Abstract

The location of the best focuses and the image quality of lenses with spherical aberration were determined by measuring the intensity distribution of light in the line image, and the results were compared with the theoretical results obtained by wave optics.

In the presence of primary spherical aberration, S₁≡δs_m/(F²λ) is introduced as a parameter, where δs_m is the marginal spherical aberration, F is the f-number, and λ is the wavelength. The best focus lies: (1) midway between the paraxial and marginal foci for S₁<36; and (2) away from the paraxial to the marginal foci by about ${(5.6/S_1)}^{\frac{1}{2}}$ for S₁>36.

In the presence of primary and secondary spherical aberration with the maximum value δs_z, the location of the best focuses, δf₀ measured from the paraxial focus and the definition |Γ|² for the line image at the corrected aperture F₀, are given by a parameter S₂≡δs_z/(F₀²λ) as

and

The best type of correction for a given value of the secondary coefficient of aberration are also discussed.

© 1955 Optical Society of America

Studies on the Image Formed by Lenses. I. On the Characteristics of an Image and Their Quantitative Representation*

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