Abstract

In the previous paper (part I), the relation between wave optics and geometrical optics has been studied generally by using the Fourier analysis. In this paper the general theory is applied to the concrete examples of the astigmatism, coma, and spherical aberration, and the following results are obtained.

In case of astigmatism, if the magnitude of the wave aberration |ωλ| is larger than 2λ (λ being the wavelength), the geometric optical response function Rg(s) approximates to the wave optical response function Rw(s) within the region of the normalized frequency s where |λs/2|<0.2.

In the case of coma, if we consider the response function corresponding to the line image being perpendicular to the sagittal direction, Rg(s) approximates to Rw(s) when |ωλ|>1.2λ and |λs/2|<0.5; furthermore, concerning the line image being perpendicular to the meridional direction, Rg(t) approaches Rw(t) when |ωλ|>1.6λ and |λt/2|<0.25.

Finally, in case of spherical aberration, Rg(s) approximates to Rw(s), if |ωλ|>1.3λ and |λs/2|<0.4.

© 1958 Optical Society of America

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