Abstract

We describe a phase plate based on the fractional-Talbot effect that converts a single expanded laser beam into a regular array of uniformly illuminated apertures with virtually 100% efficiency. The size, spacing, and fill factor of the illuminated aperture grid can be freely chosen to interface with a variety of electro-optic devices. A binary-optics phase plate is demonstrated that converts uniform illumination into an array of square illumination cells with a fill factor of 1/16.

© 1990 Optical Society of America

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References

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  1. D. A. B. Miller, J. E. Henry, A. C. Gossard, J. H. English, Appl. Phys. Lett. 49, 821 (1986).
    [CrossRef]
  2. J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
    [CrossRef]
  3. W. H. F. Talbot, Philos. Mag. 9, 401 (1836).
  4. J. T. Winthrop, C. R. Worthington, J. Opt. Soc. Am. 55, 373 (1965).
    [CrossRef]
  5. B. Packross, R. Eschbach, O. Bryngdahl, Opt. Commun. 56, 394 (1986).
    [CrossRef]
  6. A. W. Lohmann, Optik 79, 41 (1988).
  7. J. A. Thomas, Diplom Thesis (Physikalisches Institut der Universität, Erlangen-Nürnberg, Federal Republic of Germany, 1989).
  8. G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

1989

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
[CrossRef]

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

1988

A. W. Lohmann, Optik 79, 41 (1988).

1986

D. A. B. Miller, J. E. Henry, A. C. Gossard, J. H. English, Appl. Phys. Lett. 49, 821 (1986).
[CrossRef]

B. Packross, R. Eschbach, O. Bryngdahl, Opt. Commun. 56, 394 (1986).
[CrossRef]

1965

1836

W. H. F. Talbot, Philos. Mag. 9, 401 (1836).

Bryngdahl, O.

B. Packross, R. Eschbach, O. Bryngdahl, Opt. Commun. 56, 394 (1986).
[CrossRef]

English, J. H.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
[CrossRef]

D. A. B. Miller, J. E. Henry, A. C. Gossard, J. H. English, Appl. Phys. Lett. 49, 821 (1986).
[CrossRef]

Eschbach, R.

B. Packross, R. Eschbach, O. Bryngdahl, Opt. Commun. 56, 394 (1986).
[CrossRef]

Gossard, A. C.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
[CrossRef]

D. A. B. Miller, J. E. Henry, A. C. Gossard, J. H. English, Appl. Phys. Lett. 49, 821 (1986).
[CrossRef]

Henry, J. E.

D. A. B. Miller, J. E. Henry, A. C. Gossard, J. H. English, Appl. Phys. Lett. 49, 821 (1986).
[CrossRef]

Jewell, J. L.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
[CrossRef]

Lee, Y. H.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, Optik 79, 41 (1988).

McCall, S. L.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, J. E. Henry, A. C. Gossard, J. H. English, Appl. Phys. Lett. 49, 821 (1986).
[CrossRef]

Packross, B.

B. Packross, R. Eschbach, O. Bryngdahl, Opt. Commun. 56, 394 (1986).
[CrossRef]

Scherer, A.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
[CrossRef]

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Talbot, W. H. F.

W. H. F. Talbot, Philos. Mag. 9, 401 (1836).

Thomas, J. A.

J. A. Thomas, Diplom Thesis (Physikalisches Institut der Universität, Erlangen-Nürnberg, Federal Republic of Germany, 1989).

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Winthrop, J. T.

Worthington, C. R.

Appl. Phys. Lett.

D. A. B. Miller, J. E. Henry, A. C. Gossard, J. H. English, Appl. Phys. Lett. 49, 821 (1986).
[CrossRef]

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, Appl. Phys. Lett. 54, 1400 (1989).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

B. Packross, R. Eschbach, O. Bryngdahl, Opt. Commun. 56, 394 (1986).
[CrossRef]

Opt. Eng.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Optik

A. W. Lohmann, Optik 79, 41 (1988).

Philos. Mag.

W. H. F. Talbot, Philos. Mag. 9, 401 (1836).

Other

J. A. Thomas, Diplom Thesis (Physikalisches Institut der Universität, Erlangen-Nürnberg, Federal Republic of Germany, 1989).

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Figures (4)

Fig. 1
Fig. 1

Computer simulation of Fresnel diffraction from an infinite grating with a fill factor of 1/8 illuminated by coherent light. The intensity (solid line) and the phase (dotted lines) across a single period are displayed: (a) corresponds to the 1/4 Talbot plane, (b) to the 1/8 Talbot plane, and (c) to the 1/16 Talbot plane. Note that the intensity in the 1/16 Talbot plane is uniform across the entire period.

Fig. 2
Fig. 2

Two-dimensional amplitude mask illuminated with light from a He-Ne laser: (a) shows the intensity directly behind the mask; (b), (c), and (d) are the intensity distributions at Zt/4, Zt/6, and Zt/8, respectively.

Fig. 3
Fig. 3

Binary-optics element for aperture illumination: (a) shows the phase depths etched into the element, and (b) is the intensity distribution observed at Zt/8 = 15.8 mm when the element is illuminated by an expanded He–Ne laser beam.

Fig. 4
Fig. 4

Theoretically calculated edge effects of the fractional-Talbot illuminator showing the last 5 apertures of an illuminator designed to produce 128 apertures with a fill factor of 1/4. A slight distortion occurs in the apertures close to the edge and a small amount of power is deposited outside the array. The effective two-dimensional efficiency of this array is calculated to be 98.8%.

Equations (12)

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Z 0 = Z t / 2 N = d 2 / N λ .
ϕ = π I 2 / N ,
t ( I , J ) = exp [ j π ( I 2 + J 2 ) N ] ,
H ( u ) = exp { j 2 π z λ [ 1 ( λ u ) 2 ] 1 / 2 } exp ( j 2 π z λ ) exp ( j π λ z u 2 ) exp ( j π z λ 3 u 4 4 ) ,
exp ( j π z λ 3 u 4 / 4 ) = exp [ j π λ 2 N 3 / ( 4 d 2 ) ] .
exp ( j π λ 2 N 3 / 4 d 2 ) = exp [ j π λ 2 N / ( 4 h 2 ) ] .
h λ ( N / 2 ) 1 / 2 .
f = Z 0 = d 2 / λ N .
x = I ( d / N ) .
t ( x , y ) = exp [ j π ( I 2 + J 2 ) N ] = exp [ j π ( x 2 + y 2 ) λ f ] .
n = d 2 / ( 4 λ f ) ,
x min = d / N = d λ f / d 2 = λ ( f / number ) .

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