Abstract

Astigmatism in noncentered mirror systems, including gratings, is briefly discussed. A formula for meridional coma is derived. It is shown how Seidel aberration terms can be calculated for the sagittal cross section, namely spherical aberration, Petzval curvature, and others. The advantages and limitations of this approach are pointed out.

© 1962 Optical Society of America

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References

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  1. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).
    [Crossref]
  2. T. Namioka, J. Opt. Soc. Am. 49, 446 (1959).
    [Crossref]
  3. M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), Chaps. III and IV.
  4. Piepenpol and co-workers, University of Colorado Upper Air laboratory Special Report No. 2, Boulder, Colorado (1950).
  5. G. Rosendahl, J. Opt. Soc. Am. 51, 1 (1961).
    [Crossref]
  6. E. H. Linfoot, Recent Advances in Optics (Clarendon Press, Oxford, 1955), p. 1.
  7. The numeral I refers to part I; see footnote 5.
  8. A bar indicates that the magnitude concerned is measured with reference to the zero ray.
  9. John Strong, Concepts of Classical Optics (W. H. Freeman and Company, San Francisco, 1958), p. 362.
  10. M. Born and E. Wolf, reference 3, Chap. 5.5.
  11. Johannes Flügge, Das Photogratische Objektiv (Springer-Verlag, Berlin, 1955) p. 68.
    [Crossref]
  12. I. Roman, J. Opt. Soc. Am. 7, 861 (1923).
    [Crossref]

1961 (1)

1959 (1)

1945 (1)

1923 (1)

Beutler, H. G.

Born, M.

M. Born and E. Wolf, reference 3, Chap. 5.5.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), Chaps. III and IV.

Flügge, Johannes

Johannes Flügge, Das Photogratische Objektiv (Springer-Verlag, Berlin, 1955) p. 68.
[Crossref]

Linfoot, E. H.

E. H. Linfoot, Recent Advances in Optics (Clarendon Press, Oxford, 1955), p. 1.

Namioka, T.

Piepenpol,

Piepenpol and co-workers, University of Colorado Upper Air laboratory Special Report No. 2, Boulder, Colorado (1950).

Roman, I.

Rosendahl, G.

Strong, John

John Strong, Concepts of Classical Optics (W. H. Freeman and Company, San Francisco, 1958), p. 362.

Wolf, E.

M. Born and E. Wolf, reference 3, Chap. 5.5.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), Chaps. III and IV.

J. Opt. Soc. Am. (4)

Other (8)

E. H. Linfoot, Recent Advances in Optics (Clarendon Press, Oxford, 1955), p. 1.

The numeral I refers to part I; see footnote 5.

A bar indicates that the magnitude concerned is measured with reference to the zero ray.

John Strong, Concepts of Classical Optics (W. H. Freeman and Company, San Francisco, 1958), p. 362.

M. Born and E. Wolf, reference 3, Chap. 5.5.

Johannes Flügge, Das Photogratische Objektiv (Springer-Verlag, Berlin, 1955) p. 68.
[Crossref]

M. Born and E. Wolf, Principles of Optics (Pergamon Press, New York, 1959), Chaps. III and IV.

Piepenpol and co-workers, University of Colorado Upper Air laboratory Special Report No. 2, Boulder, Colorado (1950).

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Figures (1)

Fig. 1
Fig. 1

Calculation of coma. Point A refers to the apex of the optical surface producing the image.

