Abstract

Using a proposed evolutionary algorithm, we have solved the inverse problem of finding the incident field on a high-aperture lens for generating a desired focused field, for the first time (to our knowledge). Further, we have achieved the global solution to the problem using this novel algorithm.

© 2008 Optical Society of America

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References

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  1. B. Richards, and E. Wolf, Proc. R. Soc. London 253, 358 (1961).
  2. F. Massoumian, Ph.D dissertation (Oxford University, 2003).
  3. C. Papadimitriou, Computational Complexity, 1st ed., (Addison Wesley, 1994), Chap. 9, p. 181.
  4. J. R. Koza, Genetic Programming: on the Programming of Computers by Means of Natural Selection, (MIT Press, 1992).
  5. I. Rechenberg, Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution (Frommann-Holzboog, 1973).
  6. H.-P. Schwefel, Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie (Birkhäuser, 1977).
  7. L. J. Fogel, A. J. Owens, and M. J. Walsh, Artificial Intelligence through Simulated Evolution (Wiley, 1966).
  8. J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975).

1961 (1)

B. Richards, and E. Wolf, Proc. R. Soc. London 253, 358 (1961).

Fogel, L. J.

L. J. Fogel, A. J. Owens, and M. J. Walsh, Artificial Intelligence through Simulated Evolution (Wiley, 1966).

Holland, J. H.

J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975).

Koza, J. R.

J. R. Koza, Genetic Programming: on the Programming of Computers by Means of Natural Selection, (MIT Press, 1992).

Massoumian, F.

F. Massoumian, Ph.D dissertation (Oxford University, 2003).

Owens, A. J.

L. J. Fogel, A. J. Owens, and M. J. Walsh, Artificial Intelligence through Simulated Evolution (Wiley, 1966).

Papadimitriou, C.

C. Papadimitriou, Computational Complexity, 1st ed., (Addison Wesley, 1994), Chap. 9, p. 181.

Rechenberg, I.

I. Rechenberg, Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution (Frommann-Holzboog, 1973).

Richards, B.

B. Richards, and E. Wolf, Proc. R. Soc. London 253, 358 (1961).

Schwefel, H.-P.

H.-P. Schwefel, Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie (Birkhäuser, 1977).

Walsh, M. J.

L. J. Fogel, A. J. Owens, and M. J. Walsh, Artificial Intelligence through Simulated Evolution (Wiley, 1966).

Wolf, E.

B. Richards, and E. Wolf, Proc. R. Soc. London 253, 358 (1961).

Proc. R. Soc. London (1)

B. Richards, and E. Wolf, Proc. R. Soc. London 253, 358 (1961).

Other (7)

F. Massoumian, Ph.D dissertation (Oxford University, 2003).

C. Papadimitriou, Computational Complexity, 1st ed., (Addison Wesley, 1994), Chap. 9, p. 181.

J. R. Koza, Genetic Programming: on the Programming of Computers by Means of Natural Selection, (MIT Press, 1992).

I. Rechenberg, Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution (Frommann-Holzboog, 1973).

H.-P. Schwefel, Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie (Birkhäuser, 1977).

L. J. Fogel, A. J. Owens, and M. J. Walsh, Artificial Intelligence through Simulated Evolution (Wiley, 1966).

J. H. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press, 1975).

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Figures (4)

Fig. 1
Fig. 1

Incident field being focused field by a high-aperture lens.

Fig. 2
Fig. 2

Solution vector.

Fig. 3
Fig. 3

Error rate versus number of iterations for finding the solution for an elliptically polarized focused field.

Fig. 4
Fig. 4

(a) Form of the focused field after ten iterations, magnitude of the y ̂ component of the field in the focal plane. (b) Form of the focused field after 275 iterations, magnitude of the y ̂ component of the field in the focal plane. (c) Form of the focused field after 484 iterations, magnitude of the y ̂ component of the field in the focal plane.

Tables (1)

Tables Icon

Table 1 Performance of the Algorithms for Different Samples

Equations (3)

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E i = α ρ a ρ + β φ a φ ,
E ( ρ s , φ s ) = 0 α 0 2 π cos θ ( α ρ ( cos θ cos φ cos θ sin φ sin θ ) + β φ ( sin φ cos φ 0 ) ) × exp [ i k ρ s cos ( φ φ s ) sin θ ] exp ( i k f cos θ ) sin θ d θ d φ ,
σ = n = 1 N { E x ( ρ sn , φ sn ) E x d ( ρ sn , φ sn ) 2 + E y ( ρ sn , φ sn ) E y d ( ρ sn , φ sn ) 2 + E z ( ρ sn , φ sn ) E z d ( ρ sn , φ sn ) 2 } .

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