Abstract

We describe and experimentally verify the generation of a Talbot array illuminator at 1/16 of the self-image distance of a binary phase grating with phase step π.

© 1995 Optical Society of America

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References

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  1. A. W. Lohmann, “An array illuminator based on the Talbot effect,” Optik 79, 41–45 (1988).
  2. A. W. Lohmann, J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337–4340 (1990).
    [CrossRef] [PubMed]
  3. D. Xiao-Yi, “Talbot effect and array illuminators that are based on it,” Appl. Opt. 31, 2983–2986 (1992).
    [CrossRef]
  4. V. Arrizón, J. Ojeda-Castaneda, “Talbot array illuminator with binary phase gratings,” Opt. Lett. 18, 1–3 (1993).
    [CrossRef]
  5. 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]
  6. J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects,” Opt. Acta 18, 677–682 (1971).
    [CrossRef]
  7. V. Arrizón, J. Ojeda-Castaneda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 32, 5925–5931 (1994).
    [CrossRef]
  8. 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]
  9. J. Ojeda-Castaneda, V. Arrizón, “Synthesis of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
    [CrossRef]
  10. A. W. Lohmann, J. Ojeda-Castañeda, “Computer generated holography: novel procedure,” Opt. Commun. 103, 181–184 (1993).
    [CrossRef]

1994

V. Arrizón, J. Ojeda-Castaneda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 32, 5925–5931 (1994).
[CrossRef]

1993

A. W. Lohmann, J. Ojeda-Castañeda, “Computer generated holography: novel procedure,” Opt. Commun. 103, 181–184 (1993).
[CrossRef]

V. Arrizón, J. Ojeda-Castaneda, “Talbot array illuminator with binary phase gratings,” Opt. Lett. 18, 1–3 (1993).
[CrossRef]

1992

D. Xiao-Yi, “Talbot effect and array illuminators that are based on it,” Appl. Opt. 31, 2983–2986 (1992).
[CrossRef]

J. Ojeda-Castaneda, V. Arrizón, “Synthesis of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
[CrossRef]

1990

1988

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

1971

J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects,” Opt. Acta 18, 677–682 (1971).
[CrossRef]

1965

Arrizón, V.

V. Arrizón, J. Ojeda-Castaneda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 32, 5925–5931 (1994).
[CrossRef]

V. Arrizón, J. Ojeda-Castaneda, “Talbot array illuminator with binary phase gratings,” Opt. Lett. 18, 1–3 (1993).
[CrossRef]

J. Ojeda-Castaneda, V. Arrizón, “Synthesis of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
[CrossRef]

Guigay, J. P.

J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects,” Opt. Acta 18, 677–682 (1971).
[CrossRef]

Leger, J. R.

Lohmann, A. W.

A. W. Lohmann, J. Ojeda-Castañeda, “Computer generated holography: novel procedure,” Opt. Commun. 103, 181–184 (1993).
[CrossRef]

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

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

Ojeda-Castaneda, J.

V. Arrizón, J. Ojeda-Castaneda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 32, 5925–5931 (1994).
[CrossRef]

V. Arrizón, J. Ojeda-Castaneda, “Talbot array illuminator with binary phase gratings,” Opt. Lett. 18, 1–3 (1993).
[CrossRef]

J. Ojeda-Castaneda, V. Arrizón, “Synthesis of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
[CrossRef]

Ojeda-Castañeda, J.

A. W. Lohmann, J. Ojeda-Castañeda, “Computer generated holography: novel procedure,” Opt. Commun. 103, 181–184 (1993).
[CrossRef]

Swanson, G. J.

Thomas, J. A.

Winthrop, J. T.

Worthington, C. R.

Xiao-Yi, D.

Appl. Opt.

J. Opt. Soc. Am.

Microwave Opt. Technol. Lett.

J. Ojeda-Castaneda, V. Arrizón, “Synthesis of 1-D phase profiles with variable optical path,” Microwave Opt. Technol. Lett. 5, 429–432 (1992).
[CrossRef]

Opt. Acta

J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects,” Opt. Acta 18, 677–682 (1971).
[CrossRef]

Opt. Commun.

A. W. Lohmann, J. Ojeda-Castañeda, “Computer generated holography: novel procedure,” Opt. Commun. 103, 181–184 (1993).
[CrossRef]

Opt. Lett.

Optik

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

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Figures (4)

Fig. 1
Fig. 1

(a) One-dimensional binary phase distribution for our proposed Talbot array illuminator, (b) irradiance distribution generated at the distance ZT/16, behind the one-dimensional phase grating, (c) two-dimensional version of the phase distribution.

Fig. 2
Fig. 2

Schematic representation of the experimental setup used for the synthesis of the binary phase distribution in Fig. 1(a).

Fig. 3
Fig. 3

(a) Portion of the input mask employed in the experiment, (b) auxiliary function F(x) for the representation of the input transmittance.

Fig. 4
Fig. 4

(a) Fraunhofer diffraction pattern of the input mask, (b) irradiance pattern registered at the distance z = ZT/16 behind the plane z = 0 of the experimental setup.

Tables (1)

Tables Icon

Table 1 Parameters of the Proposed Binary Phase Grating and Its Amplitude Wave Field at ZT/16

Equations (19)

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U ( x ; z = Z t / N ) = L = 0 N 1 C ( L , N ) G ( x L d / N ) ,
C ( L , N ) = 1 N q = 0 N 1 exp [ i ( 2 π / N ) q ( L q ) ] .
C ( L , N ) = | C ( L , N ) | exp ( i ϕ; L ) ,
| C ( L , N ) | = { 1 / N for odd N and arbitrary L 2 / N for even N ( and L with the parity of N / 2 ) , 0 otherwise
ϕ L = ( L 2 / 2 N ) π .
B ( x ) = q = rect ( x q d d / 8 ) ,
G ( x ) = m = 0 7 a m B ( x m d / 8 ) ,
U ( x ; Z T / 16 ) = 1 8 n = 0 7 exp ( i ϕ n ) G ( x n d / 8 ) ,
U ( x ; Z T / 16 ) = 1 8 m = 0 7 n = 0 7 a m exp ( i ϕ n ) × B [ x ( m + n ) d / 8 ] .
U ( x ; Z T / 16 ) = k = 0 7 a k B ( x k d / 8 ) ,
a k = 1 8 [ n = 0 7 a k n exp ( i ϕ n ) + n = k + 1 7 a k n + 8 exp ( i ϕ n ) ] .
I ( x ; Z T / 16 ) = k = 0 7 | a k | 2 B ( x k d / 8 ) .
p ( x , y ) = δ ( x ) exp ( i 2 π y 0 λ f y ) ,
t ( x , y ) = m = N N rect [ y F ( x ) 2 m a a ] ,
υ ( x , y ) = exp ( i π y a ) exp [ i π F ( x ) a ] .
2 exp ( i π / 8 )
2 exp ( i π / 8 )
2 exp ( i π / 8 )
2 exp ( i π / 8 )

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