Equations (34)

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C 1 = C 2 = 0 ,
1 s ¯ s - 1 s ¯ s = - cos σ 0 + cos σ 0 r ;
cos 2 σ 0 s ¯ m - cos 2 σ 0 s ¯ m = - 1 r ( cos σ 0 + cos σ 0 ) .
z s ¯ m + z s ¯ m = h s ( cos σ 0 + cos σ 0 r - 1 s ¯ m ) ,
C = cos σ 0 cos σ 0 ;             C = 1 C = cos σ 0 cos σ 0 ;
S = s ¯ m r cos σ 0 ;             S = s ¯ m r cos σ 0 .
y ¯ c = [ s ¯ m - s ¯ m ( δ ) ] δ ,
s ¯ m = s ¯ m / [ C - S - S C ) C ] .
s ¯ m ( δ ) · δ = s ¯ m δ ( 1 / C ) [ 1 + ( δ - 1 2 φ ) tan σ 0 - ( δ + 1 2 φ ) tan σ 0 ] .
δ = φ ( 1 + C ) + δ C ,
δ - 1 2 φ = φ ( 1 2 + C ) + δ C .
φ = - S δ [ 1 - δ tan σ 0 ( 1 - 1 2 S ) ] ,
δ = δ ( C - S - S C ) + δ 2 tan σ 0 ( 1 + C - 1 2 S - 1 2 S C ) S ,
δ - 1 2 φ = δ ( C - 1 2 S - S C ) ,
δ + 1 2 φ = δ ( 1 - 1 2 S ) .
s ¯ m ( δ ) · δ = s ¯ m · δ ( 1 / C ) [ 1 + ( C - 1 2 S - S C ) δ tan σ 0 - ( 1 - 1 2 S ) δ tan σ 0 ] .
s ¯ m · δ = s ¯ m δ ( 1 / C ) [ 1 + ( 1 + 1 2 C C - S - S C + 1 2 ) δ S tan σ 0 ] .
y ¯ c = s ¯ m δ 2 · ( 1 / C ) [ C - 1 2 S C C - S - S C tan σ 0 - ( C - 1 2 S - S C ) tan σ 0 ] .
h ¯ = - s ¯ m δ ;             h ¯ = - s ¯ m δ ,
y ¯ c = h ¯ 2 r cos σ 0 [ s ¯ m s ¯ m ( r cos σ 0 s ¯ m - 1 2 ) sin σ 0 cos σ 0 - ( r cos σ 0 s ¯ m + 1 2 ) sin σ 0 cos σ 0 ] .
y ¯ c = h ¯ 2 tan σ 0 r cos σ 0 [ s ¯ m s ¯ m ( r cos σ 0 s ¯ m - 1 2 ) - ( r cos σ 0 s ¯ m + 1 2 ) ] .
y ¯ c = h ¯ 2 r cos σ 0 [ ( r cos σ 0 s ¯ m - 1 2 ) sin σ 0 cos σ 0 - s ¯ m s ¯ m ( r cos σ 0 s ¯ m + 1 2 ) sin σ 0 cos σ 0 ] .
δ cos σ 0 = δ cos σ 0
h ¯ / cos σ 0 = h ¯ / cos σ 0 .
y ¯ c = ν = 1 k β m ( ν + 1 ) · y ¯ c ( ν ) ;
y ¯ = - s ¯ m d σ 0 ,
y ¯ = - s ¯ m d σ 0 ,
cos σ 0 d σ 0 = cos σ 0 d σ 0 .
M m = y ¯ y ¯ = s ¯ m cos σ 0 s ¯ m cos σ 0 ;
β m ( ν + 1 ) = μ = ν + 1 k s ¯ m ( μ ) cos σ 0 ( μ ) s ¯ m ( μ ) cos σ 0 ( μ ) .
β s ( ν + 1 ) = μ = ν + 1 k s ¯ s ( μ ) / s ¯ s ( μ ) .
Q 0 ν = ( cos σ 0 r - 1 s ¯ s ) ν = - ( cos σ 0 r - 1 s ¯ s ) ν .
Q ν 2 ( 1 s ¯ s - 1 s ¯ s ) = [ Q 0 2 ( 1 s ¯ s - 1 s ¯ s ) + 2 E r 0 3 ] ν ,
P ν = + f cos σ 0 ( ν ) + cos σ 0 ( ν ) r ( ν ) .