Abstract

A new hybrid optical device that is capable of splitting a monochromatic laser beam into an arbitrary number of lines over a wide angle is presented. It consists of a binary surface-relief computer-generated phase hologram and a continuous parabolic surface-relief grating. In this device the phase hologram serves to generate three small, parallel lines while the continuous parabolic surface-relief phase grating acts as an array of diverging parabolic lenses to widen these lines. The binary surface-relief was generated into one side of a quartz substrate through a plasma-etching process, and the parabolic profile was generated into a thick photoresist deposited on the other side of the quartz substrate. Calculations showed that a diverging parabolic lens with a f-number of 0.5 would deliver the desired optical pattern of multiple beams distributed over 90°. A surface-relief depth of 6.0 µm was calculated with consideration of the phase distributions of such lens. The parabolic profiles were fabricated in a 10-µm-thick photoresist, by use of a contact exposure through a mask with a space pattern of repetitive 4- and 6-µm lines. He–Ne laser light was passed through a device that generated three parallel lines over a 90° angle. The resulting diffraction patterns were characterized, and a satisfying result was obtained. The resulting multiple-line pattern can be used in robot vision and other applications.

© 2001 Optical Society of America

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References

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  1. H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications, 1st ed., J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), Chap. 6, pp. 165–188.
  2. D. C. O’Shea, Elements of Modern Optical Design (Wiley, New York, 1985), pp. 76–77.
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    [CrossRef] [PubMed]
  4. R. Magnusson, D. Shin, “Diffraction by periodic arrays of dielectric cylinders,” J. Opt. Soc. Am. A 6, 412–414 (1989).
    [CrossRef]
  5. I. Aubrecht, M. Miller, “Profile of relief phase gratings used for uniform multiple beam splitting,” Opt. Lett. 18, 1287–1289 (1993).
    [CrossRef] [PubMed]
  6. 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]
  7. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 22–26.
  8. J. R. Fienup, “Iterative method applied to image reconstruction and computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).
  9. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blase phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990).
    [CrossRef]
  10. F. Wyrowski, O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
    [CrossRef]
  11. R. D. Mansano, P. Verdonck, H. S. Maciel, “Anisotropic reactive ion etching in silicon, using a graphite electrode,” Sens. Actuators A 65/2-3, 180–186 (1998).
  12. L. Ephrath, “Selective etching of silicon dioxide using reactive ion etching with CF4/H2,” J. Electrochem. Soc. 126, 1419–1421 (1979).
    [CrossRef]
  13. W. B. Glendinning, J. N. Helbert, Handbook of VLSI Microlithography (Noyes, Park Ridge, N.J., 1991).

1998 (1)

R. D. Mansano, P. Verdonck, H. S. Maciel, “Anisotropic reactive ion etching in silicon, using a graphite electrode,” Sens. Actuators A 65/2-3, 180–186 (1998).

1993 (1)

1990 (2)

1989 (2)

1984 (1)

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

1979 (1)

L. Ephrath, “Selective etching of silicon dioxide using reactive ion etching with CF4/H2,” J. Electrochem. Soc. 126, 1419–1421 (1979).
[CrossRef]

Aagedal, H.

H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications, 1st ed., J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), Chap. 6, pp. 165–188.

Aubrecht, I.

Beaulieu, R.

Bryngdahl, O.

Ephrath, L.

L. Ephrath, “Selective etching of silicon dioxide using reactive ion etching with CF4/H2,” J. Electrochem. Soc. 126, 1419–1421 (1979).
[CrossRef]

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

Glendinning, W. B.

W. B. Glendinning, J. N. Helbert, Handbook of VLSI Microlithography (Noyes, Park Ridge, N.J., 1991).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 22–26.

Helbert, J. N.

W. B. Glendinning, J. N. Helbert, Handbook of VLSI Microlithography (Noyes, Park Ridge, N.J., 1991).

Kobayashi, H.

Langois, P.

Machida, H.

Maciel, H. S.

R. D. Mansano, P. Verdonck, H. S. Maciel, “Anisotropic reactive ion etching in silicon, using a graphite electrode,” Sens. Actuators A 65/2-3, 180–186 (1998).

Magnusson, R.

Mansano, R. D.

R. D. Mansano, P. Verdonck, H. S. Maciel, “Anisotropic reactive ion etching in silicon, using a graphite electrode,” Sens. Actuators A 65/2-3, 180–186 (1998).

Miller, M.

Nitta, J.

O’Shea, D. C.

D. C. O’Shea, Elements of Modern Optical Design (Wiley, New York, 1985), pp. 76–77.

Schmid, M.

H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications, 1st ed., J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), Chap. 6, pp. 165–188.

Seko, A.

Shin, D.

Verdonck, P.

R. D. Mansano, P. Verdonck, H. S. Maciel, “Anisotropic reactive ion etching in silicon, using a graphite electrode,” Sens. Actuators A 65/2-3, 180–186 (1998).

Wyrowski, F.

F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blase phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990).
[CrossRef]

F. Wyrowski, O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 6, 1171–1174 (1989).
[CrossRef]

H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications, 1st ed., J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), Chap. 6, pp. 165–188.

