Abstract

The performance is reported of new optimization software that maximizes the relative modulation transfer function (MTF) by minimizing the merit function (1 minus the approximate relative MTF). Contrary to the predictions of earlier studies, this merit function, whose only variable part is the variance of the wave aberration difference function, is shown to be effective for both poorly and well-corrected systems. In addition, the new software is significantly faster than our in-house software for the direct optimization of the actual MTF.

© 1998 Optical Society of America

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References

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  1. H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. B 70, 449–470 (1957).
    [CrossRef]
  2. H. H. Hopkins, “The use of diffraction-based criteria of image quality in automatic optical design,” Opt. Acta 13, 343–369 (1966).
    [CrossRef]
  3. A. Marechal, “Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux,” Rev. Opti. 26, 257–277 (1947).
  4. W. B. King, “A direct approach to the evaluation of the variance of the wave aberration,” Appl. Opt. 7, 489–494 (1968).
    [CrossRef] [PubMed]
  5. W. B. King, “Dependence of the Strehl ratio on the magnitude of the variance of the wave aberration,” J. Opt. Soc. Am. 58, 655–661 (1968).
    [CrossRef]
  6. H. H. Hopkins, “Canonical and real space coordinates used in the theory of image formation,” in Applied Optics and Optical Engineering, Vol. 9 (Academic, New York, 1983), Chap. 8, pp. 307–369.
    [CrossRef]
  7. W. B. King, J. Kitchen, “The evaluation of the variance of the wave-aberration difference function,” Appl. Opt. 7, 1193–1197 (1968).
    [CrossRef] [PubMed]
  8. W. B. King, “Correlation between the relative modulation function and the magnitude of the variance of the wave-aberration difference function,” J. Opt. Soc. Am. 59, 692–697 (1969).
    [CrossRef]

1969 (1)

1968 (3)

1966 (1)

H. H. Hopkins, “The use of diffraction-based criteria of image quality in automatic optical design,” Opt. Acta 13, 343–369 (1966).
[CrossRef]

1957 (1)

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. B 70, 449–470 (1957).
[CrossRef]

1947 (1)

A. Marechal, “Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux,” Rev. Opti. 26, 257–277 (1947).

Hopkins, H. H.

H. H. Hopkins, “The use of diffraction-based criteria of image quality in automatic optical design,” Opt. Acta 13, 343–369 (1966).
[CrossRef]

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. B 70, 449–470 (1957).
[CrossRef]

H. H. Hopkins, “Canonical and real space coordinates used in the theory of image formation,” in Applied Optics and Optical Engineering, Vol. 9 (Academic, New York, 1983), Chap. 8, pp. 307–369.
[CrossRef]

King, W. B.

Kitchen, J.

Marechal, A.

A. Marechal, “Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux,” Rev. Opti. 26, 257–277 (1947).

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Opt. Acta (1)

H. H. Hopkins, “The use of diffraction-based criteria of image quality in automatic optical design,” Opt. Acta 13, 343–369 (1966).
[CrossRef]

Proc. Phys. Soc. B (1)

H. H. Hopkins, “The aberration permissible in optical systems,” Proc. Phys. Soc. B 70, 449–470 (1957).
[CrossRef]

Rev. Opti. (1)

A. Marechal, “Etude des effets combines de la diffraction et des aberrations geometriques sur l’image d’un point lumineux,” Rev. Opti. 26, 257–277 (1947).

Other (1)

H. H. Hopkins, “Canonical and real space coordinates used in the theory of image formation,” in Applied Optics and Optical Engineering, Vol. 9 (Academic, New York, 1983), Chap. 8, pp. 307–369.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Triplet for optimization.

Fig. 2
Fig. 2

MTF before optimization.

Fig. 3
Fig. 3

MTF after optimization.

Tables (1)

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Table 1 Results of Optimization of Triplet

Equations (7)

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MF = i ω i g i 2 ,
D s ,   ψ = T s ,   ψ exp   i θ s ,   ψ = 1 / π   S exp   i 2 π W x ,   y - W x - s   cos   ψ , y - s   sin   ψ d x d y ,
D R s ,   ψ = D s ,   ψ exp   i θ s ,   ψ / D 0 s ,   ψ = M s ,   ψ exp   i θ s ,   ψ ,
M * s ,   ψ = 1 - 2 π 2 s 2 K s ,   ψ M s ,   ψ ,
K s ,   ψ = 1 / S s   S   V 2 x ,   y ;   s ,   ψ d x d y - 1 / S s S   V x ,   y ;   s ,   ψ d x d y 2 ,
V x ,   y ;   s ,   ψ = 1 / S W x ,   y - W x - s   cos   ψ , y - s   sin   ψ .
K s = i j   P i ,   j ;   s W i W j .

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