Abstract

Nondiffracting beams are useful for alignment applications because the size of the beam does not change as the beam propagates. In this research we report a technique that allows for distance measurements with nondiffracting beams. With our approach a diffractive optical element is designed that generates two off-axis, tilted, nondiffracting Bessel function beams. These beams intersect at a desired distance from the input plane, producing interference. We generate these Bessel function arrays with a programmable spatial light modulator allowing external control over the intersection distance.

© 1996 Optical Society of America

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References

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  1. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
  2. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
  3. J. A. Davis, J. Guertin, D. M. Cottrell, “Diffraction-free beams generated with programmable spatial light modulators,” Appl. Opt. 32, 6368–6370 (1993).
  4. A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
  5. J. A. Davis, E. Carcole, D. M. Cottrell, “Intensity and phase measurements of nondiffracting beams generated with the magneto-optic spatial light modulator,” Appl. Opt. 35, 593–598 (1996).
  6. W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
  7. D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).
  8. E. Carcole, J. A. Davis, D. M. Cottrell, “Astigmatic phase correction for the magneto-optic spatial light modulator,” Appl. Opt. 34, 5118–5120 (1995).

1996 (1)

1995 (1)

1993 (1)

1989 (1)

1988 (1)

1987 (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

1984 (1)

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

1983 (1)

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Anderson, R. H.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Carcole, E.

Cottrell, D. M.

Davis, J. A.

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

Friberg, A. T.

Guertin, J.

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Ross, W. E.

W. E. Ross, D. Psaltis, R. H. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).

Turunen, J.

Vasara, A.

Venkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

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Figures (4)

Fig. 1
Fig. 1

Binary patterns written onto the SLM that form (a) a centered zero-order Bessel function beam in which q = 4, (b) a shifted and tilted Bessel function beam, (c) two zero-order Bessel function beams that are shifted in opposite directions and tilted toward each other.

Fig. 2
Fig. 2

Intersection of the two shifted and tilted nondiffracting Bessel function beams at a location Z from the plane of the hologram.

Fig. 3
Fig. 3

Output intensity for the two nondiffracting beams measured at distances of (a) 1.00 m, (b) 1.14 m, and (c) 1.28 m.

Fig. 4
Fig. 4

Output intensity with a linear diode array for the two nondiffracting beams showing interference at distances of (a) 1.125 m, (b) 1.140 m, and (c) 1.155 m.

Equations (6)

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T ( r ) = exp ( i 2 π r / r 0 ) exp ( i 2 πα x / λ ) .
E ( ρ ) J 0 ( 2 π ρ r 0 ) .
L q N Δ 2 2 λ ,
W = 0 . 766 q Δ .
T ( r ) = exp ( i 2 π r A / r 0 ) exp ( i 2 πα x / λ ) + exp ( i 2 π r B / r 0 ) exp ( + i 2 πα x / λ ) .
Z = n N Δ 2 / ∊λ .

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