Abstract

Wave-front aberration is a basic characteristic of the imaging properties of optical systems. The value of the wave-front aberration is obtained by calculating the difference between the optical path lengths of the real wave front and the reference sphere. The general relations for calculated dependence of the wave-front aberration on the radius of the reference sphere are given.

© 2002 Optical Society of America

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References

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  1. P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997).
  2. M. Born, E. Wolf, Principles of Optics (Oxford U. Press, New York, 1964).
  3. H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, New York, 1950).
  4. A. Cox, A System of Optical Design (Focal, London, 1964).
  5. H. Haferkorn, Bewertung optisher systeme (VEB Deutscher Verlag der Wissenschaften, Berlin, 1986).
  6. W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, London, 1974).
  7. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, UK, 1970).
  8. W. J. Smith, Modern Lens Design (McGraw-Hill, New York, 1992).
  9. A. Marechal, M. Francon, Diffraction Structure des Images (Edition de la Revue d’Optique, Paris, 1960).

Born, M.

M. Born, E. Wolf, Principles of Optics (Oxford U. Press, New York, 1964).

Buchdahl, H. A.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, UK, 1970).

Cox, A.

A. Cox, A System of Optical Design (Focal, London, 1964).

Francon, M.

A. Marechal, M. Francon, Diffraction Structure des Images (Edition de la Revue d’Optique, Paris, 1960).

Haferkorn, H.

H. Haferkorn, Bewertung optisher systeme (VEB Deutscher Verlag der Wissenschaften, Berlin, 1986).

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, New York, 1950).

Macdonald, J.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997).

Marechal, A.

A. Marechal, M. Francon, Diffraction Structure des Images (Edition de la Revue d’Optique, Paris, 1960).

Mouroulis, P.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997).

Smith, W. J.

W. J. Smith, Modern Lens Design (McGraw-Hill, New York, 1992).

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, London, 1974).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Oxford U. Press, New York, 1964).

Other (9)

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997).

M. Born, E. Wolf, Principles of Optics (Oxford U. Press, New York, 1964).

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, New York, 1950).

A. Cox, A System of Optical Design (Focal, London, 1964).

H. Haferkorn, Bewertung optisher systeme (VEB Deutscher Verlag der Wissenschaften, Berlin, 1986).

W. T. Welford, Aberrations of the Symmetrical Optical Systems (Academic, London, 1974).

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, UK, 1970).

W. J. Smith, Modern Lens Design (McGraw-Hill, New York, 1992).

A. Marechal, M. Francon, Diffraction Structure des Images (Edition de la Revue d’Optique, Paris, 1960).

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Figures (3)

Fig. 1
Fig. 1

Propagation of a wave front through an optical system.

Fig. 2
Fig. 2

Wave fronts in image space.

Fig. 3
Fig. 3

Rays in image space.

Equations (25)

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W=[B, Q]-[B, G]=VQ-VG,
W=VQ-VG=VQ-VE.
VQ=VA-n(rA-rQ)s=VB-n(rB-rQ)s=VB+nrFs-nR cos θ,
VE=VBE+nrFsE-nR cos θE.
W=VB-VBE+n(s-sE)rF-nR(cos θ-cos θE).
W0=VB-VBE+n(s-sE)rF0
W=W0+n(s-sE)(rF-rF0)-nR(cos θ-cos θE).
BQ¯=(rQE-rB)(s+sE)1+ssE
(s-sE)(rF-rF0)=CEDE¯-CD¯.
δW=(s-sE)(rF-rF0)=(rC-rCE)(s+sE)1+ssE.
W=W0+nδW-nR(cos θ-cos θE).
rC-rCE=a-s(sa),cos θE=1,
δW=[sE-s(ssE)]a1+ssE.
sin2 θ=aa-(sa)2R2,
R(1-cos θ)=aa-(sa)2R(1+cos θ).
W=W0+n[sE-s(ssE)]a1+ssE+naa-(sa)2R(1+cos θ).
W=W0+n[sE-s(ssE)]a1+ssE
W=W+naa-(sa)2R(1+cos θ).
cos θ=1-sin2 θ1-12sin2 θ=1-aa-(sa)22R2.
WW+naa-(sa)22R1+aa-(sa)24R2=W+δWR.
δWδW=n[sE-s(ssE)]δa1+ssE,
δW=n[sE-s(ssE)]δa1+ssE=nsin2 U1+cos U δZ12 nδZ sin2 U.
WW+naa-(sa)22R1+aa-(sa)24R2W+naa2R,
δW-naa2R2 δR=-n2 θ2δR,
δWR=0.032-(0.18×0.03)22×50=8.7×10-6mm.

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