Abstract

A method for obtaining the best image plane for holographic optical elements by the use of the concept of entropy is described. This method is applied to in-line holographic lenses with different values of spherical aberration. Numerical results show that for holograms with large aberrations the best image plane (obtained by the use of the concept of entropy) is different from the minimum-aberration-variance plane.

© 1994 Optical Society of America

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References

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  1. R. Torroba, H. Rabal, B. Ruiz, J. Mod. Opt. 39, 1939 (1992).
    [CrossRef]
  2. V. Michael Bove, J. Opt. Soc. Am. A 10, 561 (1993).
    [CrossRef]
  3. B. R. Frieden, J. Opt. Soc. Am. 62, 511 (1972).
    [CrossRef] [PubMed]
  4. B. R. Frieden, J. J. Burke, J. Opt. Soc. Am. 62, 1202 (1972).
    [CrossRef]
  5. E. H. Linfoot, J. Opt. Soc. Am. 45, 808 (1955).
    [CrossRef]
  6. E. L. O’Neill, Introduction to Statistical Optics (Dover, New York, 1991).
  7. C. Dähne, F. Lanzl, Optik 55, 437 (1980).
  8. B. R. Frieden, J. Mod. Opt. 35, 1297 (1988).
    [CrossRef]
  9. E. B. Champagne, J. Opt. Soc. Am. 57, 51 (1967).
    [CrossRef]
  10. A. Beléndez, L. Carretero, A. Fimia, J. Opt. 22, 163 (1991).
    [CrossRef]
  11. J. N. Latta, Appl. Opt. 10, 599 (1971).
    [CrossRef] [PubMed]
  12. H. Chen, R. R. Hershey, E. N. Leith, Appl. Opt. 26, 1983 (1987).
    [CrossRef] [PubMed]
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987), p. 461.

1993 (1)

1992 (1)

R. Torroba, H. Rabal, B. Ruiz, J. Mod. Opt. 39, 1939 (1992).
[CrossRef]

1991 (1)

A. Beléndez, L. Carretero, A. Fimia, J. Opt. 22, 163 (1991).
[CrossRef]

1988 (1)

B. R. Frieden, J. Mod. Opt. 35, 1297 (1988).
[CrossRef]

1987 (1)

1980 (1)

C. Dähne, F. Lanzl, Optik 55, 437 (1980).

1972 (2)

1971 (1)

1967 (1)

1955 (1)

Beléndez, A.

A. Beléndez, L. Carretero, A. Fimia, J. Opt. 22, 163 (1991).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987), p. 461.

Burke, J. J.

Carretero, L.

A. Beléndez, L. Carretero, A. Fimia, J. Opt. 22, 163 (1991).
[CrossRef]

Champagne, E. B.

Chen, H.

Dähne, C.

C. Dähne, F. Lanzl, Optik 55, 437 (1980).

Fimia, A.

A. Beléndez, L. Carretero, A. Fimia, J. Opt. 22, 163 (1991).
[CrossRef]

Frieden, B. R.

Hershey, R. R.

Lanzl, F.

C. Dähne, F. Lanzl, Optik 55, 437 (1980).

Latta, J. N.

Leith, E. N.

Linfoot, E. H.

Michael Bove, V.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Dover, New York, 1991).

Rabal, H.

R. Torroba, H. Rabal, B. Ruiz, J. Mod. Opt. 39, 1939 (1992).
[CrossRef]

Ruiz, B.

R. Torroba, H. Rabal, B. Ruiz, J. Mod. Opt. 39, 1939 (1992).
[CrossRef]

Torroba, R.

R. Torroba, H. Rabal, B. Ruiz, J. Mod. Opt. 39, 1939 (1992).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987), p. 461.

Appl. Opt. (2)

J. Mod. Opt. (2)

R. Torroba, H. Rabal, B. Ruiz, J. Mod. Opt. 39, 1939 (1992).
[CrossRef]

B. R. Frieden, J. Mod. Opt. 35, 1297 (1988).
[CrossRef]

J. Opt. (1)

A. Beléndez, L. Carretero, A. Fimia, J. Opt. 22, 163 (1991).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (1)

Optik (1)

C. Dähne, F. Lanzl, Optik 55, 437 (1980).

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987), p. 461.

E. L. O’Neill, Introduction to Statistical Optics (Dover, New York, 1991).

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Figures (3)

Fig. 1
Fig. 1

(a) Entropy and axial irradiance for holographic lenses with a diameter of 5 cm, (b) ray tracing: Ma, marginal plane; LC, last confusion plane; M, medium plane (minimum aberration variance); G, Gaussian plane.

Fig. 2
Fig. 2

(a) Entropy and axial irradiance for holographic lenses with a diameter of 8 cm, (b) ray tracing (notation is the same as that of Fig. 1).

Fig. 3
Fig. 3

Diffraction patterns for a lens diameter equal to 8 cm in (a) Gaussian plane (G), (b) the minimum-aberration-variance plane (M), (c) the minimum-entropy plane.

Equations (8)

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Δ ( x , y ) = ϕ c ( x , y ) - ϕ i ( x , y ) ± [ ϕ 0 ( x , y ) - ϕ r ( x , y ) ] ;
ϕ q ( x , y ) = 2 π λ q [ r q ( x , y ) - R q ] .
W = r c - r i ± μ ( r o - r r ) - [ R c - R i ± μ ( R o - R r ) ] ,
1 R g = 1 R c ± μ ( 1 R o - 1 R r ) ,
sin α g = sin α c ± μ ( sin α o - sin α r ) .
I ( x , y ; z ) = 1 B 2 | S A ( x , y ) exp [ i Δ ( x , y ; x , y ; z ) ] d x d y | 2 ,
P ( x , y ; z ) = I ( x , y ; z ) A I ( x , y ; z ) d x d y ,
S ( z ) = - A P ( x , y ; z ) ln [ P ( x , y ; z ) ] d x d y ,

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