Abstract

The aberrations of axisymmetric imaging systems can be calculated to third order by use of the Seidel formulas. The Coddington equations give aberrations that have quadratic dependence on the pupil, for all field points. The pupil astigmatism conditions were recently developed to predict and control aberrations that have quadratic field dependence and arbitrary pupil dependence. We investigate the relationship between the exact pupil astigmatism conditions and the classical Seidel treatment of pupil aberrations.

© 2002 Optical Society of America

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References

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  1. W. T. Welford, Aberrations of Optical Systems (Hilgler, Bristol, UK, 1986).
  2. R. V. Shack, Introduction to Aberration Theory, Class Notes (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998).
  3. R. V. Shack, Advanced Aberration Theory, Class Notes (Optical Sciences Center, the University of Arizona, Tucson, Ariz., 1998).
  4. M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).
  5. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).
  6. H. A. Buchdall, An Introduction to Hamiltonian Optics (Cambridge U. Press, Cambridge, UK, 1970).
  7. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990).

Born, M.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

Buchdall, H. A.

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

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).

Shack, R. V.

R. V. Shack, Introduction to Aberration Theory, Class Notes (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998).

R. V. Shack, Advanced Aberration Theory, Class Notes (Optical Sciences Center, the University of Arizona, Tucson, Ariz., 1998).

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990).

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilgler, Bristol, UK, 1986).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

Other (7)

W. T. Welford, Aberrations of Optical Systems (Hilgler, Bristol, UK, 1986).

R. V. Shack, Introduction to Aberration Theory, Class Notes (Optical Sciences Center, University of Arizona, Tucson, Ariz., 1998).

R. V. Shack, Advanced Aberration Theory, Class Notes (Optical Sciences Center, the University of Arizona, Tucson, Ariz., 1998).

M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964).

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, Calif., 1966).

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

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1990).

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Figures (4)

Fig. 1
Fig. 1

Three-dimensional illustration of an aplanatic optical system with the object a finite distance away.

Fig. 2
Fig. 2

Three-dimensional illustration of an aplanatic optical system with the object at infinity.

Fig. 3
Fig. 3

Illustration of the definitions of the ray angles and heights at a surface.

Fig. 4
Fig. 4

Illustration of a system with the entrance pupil at infinity, where s′ and t′ denote the sagittal and tangential pupil curves.

Tables (1)

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Table 1 Summary of Seidel Aberrations

Equations (41)

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tθcos2θ=const.
sθ=const.
sθ=tθcos2θ.
sθ=tθcos2θ=const.
P= cΔ1n,
H=nu¯y-nuy¯,
A=ni, A¯=nī.
SIII=- A¯2yΔun,
SIV=- H2cΔ1n,
S¯III=- A2y¯Δu¯n,
S¯IV=- H2cΔ1n.
S¯III=SIII+HΔuu¯, S¯IV=SIV.
S¯IV+S¯III=SIV+SIII+HΔuu¯,
S¯IV+2S¯III=SIV+2SIII+2HΔuu¯,
S¯IV+3S¯III=SIV+3SIII+3HΔuu¯.
δz¯sSeidel=-12nu¯2S¯IV+S¯III,
δz¯mSeidel=-12nu¯2S¯IV+2S¯III,
δz¯tSeidel=-12nu¯2S¯IV+3S¯III,
δz¯tSeidel-δz¯sSeidel=-S¯IIInu¯2,
δz¯tSeidel-3δz¯sSeidel=S¯IVnu¯2,
u¯=y¯/R, H=-nuy¯.
HΔuu¯=-nRu2u¯2.
tucos2u=R,
δz¯t=R-t cosu=R1-cos3u.
δz¯tSeidel=3Ru2/2.
S¯IV+3S¯III=-3nRu2u¯2=3HΔuu¯.
SIV+3SIII=0,
su=R,
δz¯s=R1-cosu.
δz¯sSeidel=Ru22.
S¯IV+S¯III=-nRu2u¯2=HΔuu¯.
SIV+SIII=0,
su=tucos2u=Ru.
δz¯t=R-Rucos3u,
δz¯s=R-Rucosu.
δz¯t-δz¯s=Rucosu1-cos2u.
δz¯tSeidel-δz¯sSeidel=Ru2.
S¯III=-nRu2u¯2.
SIII=0,
su=tucos2u=R,
SIII=0, SIV=0,

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