Abstract

Equations for the third-order aberrations in the meridional plane of a symmetrical optical system in the presence of finite tilts and decentrations are derived, based on the stop-shift equations of H. H. Hopkins. To demonstrate the application of these formulas and to show the degree of agreement between these equations and an exact ray trace, a numerical example is included.

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References

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  1. Many early references as to the first-order properties of tilted or decentered lenses may be found in the book by S. Czapski and O. Eppenstein, Grundzüge der Theorie der Optischen Instrumente (Johann Ambrosius Barth, Leipzig, Germany, 1924), especially on p. 65.
  2. A. Maréchal, Rev. Opt., 1–24 (1950). Many references are also found in the bibliography on p. 24.
  3. A. L. Ingalls and K. Pestrecov, J. Opt. Soc. Am. 38, 343–349 (1948).
  4. P. C. Foote and R. A. Woodson, J. Opt. Soc. Am. 39, 590–599 (1949).
  5. L. I. Epstein, J. Opt. Soc. Am. 39, 847–853 (1949).
  6. G. Wooters, J. Opt. Soc. Am. 40, 521–523 (1950).
  7. H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, New York, 1950), pp. 76–118.
  8. C. G. Wynne, Proc. Phys. Soc. (London) B65, 429–437 (1952).
  9. Reference 7, p. 87.
  10. Reference 8, p. 430.
  11. Reference 7, p. 104.
  12. Reference 8, p. 431.

Czapski, S.

Many early references as to the first-order properties of tilted or decentered lenses may be found in the book by S. Czapski and O. Eppenstein, Grundzüge der Theorie der Optischen Instrumente (Johann Ambrosius Barth, Leipzig, Germany, 1924), especially on p. 65.

Eppenstein, O.

Many early references as to the first-order properties of tilted or decentered lenses may be found in the book by S. Czapski and O. Eppenstein, Grundzüge der Theorie der Optischen Instrumente (Johann Ambrosius Barth, Leipzig, Germany, 1924), especially on p. 65.

Epstein, L. I.

L. I. Epstein, J. Opt. Soc. Am. 39, 847–853 (1949).

Foote, P. C.

P. C. Foote and R. A. Woodson, J. Opt. Soc. Am. 39, 590–599 (1949).

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, New York, 1950), pp. 76–118.

Ingalls, A. L.

A. L. Ingalls and K. Pestrecov, J. Opt. Soc. Am. 38, 343–349 (1948).

Maréchal, A.

A. Maréchal, Rev. Opt., 1–24 (1950). Many references are also found in the bibliography on p. 24.

Pestrecov, K.

A. L. Ingalls and K. Pestrecov, J. Opt. Soc. Am. 38, 343–349 (1948).

Woodson, R. A.

P. C. Foote and R. A. Woodson, J. Opt. Soc. Am. 39, 590–599 (1949).

Wooters, G.

G. Wooters, J. Opt. Soc. Am. 40, 521–523 (1950).

Wynne, C. G.

C. G. Wynne, Proc. Phys. Soc. (London) B65, 429–437 (1952).

Other

Many early references as to the first-order properties of tilted or decentered lenses may be found in the book by S. Czapski and O. Eppenstein, Grundzüge der Theorie der Optischen Instrumente (Johann Ambrosius Barth, Leipzig, Germany, 1924), especially on p. 65.

A. Maréchal, Rev. Opt., 1–24 (1950). Many references are also found in the bibliography on p. 24.

A. L. Ingalls and K. Pestrecov, J. Opt. Soc. Am. 38, 343–349 (1948).

P. C. Foote and R. A. Woodson, J. Opt. Soc. Am. 39, 590–599 (1949).

L. I. Epstein, J. Opt. Soc. Am. 39, 847–853 (1949).

G. Wooters, J. Opt. Soc. Am. 40, 521–523 (1950).

H. H. Hopkins, Wave Theory of Aberrations (Oxford University Press, New York, 1950), pp. 76–118.

C. G. Wynne, Proc. Phys. Soc. (London) B65, 429–437 (1952).

Reference 7, p. 87.

Reference 8, p. 430.

Reference 7, p. 104.

Reference 8, p. 431.

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