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 R_g(s) approximates to the wave optical response function R_w(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, R_g(s) approximates to R_w(s) when |ωλ|>1.2λ and |λs/2|<0.5; furthermore, concerning the line image being perpendicular to the meridional direction, R_g(t) approaches R_w(t) when |ωλ|>1.6λ and |λt/2|<0.25.

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

© 1958 Optical Society of America

On a Comparison between Wave Optics and Geometrical Optics by Using Fourier Analysis. I. General Theory

Kenrō Miyamoto
J. Opt. Soc. Am. 48(1) 57-63 (1958)

On a Comparison between Wave Optics and Geometrical Optics by Using Fourier Analysis. III. Image Evaluation by Spot Diagram

Kenyō Miyamoto
J. Opt. Soc. Am. 49(1) 35-40 (1959)

Relationship between the Sine-Wave Response and the Distribution of Energy in the Optical Image of a Line*

Robert L. Lamberts
J. Opt. Soc. Am. 48(7) 490-495 (1958)

Analysis of Interference Fringes from a Flame*

Boyd W. Harned and N. Ginsburg
J. Opt. Soc. Am. 48(3) 178-183 (1958)

Optical Aberration Coefficients. IV. The Coefficient of Quaternary Spherical Aberration

H. A. Buchdahl
J. Opt. Soc. Am. 48(10) 757-759 (1958)