Abstract

The simple formula suggested below contains, as a special case, the so-called Petzval formula, which gives the field curvature of an optical system in a form which contains a general invariant of the optical system and which is expressed by the powers alone, independent of the center distances.

Let x, y, z, be the coordinates of the object point, and the coordinate of a diapoint where the origins are assumed at the centers of the first and last surfaces, and where the z axis has the direction of the axis of symmetry. If ξ_ν, η_ν, ζ_ν are the direction cosines of the ray in the νth medium multiplied by n_ν, equations can be derived of the form

whereas 1/z′ζ′ is given as a continued fraction containing ϕ_ν/ζ_νζ_ν′ and the center distances c_ν multiplied by ζ_ν.

Equation (1) permits the computation of the contributions of the single surfaces to the diapoint errors. The values ϕ_ν in (1) are the powers of the different surfaces for the ray. The quantity ϕ_ν is practically equal to the Gaussian power of the surface (n_ν′−n_ν)/r_ν, an approximate equality permitting the prediction of the effect of a surface change on the quality of the image.

© 1952 Optical Society of America

Image Error Theory for Finite Aperture and FieldI. The Image of a Point; Geometry of the Wave Surface*,†

Max Herzberger
J. Opt. Soc. Am. 38(8) 736-738 (1948)

Image Error Theory for Finite Aperture and Field*

M. Herzberger and E. Marchand
J. Opt. Soc. Am. 42(5) 306-321 (1952)

Performance of an Optical System as the Sum of the Contributions of Its Construction Elements*

M. Herzberger
J. Opt. Soc. Am. 38(4) 324-328 (1948)

A General Contribution Formula for Tangential Rays

Erwin Delano
J. Opt. Soc. Am. 42(9) 631-633 (1952)

On a New Aberration Function of Optical Instruments

E. Wolf
J. Opt. Soc. Am. 42(8) 547-552 (1952)