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, S1δsm/(F2λ) is introduced as a parameter, where δsm 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/S1)12 for S1>36.

In the presence of primary and secondary spherical aberration with the maximum value δsz, 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 S2δsz/(F02λ) as

Γ2=1-1.955×10-4S22         δf0=0.80δsz         for         S2<20,

and

Γ2=5.35(1/S2)23         δf0=[1-(2.62/S2)23]δsz         for         S2>45.

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

© 1955 Optical Society of America

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