appl. Opt. 35, 1820–1826 (1996).
[CrossRef] [PubMed]

J. Jahns, A. Huang, “Planar integration of free space optical components,” Appl. Opt. 28, 1602–1605 (1989).
[CrossRef] [PubMed]

T. Shiono, H. Ogawa, “Diffraction-limited blazed reflection diffractive microlenses for oblique incidence fabricated by electron-beam lithography,” Appl. Opt. 30, 3643–3649 (1991).
[CrossRef] [PubMed]

V. Arrizón, J. Ojeda-Castañeda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (4)

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129, 167–172 (1996).
[CrossRef]

H. Dammann, K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

M. Testorf, J. Jahns, N. A. Khilo, A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 132, 205–211 (1996).
[CrossRef]

V. Arrizón, J. G. Ibarra, “Trading visibility and opening ratio in Talbot arrays,” Opt. Commun. 112, 271–277 (1994).
[CrossRef]

Opt. Eng. (1)

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Opt. Lett. (2)

Optik (Stuttgart) (1)

A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).

Proc. IEEE (1)

J. Jahns, “Planar packaging of free-space optical interconnections,” Proc. IEEE 82, 1623–1631 (1994).
[CrossRef]

Other (3)

U. Krackhardt, “Optimum quantization rules for computer generated holograms,” in Diffractive Optical Elements: Design, Fabrication, and Testing, Vol. 11 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 139–142.

Further research investigates nonlinear numerical optimization methods to calculate optimized TAI structures. The optimization procedure can be understood mainly as a quantization algorithm for ideal TAI gratings.

K. Patorski, “The self-imaging phenomenon and its applications,” Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1989), Vol. XXVII, pp. 1–108.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Basic configuration of a planar-integrated TAI. A plane wave is converted into a 1-D spot array. The input and the output planes are located on the bottom surface of a transparent glass substrate.

Fig. 2
Fig. 2

Geometries of the planar-integrated systems investigated.

Fig. 3
Fig. 3

Theoretical intensity profiles for the TAI’s listed in Table 2.

Fig. 4
Fig. 4

(a) CCD camera pictures of the planar-integrated systems. (b) Enlarged picture of the array illuminator of system 4. (c) Section of the array illuminator of system 3.

Fig. 5
Fig. 5

(a) Intensity pattern of the spot array generated by system 4. (b) Interlaced spots of low intensity can be found in the overexposed camera picture.

Fig. 6
Fig. 6

Examples of 1-D line scans through both the focal line of the cylindrical lenses and the spot arrays.

Tables (3)

Tables Icon

Table 1 Design Parameters of the Diffractive Cylindrical Lenses

Tables Icon

Table 2 Optimum Design of TAI’s with Four Equidistant Phase Levels

Tables Icon

Table 3 Comparison of Theoretical and Experimental Results

Equations (6)

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

ϕ oa x = - 2 π λ   n x 2 + f 2 - 2 xf   sin α 1 / 2 + x   sin α ,
ϕ l = 2 π L   l ,     l = 0 ,   1 , ,   L - 1 ,
z F = M N 2 d 2 λ .
ϕ q = π   q 2 Q ,     q = - Q / 2 , ,   Q / 2 - 1 .
cos   α = N M z D λ 2 d 2 .
cos   α = M N 2 d 2 z D λ - 1 - 1 .

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