Abstract

The effect of the form of the illuminating wave on array illuminators is investigated. Attention is focused on spherical illumination, and relevant parameters such as spot size and compression ratio are discussed. In addition, a general approach is presented to designing a Talbot array illuminator that operates under spherical illumination. It is shown how spherical illumination can be used as a degree of freedom, and an example of application in the field of human eye aberration correction is given.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
    [CrossRef]
  2. A. Lohmann, J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337–4340 (1990).
    [CrossRef] [PubMed]
  3. Z. D. Popovic, R. A. Sprague, G. A. Neville Connell, “Technique for monolithic fabrication of microlens arrays,” Appl. Opt. 27, 1281–1284 (1988).
    [CrossRef] [PubMed]
  4. M. Barge, H. Hamam, Y. Defosse, R. Chevallier, J. L. de Bougrenet de la Tocnaye, “Les illuminateurs de tableaux utilisant des éléments diffractifs,” J. Opt. 27, 151–170 (1996).
    [CrossRef]
  5. H. Dammann, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  6. N. Streibl, N. Nolsher, J. Jahns, S. Walker, “Array generation with lenslet arrays,” Appl. Opt. 30, 2739–2742 (1991).
    [CrossRef] [PubMed]
  7. J. W. Goodman, Introduction to Fourier Optics (MacGraw-Hill, New York, 1968).
  8. A. Papoulis, The Fourier Integral and its Applications (MacGraw-Hill, New York, 1968).
  9. K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–110 (1989).
    [CrossRef]
  10. H. Hamam, “Design of Talbot array illuminators,” Opt. Commun. 131, 359–370 (1996).
    [CrossRef]
  11. H. Hamam, J. L. de Bougrenet de la Tocnaye, “An efficient Fresnel transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920–1931 (1995).
    [CrossRef]
  12. R. E. Loseliani, “Fresnel diffraction by two-dimensional periodic structures,” Opt. Spectrosc. 55, 544–547 (1983).
  13. O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
    [CrossRef]
  14. A. Lohmann, “Array illuminators and complexity theory,” Opt. Commun. 89, 167–172 (1992).
    [CrossRef]
  15. H. Hamam, J. L. de Bougrenet de la Tocnaye, “Array illuminators using multilayer binary phase plates at fractional Talbot planes,” Appl. Opt. 35, 1820–1826 (1996).
    [CrossRef] [PubMed]
  16. J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
    [CrossRef]
  17. D. Malacara, Z. Malacara, Handbook of Lens Design (Marcel Dekker, New York, 1994), Chap. 8.
  18. R. Cubalchini, “Modal wave-front estimation from derivative measurements,” J. Opt. Soc. Am. 69, 972–977 (1979).
    [CrossRef]

1996 (4)

M. Barge, H. Hamam, Y. Defosse, R. Chevallier, J. L. de Bougrenet de la Tocnaye, “Les illuminateurs de tableaux utilisant des éléments diffractifs,” J. Opt. 27, 151–170 (1996).
[CrossRef]

H. Hamam, “Design of Talbot array illuminators,” Opt. Commun. 131, 359–370 (1996).
[CrossRef]

O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
[CrossRef]

H. Hamam, J. L. de Bougrenet de la Tocnaye, “Array illuminators using multilayer binary phase plates at fractional Talbot planes,” Appl. Opt. 35, 1820–1826 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

1992 (1)

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

1991 (1)

1990 (1)

1989 (2)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–110 (1989).
[CrossRef]

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

1988 (1)

1983 (1)

R. E. Loseliani, “Fresnel diffraction by two-dimensional periodic structures,” Opt. Spectrosc. 55, 544–547 (1983).

1979 (1)

1971 (1)

H. Dammann, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Barge, M.

M. Barge, H. Hamam, Y. Defosse, R. Chevallier, J. L. de Bougrenet de la Tocnaye, “Les illuminateurs de tableaux utilisant des éléments diffractifs,” J. Opt. 27, 151–170 (1996).
[CrossRef]

Bille, J. F.

Chevallier, R.

M. Barge, H. Hamam, Y. Defosse, R. Chevallier, J. L. de Bougrenet de la Tocnaye, “Les illuminateurs de tableaux utilisant des éléments diffractifs,” J. Opt. 27, 151–170 (1996).
[CrossRef]

Cubalchini, R.

Dammann, H.

H. Dammann, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

de Bougrenet de la Tocnaye, J. L.

Defosse, Y.

M. Barge, H. Hamam, Y. Defosse, R. Chevallier, J. L. de Bougrenet de la Tocnaye, “Les illuminateurs de tableaux utilisant des éléments diffractifs,” J. Opt. 27, 151–170 (1996).
[CrossRef]

Goelz, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (MacGraw-Hill, New York, 1968).

Grimm, B.

Guyot, O.

O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
[CrossRef]

Hamam, H.

O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
[CrossRef]

H. Hamam, “Design of Talbot array illuminators,” Opt. Commun. 131, 359–370 (1996).
[CrossRef]

H. Hamam, J. L. de Bougrenet de la Tocnaye, “Array illuminators using multilayer binary phase plates at fractional Talbot planes,” Appl. Opt. 35, 1820–1826 (1996).
[CrossRef] [PubMed]

M. Barge, H. Hamam, Y. Defosse, R. Chevallier, J. L. de Bougrenet de la Tocnaye, “Les illuminateurs de tableaux utilisant des éléments diffractifs,” J. Opt. 27, 151–170 (1996).
[CrossRef]

H. Hamam, J. L. de Bougrenet de la Tocnaye, “An efficient Fresnel transform algorithm based on fractional Fresnel diffraction,” J. Opt. Soc. Am. A 12, 1920–1931 (1995).
[CrossRef]

Jahns, J.

