Abstract

<p>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.</p><p>Let <i>x, y, z</i>, 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<sub>ν</sub>, η<sub>ν</sub>, ζ<sub>ν</sub> are the direction cosines of the ray in the νth medium multiplied by <i>n</i><sub>ν</sub>, equations can be derived of the form [Equation] whereas 1/<i>z</i>′ζ′ is given as a continued fraction containing <i>ϕ</i><sub>ν</sub>/ζ<sub>ν</sub>ζ<sub>ν</sub>′ and the center distances <i>c</i><sub>ν</sub> multiplied by ζ<sub>ν</sub>.</p><p>Equation (1) permits the computation of the contributions of the single surfaces to the diapoint errors. The values <i>ϕ</i><sub>ν</sub> in (1) are the powers of the different surfaces for the ray. The quantity <i>ϕ</i><sub>ν</sub> is practically equal to the Gaussian power of the surface (<i>n</i><sub>ν</sub>′-<i>n</i><sub>ν</sub>)/<i>r</i><sub>ν</sub>, an approximate equality permitting the prediction of the effect of a surface change on the quality of the image.</p>

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