Abstract

A criterion is established for determining when portions of a wave front can be said to be optically isolated from the rest of the wave front in the sense that they can subsequently be treated separately when one is considering the formation of images. The subarea of the wave front is treated as a separate aperture, and it is said to be isolated if diffraction maxima for the majority of the wave front fall at or beyond the first minima for the subarea. An illustrative example employing two circular unequal-diameter apertures is presented. A method is given for identifying portions of wave front that may be optically isolated; the method uses the technique of fitting a reference surface to the actual wave front and then finding what is defined as the differential deflection of the actual surface with respect to the reference surface at all locations. Subpopulations of locations with similar differential deflection values, sufficient numbers, and sufficient differential deflection are candidates for area of optical isolation.

© 1998 Optical Society of America

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References

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  1. Rayleigh, Philos. Mag. 8, 261 (1879).
    [CrossRef]
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 333.
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    [CrossRef] [PubMed]
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  6. J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–916 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. C. Campbell, “Corneal aberrations, monocular diplopia and ghost images: analysis using corneal topographical data,” Optom. Vision Sci. 75, 197–207 (1998).
    [CrossRef]
  9. C. Campbell, “Caustics in astigmatic systems,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 20–23.
  10. S. A. Klein, Z. Ho, “Multizone bifocal contact lens design,” in Current Developments in Optical Engineering and Diffraction Phenomena, R. E. Fischer, J. E. Harvey, W. J. Smith, eds., Proc. SPIE679, 25–35 (1986).
    [CrossRef]

1998 (1)

C. Campbell, “Corneal aberrations, monocular diplopia and ghost images: analysis using corneal topographical data,” Optom. Vision Sci. 75, 197–207 (1998).
[CrossRef]

1997 (1)

J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–916 (1997).
[CrossRef]

1980 (1)

1977 (1)

1879 (1)

Rayleigh, Philos. Mag. 8, 261 (1879).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 333.

Campbell, C.

C. Campbell, “Corneal aberrations, monocular diplopia and ghost images: analysis using corneal topographical data,” Optom. Vision Sci. 75, 197–207 (1998).
[CrossRef]

C. Campbell, “Caustics in astigmatic systems,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 20–23.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), p. 64.

Greivenkamp, J. E.

J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–916 (1997).
[CrossRef]

Ho, Z.

S. A. Klein, Z. Ho, “Multizone bifocal contact lens design,” in Current Developments in Optical Engineering and Diffraction Phenomena, R. E. Fischer, J. E. Harvey, W. J. Smith, eds., Proc. SPIE679, 25–35 (1986).
[CrossRef]

Howland, B.

Howland, H.

Klein, S. A.

S. A. Klein, Z. Ho, “Multizone bifocal contact lens design,” in Current Developments in Optical Engineering and Diffraction Phenomena, R. E. Fischer, J. E. Harvey, W. J. Smith, eds., Proc. SPIE679, 25–35 (1986).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), pp. 489–505, 507–511.

Rayleigh,

Rayleigh, Philos. Mag. 8, 261 (1879).
[CrossRef]

Schwiegerling, J.

J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–916 (1997).
[CrossRef]

Silva, D. E.

Wang, J. Y.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 333.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Optom. Vision Sci. (2)

J. Schwiegerling, J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vision Sci. 74, 906–916 (1997).
[CrossRef]

C. Campbell, “Corneal aberrations, monocular diplopia and ghost images: analysis using corneal topographical data,” Optom. Vision Sci. 75, 197–207 (1998).
[CrossRef]

Philos. Mag. (1)

Rayleigh, Philos. Mag. 8, 261 (1879).
[CrossRef]

Other (5)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), p. 333.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), p. 64.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978), pp. 489–505, 507–511.

C. Campbell, “Caustics in astigmatic systems,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 20–23.

S. A. Klein, Z. Ho, “Multizone bifocal contact lens design,” in Current Developments in Optical Engineering and Diffraction Phenomena, R. E. Fischer, J. E. Harvey, W. J. Smith, eds., Proc. SPIE679, 25–35 (1986).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Amplitude and intensity plots for two circular apertures for two angular separation conditions. The larger aperture has four times the area of the smaller. (a) and (c) show the amplitude and intensity for the separation that fulfills the criterion for optical isolation, i.e., the first minima of the smaller aperture coincides with the maxima of the larger. The plots for the individual apertures are shown as dashed curves. The combined effect is shown as a solid curve. (b) and (d) show the condition for the same two apertures with a lesser separation, one equal to the mean distance to first minima for the two apertures.

Equations (5)

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A=-i exp(ikz)expika22z ka22z2J1karzkarz,
A=Cka22z2J1karzkarz,
A=Cπa2λz2J12πaδλ2πaδλ.
2aδλ=1.22,
δ=0.61λa.

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