Appl. Opt. (2)

J. Electrochem. Soc. (1)

L. Ephrath, “Selective etching of silicon dioxide using reactive ion etching with CF4/H2,” J. Electrochem. Soc. 126, 1419–1421 (1979).
[CrossRef]

J. Opt. Soc. Am. A (3)

Opt. Eng. (1)

J. R. Fienup, “Iterative method applied to image reconstruction and computer-generated holograms,” Opt. Eng. 19, 297–305 (1980).

Opt. Lett. (1)

Sens. Actuators A (1)

R. D. Mansano, P. Verdonck, H. S. Maciel, “Anisotropic reactive ion etching in silicon, using a graphite electrode,” Sens. Actuators A 65/2-3, 180–186 (1998).

Other (4)

H. Aagedal, F. Wyrowski, M. Schmid, “Paraxial beam splitting and shaping,” in Diffractive Optics for Industrial and Commercial Applications, 1st ed., J. Turunen, F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), Chap. 6, pp. 165–188.

D. C. O’Shea, Elements of Modern Optical Design (Wiley, New York, 1985), pp. 76–77.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 22–26.

W. B. Glendinning, J. N. Helbert, Handbook of VLSI Microlithography (Noyes, Park Ridge, N.J., 1991).

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Figures (13)

Fig. 1
Fig. 1

(a) Image obtained by laser light, deflected through a traditional DOE. As the smallest DOE structure must be ten times larger than the wavelength λ, the size of the reconstructed image distribution in the reconstruction plan and, consequently, the fan-out angle θ d is severely limited. (b) Hologram with a finite array of rectangular pixels of width U* and V*.

Fig. 2
Fig. 2

Line distribution generated over a wide angle by use of a low f-number cylindrical converging lens.

Fig. 3
Fig. 3

Line distribution generated over a wide angle by use of an array of dielectric cylinders or parabolic sections that act as an array of converging or diverging low f-number cylindrical lenses.

Fig. 4
Fig. 4

(a) Hybrid diffractive optical phase element capable of splitting a laser beam into an arbitrary number of lines over 90°. The element is formed by a binary surface-relief computer-generated phase hologram and a continuous parabolic surface-relief phase grating. (b) Optical setup and reconstruction image of a laser beam deflected by this hybrid DOE.

Fig. 5
Fig. 5

(a) Binary computer-generated phase hologram, signed by application of the iterative Fourier transform algorithm. (b) Computer hologram reconstruction with the intensity of three lines uniformly distributed in the reconstruction plane.

Fig. 6
Fig. 6

(a) Fabricated binary phase hologram by use of a binary mask. The mask consists of 24 of these devices. (b) Optical hologram reconstruction with the intensity of three lines uniformly distributed in the reconstruction plane.

Fig. 7
Fig. 7

Schematic view of the desired parabolic surface relief in photoresist.

Fig. 8
Fig. 8

Schematic view of the lithographic mask used to fabricate the parabolic profile into the photoresist. The mask consists of 1024 lines 10,240 µm long and 4 µm wide, with spaces of 6 µm between them (the final binary hologram is 10,240 × 10,240 µm wide). Each mask consists of 24 of these devices, spaced at the same distance used for the fabrication of the binary holograms.

Fig. 9
Fig. 9

Effect of light diffraction through a mask with relatively small line-space features13 used to generate the parabolic relief depth. The modulation of the light behind the mask is less than 1: Light penetrates under the metal line on the mask, and its intensity is not constant under the open space.

Fig. 10
Fig. 10

Parabolic profile fabricated in photoresist by use of a contact exposure through a mask with a space pattern of a repetitive 4- and 6-µm lines, as shown in Fig. 8.

Fig. 11
Fig. 11

Quartz wafer with 24 hybrid diffractive optical phase elements.

Fig. 12
Fig. 12

Optical setup used to obtain the optical reconstruction of the hybrid phase element placed against a converging lens.

Fig. 13
Fig. 13

Three reconstruction images observed with a CCD camera. These three images were recorded to capture the split of the multiple beams over 90°.

Equations (14)

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Δw=λfdmin,
Δwf10,
θd2 arctgΔw/2f=2 arctg120=5.72°.
θ1=2 arctgD2f1=2 arctg12f-number,
Gsu, v=rectuU*rectvV* combuUcombvVGu, vrectuNUrectvMV,
gsx, y=NMU2V2U*V*(sin cU*xsin cV*ycombUxcombVy  gx, y) sin cNUxsin cMVy,
Gsu, v=δurectvV combuUcombvVGu, v×rectuNUrectvMV.
gsx, y=NMU2V3(sin cVycombUxcombVy gx, y)  sin cNUxsin cMVy.
Gsu, v=Gsu, vexpj k2f u2rectuUrectvMV× combuU,
gsx, y=gsx, y  U2λfexp-jπλfx2× sin cUxcombUx.
gsx, y=Sfgsx, y  combUx,
Gsu, v=Gsu, vI0 combuU.
gsx, y=UI0gsx, y  combUx,
expj k2f umax2=expj2π Δpλn-1,

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