Abstract

This paper develops the theory of aberrations of concentric optical systems, supposed nontelescopic. In Part One the monochromatic-aberration coefficients of orders three, five, and seven, and some paraxial and nonparaxial chromatic-aberration coefficients are obtained explicitly on the basis of known relations from the algebraic theory of general systems. Part Two extends the algebraic theory of concentric systems to all orders, the displacement being exhibited in closed form involving a single unspecified function, i.e., the spherical-aberration function. The Hamiltonian theory of concentric systems is briefly considered in Part Three.

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  1. For example, M. Herzberger, Modern Geometrical Optics (Interscience Publishers, Inc., New York, 1958), Chaps. 18 and 19, p. 193.
  2. A. Bouwvers, Achievements in Optics (Elsevier Publishing Company, Inc., New York, 1950), Chap. 1, p. 25.
  3. H. A. Buchdahl, J. Opt. Soc. Am. 51, 608 (1961).
  4. H. A. Buchdahl, Optical Aberration Coefficients (Oxford University Press, New York, 1954), hereafter referred to as M.
  5. H. A. Buchdahl, J. Opt. Soc. Am. 48, 563 (1958) and 48, 747 (1958); these papers are distinguished by II and III, respectively.
  6. S. Rosin, J. Opt. Soc. Am. 49, 862 (1959).
  7. The refractive indices in the object and image spaces are taken as unity.
  8. Here ρ1, H and θ are the variables which were denoted by ρ, H¯, θ in M Sec. 31(a); i.e., H is the ideal image height and ρ1, θ are polar variables in the plane of the (equivalent) entrance pupil.
  9. In M the subscript which specifies the chromatic order appears under the kernel symbol instead of to the left of it.
  10. Since one is now concerned with quantities solely in the object and image spaces these may simply be denoted by unprimed and primed symbols respectively.

Bouwvers, A.

A. Bouwvers, Achievements in Optics (Elsevier Publishing Company, Inc., New York, 1950), Chap. 1, p. 25.

Buchdahl, H. A.

H. A. Buchdahl, Optical Aberration Coefficients (Oxford University Press, New York, 1954), hereafter referred to as M.

H. A. Buchdahl, J. Opt. Soc. Am. 51, 608 (1961).

H. A. Buchdahl, J. Opt. Soc. Am. 48, 563 (1958) and 48, 747 (1958); these papers are distinguished by II and III, respectively.

Herzberger, M.

For example, M. Herzberger, Modern Geometrical Optics (Interscience Publishers, Inc., New York, 1958), Chaps. 18 and 19, p. 193.

Rosin, S.

S. Rosin, J. Opt. Soc. Am. 49, 862 (1959).

Other

For example, M. Herzberger, Modern Geometrical Optics (Interscience Publishers, Inc., New York, 1958), Chaps. 18 and 19, p. 193.

A. Bouwvers, Achievements in Optics (Elsevier Publishing Company, Inc., New York, 1950), Chap. 1, p. 25.

H. A. Buchdahl, J. Opt. Soc. Am. 51, 608 (1961).

H. A. Buchdahl, Optical Aberration Coefficients (Oxford University Press, New York, 1954), hereafter referred to as M.

H. A. Buchdahl, J. Opt. Soc. Am. 48, 563 (1958) and 48, 747 (1958); these papers are distinguished by II and III, respectively.

S. Rosin, J. Opt. Soc. Am. 49, 862 (1959).

The refractive indices in the object and image spaces are taken as unity.

Here ρ1, H and θ are the variables which were denoted by ρ, H¯, θ in M Sec. 31(a); i.e., H is the ideal image height and ρ1, θ are polar variables in the plane of the (equivalent) entrance pupil.

In M the subscript which specifies the chromatic order appears under the kernel symbol instead of to the left of it.

Since one is now concerned with quantities solely in the object and image spaces these may simply be denoted by unprimed and primed symbols respectively.

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