Abstract

A flexible array illuminator, comprising only two conventional optical elements, with a variable density of bright white-light spots is presented. The key to our method is to obtain with a single diffractive lens an achromatic version of different fractional Talbot images, produced by free-space propagation, of the amplitude distribution at the back focal plane of a periodic refractive microlens array under a broadband point-source illumination. Some experimental results of our optical procedure are also shown.

© 1998 Optical Society of America

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References

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  1. N. Streibl, “Multiple beamsplitters,” in Optical Computer Hardware, J. Jahns, S. H. Lee, eds. (Academic, San Diego, Calif., 1993), pp. 227–248.
  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. 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]
  4. V. Arrizon, J. Ojeda-Castañeda, “Talbot array illuminators with binary phase gratings,” Opt. Lett. 18, 1–3 (1993).
    [CrossRef] [PubMed]
  5. V. Arrizon, J. Ojeda-Castañeda, “Multilevel phase gratings for array illuminators,” Appl. Opt. 33, 5925–5931 (1994).
    [CrossRef] [PubMed]
  6. H. Hamam, J. L. de Bougrenet de la Tocnaye, “Multilayer array illuminators with binary phase plates at fractional Talbot distances,” Appl. Opt. 35, 1820–1826 (1996).
    [CrossRef] [PubMed]
  7. H. Hamam, “Talbot array illuminators: a general approach,” Appl. Opt. 36, 2319–2327 (1997).
    [CrossRef] [PubMed]
  8. A. W. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
    [CrossRef]
  9. E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of a periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
    [CrossRef]
  10. B. Besold, N. Lindlein, “Fractional Talbot effect for periodic microlens arrays,” Opt. Eng. 36, 1099–1105 (1997).
    [CrossRef]
  11. 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]
  12. J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichín, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997).
    [CrossRef]

1997

B. Besold, N. Lindlein, “Fractional Talbot effect for periodic microlens arrays,” Opt. Eng. 36, 1099–1105 (1997).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichín, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997).
[CrossRef]

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

1996

1994

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of a periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

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

1993

1992

A. W. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
[CrossRef]

1990

1965

Andrés, P.

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichín, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997).
[CrossRef]

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of a periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

Arrizon, V.

Barreiro, J. C.

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of a periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

Besold, B.

B. Besold, N. Lindlein, “Fractional Talbot effect for periodic microlens arrays,” Opt. Eng. 36, 1099–1105 (1997).
[CrossRef]

Bonet, E.

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of a periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

Climent, V.

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichín, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997).
[CrossRef]

de Bougrenet de la Tocnaye, J. L.

Hamam, H.

Lancis, J.

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichín, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997).
[CrossRef]

Leger, J. R.

Lindlein, N.

B. Besold, N. Lindlein, “Fractional Talbot effect for periodic microlens arrays,” Opt. Eng. 36, 1099–1105 (1997).
[CrossRef]

Lohmann, A. W.

Ojeda-Castañeda, J.

Pons, A.

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of a periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

Streibl, N.

N. Streibl, “Multiple beamsplitters,” in Optical Computer Hardware, J. Jahns, S. H. Lee, eds. (Academic, San Diego, Calif., 1993), pp. 227–248.

Swanson, G. J.

Tajahuerce, E.

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichín, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997).
[CrossRef]

Tepichín, E.

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichín, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997).
[CrossRef]

Thomas, J. A.

Winthrop, J. T.

Worthington, C. R.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Commun.

A. W. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
[CrossRef]

E. Bonet, P. Andrés, J. C. Barreiro, A. Pons, “Self-imaging properties of a periodic microlens array: versatile array illuminator realization,” Opt. Commun. 106, 39–44 (1994).
[CrossRef]

J. Lancis, E. Tajahuerce, P. Andrés, V. Climent, E. Tepichín, “Single-zone-plate achromatic Fresnel-transform setup: pattern tunability,” Opt. Commun. 136, 297–305 (1997).
[CrossRef]

Opt. Eng.

B. Besold, N. Lindlein, “Fractional Talbot effect for periodic microlens arrays,” Opt. Eng. 36, 1099–1105 (1997).
[CrossRef]

Opt. Lett.

Other

N. Streibl, “Multiple beamsplitters,” in Optical Computer Hardware, J. Jahns, S. H. Lee, eds. (Academic, San Diego, Calif., 1993), pp. 227–248.

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Figures (8)

Fig. 1
Fig. 1

Fresnel image generated by the focal amplitude distribution of a periodic refractive microlens array under parallel monochromatic illumination.

Fig. 2
Fig. 2

Chromatic dispersion of the Fresnel image in Fig. 1 under white-light illumination.

Fig. 3
Fig. 3

Single-zone-plate achromatic Fresnel transformer: optical arrangement.

Fig. 4
Fig. 4

White-light-modified Talbot array generator.

Fig. 5
Fig. 5

Irradiance distribution at the one-fourth fractional Talbot image under white-light illumination: (a) Gray-level picture of the irradiance at the output plane of the conventional AI. (b) Irradiance profile along a horizontal line in (a) for each RGB component of the incident light. (c) Achromatic pattern in gray levels provided by our optical configuration in Fig. 4. (d) RGB irradiance profiles along a horizontal line in (c).

Fig. 6
Fig. 6

Same as Fig. 5 but for the one-third fractional Talbot image.

Fig. 7
Fig. 7

Efficiency (in percent) measured for each RGB component of the incident light at the central region of the output plane provided by both the conventional and the achromatic AI.

Fig. 8
Fig. 8

Uniformity error (in percent) of the white-light spots provided by the achromatic AI. Measurements are made on the Fresnel image in Fig. 5.

Tables (1)

Tables Icon

Table 1 Multiplicity m at the Output Plane of the White-Light-Modified Talbot Array Generator Shown in Fig. 4 for Different Fresnel Images Characterized by the Value of Q + N/M

Equations (13)

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R = 2 d 2 σ Q + N M ,
R σ = R 0 σ σ 0 .
z = - 1 α   Z 0 ,
α = Z 0 / | R 0 | .
D 0 = 1 2 - α   Z 0 .
M = D 0 z = - α 2 - α .
R 0 = 2 d 2 Q + N M σ 0 .
h = - f + z = - f - 1 α   Z 0 ,
d = | M |   d r = α 2 - α d r ,
s = r 2 n ,
m = d 2 d 2 = 2 - α 2 α   r 2 .
CA σ = 100 1 + 2 - α σ σ 0 σ - σ 0 2 ,
0 0.61 J 1 2 π Ax / Ax 2 A 2 2 π x d x 0 0.61 J 1 2 π x / x 2 2 π x d x = 0.95 ,

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