Liang, J.

Lohmann, A.

Loseliani, R. E.

R. E. Loseliani, “Fresnel diffraction by two-dimensional periodic structures,” Opt. Spectrosc. 55, 544–547 (1983).

Malacara, D.

D. Malacara, Z. Malacara, Handbook of Lens Design (Marcel Dekker, New York, 1994), Chap. 8.

Malacara, Z.

D. Malacara, Z. Malacara, Handbook of Lens Design (Marcel Dekker, New York, 1994), Chap. 8.

Neville Connell, G. A.

Nolsher, N.

Papoulis, A.

A. Papoulis, The Fourier Integral and its Applications (MacGraw-Hill, New York, 1968).

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–110 (1989).
[CrossRef]

Popovic, Z. D.

Sprague, R. A.

Streibl, N.

Thomas, J. A.

Walker, S.

Appl. Opt. (4)

J. Mod. Opt. (1)

N. Streibl, “Beam shaping with optical array generators,” J. Mod. Opt. 36, 1559–1573 (1989).
[CrossRef]

J. Opt. (1)

M. Barge, H. Hamam, Y. Defosse, R. Chevallier, J. L. de Bougrenet de la Tocnaye, “Les illuminateurs de tableaux utilisant des éléments diffractifs,” J. Opt. 27, 151–170 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (4)

O. Guyot, H. Hamam, “Logic operations based on the fractional Talbot effect,” Opt. Commun. 127, 96–106 (1996).
[CrossRef]

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

H. Hamam, “Design of Talbot array illuminators,” Opt. Commun. 131, 359–370 (1996).
[CrossRef]

H. Dammann, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Spectrosc. (1)

R. E. Loseliani, “Fresnel diffraction by two-dimensional periodic structures,” Opt. Spectrosc. 55, 544–547 (1983).

Prog. Opt. (1)

K. Patorski, “The self-imaging phenomenon and its applications,” Prog. Opt. 27, 1–110 (1989).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (MacGraw-Hill, New York, 1968).

A. Papoulis, The Fourier Integral and its Applications (MacGraw-Hill, New York, 1968).

D. Malacara, Z. Malacara, Handbook of Lens Design (Marcel Dekker, New York, 1994), Chap. 8.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) Lenslet array used as an AIL. (b) A lens added to introduce degrees of freedom to the system.

Fig. 2
Fig. 2

Talbot AIL illuminated by a convergent spherical wave. The Talbot planes come closer together as the observation distance increases. To obtain the normal periodic distribution of the Talbot planes again, one can add a divergent lens.

Fig. 3
Fig. 3

Dammann grating illuminated by a spherical wave. The grating can be moved between the lens and its back focal plane without modification of the position of the replay field.

Fig. 4
Fig. 4

Measurement of human eye aberration by means of a lenslet array: L 1 and L 2 are two convex lenses that form a modified telescope. This subsystem provides a spherical wave that illuminates the lenslet array.

Fig. 5
Fig. 5

Lenslet array used for measuring the wave-front aberration.

Fig. 6
Fig. 6

Lenslet array used to measure the aberration of the author’s right eye. Local shifts of the spots are used to obtain the derivative of the wave-front aberration.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

h x ,   z = FR z h x = exp i 2 π   z λ exp - i   π 4 λ z exp i π   x 2 λ z - +   h x 1 × exp i π   x 1 2 λ z exp - i 2 π   x 1 x λ z d x 1 ,
L x ,   z 1 = L x = exp - i π   x 2 λ F ,
h x ,   z = exp i π   x 2 λ z - +   l x 1 exp i π   x 1 2 λ 1 z - 1 F × exp - i 2 π   x 1 x λ z d x 1 ,
l x = m = - M / 2 M / 2 rect x D - m exp - i π   x - mD 2 λ f = rect x M + 1 D m = - + rect x D - m × exp - i π   x - mD 2 λ f ,
x = z z   x 1 ,     z = F - z F   z .
h x ,   z = z z exp - i π   x 2 λ F - z exp i π x 2 λ z - +   l z z   x × exp i π   x 2 λ z exp - i 2 π   x x λ z d x .
h x ,   z = z z exp - i π   x 2 λ F - z × Fr z m = - M / 2 M / 2 rect zx z D - m × exp - i π   x - m   z z   D 2 λ   z 2 z 2   f .
z = rf ,   f = r 2 f ,   Δ D = r Δ D ,
r = F f + F .
L x ,   z 1 = FR z 1 L x = exp - i π   x 2 λ F - z 1 .
r = F - z 1 f + F - z 1 .
h x ,   z = a = 0 q / 2 - 1   T a ,   p ,   q h x - D 2 + 2 aD q , T a ,   p ,   q = 2 q b = 0 q / 2 - 1 exp - i π 2   b 2 q   p + b × exp i π   4 ba q ,
h γ x ,   z = Z f = α   exp i π   γ 2 x 2 λ R + Z f × a = 0 q / 2 - 1   T a ,   p ,   q h x - D 2 + 2 aD q ,   z = 0 ,
a = 0 q / 2 - 1   | h x + 2 aD q ,   0 | 2 = a = 0 q / 2 - 1   | h x + 2 γ aD q ,   z | 2 = E ,
h x - D 2 + 2 aD q = 2 / q T a ,   p ,   q .
T a ,   p ,   p ,   q = exp i π a 2   a q   p - 1 T 0 ,   p ,   q
h x - D 2 + 2 aD q   p = exp - i π a 2   a q   p - 1 .
h x ,   z = exp i π   x 2 λ z - + h x 1 - i π   x 1 2 λ f × exp i π   x 1 2 λ z exp - i 2 π   x 1 x λ z d x 1 .
W x ,   y x = dx f ,   W x ,   y y = dy f ,

Metrics