円周方向に正弦的構造をもつ開口による廻折像

抄録

Recently, it was reported by H. Kubota that the diffraction image formed by polarizing microscope is quite different from the regular Airy disc. This is due to the rotation of the plane of polarization of light during the passage through the system and the diffraction image is four-leaf clover in the case of crossed Nicols. The diffraction image of a point source by an optical system is obtained as the Fourier transform of the pupil function, and it is treated in this paper the case when the angular variation of the amplitude of waves in the pupil (pupil function) is sinusoidal. When the pupil function is represented by ƒ (r, θ)=a_n sin nθ (for r_??_1), the amplitude of diffraction image is obtained as the Fourier transform as:
F(ρ.φ)=a_n/2π_??__??_sinnθ·exp{iρrcos(θ-φ)}rdrds=a_n(i)ⁿsinnφ_??_J_n(ρr)rdr.
This clearly shows that the amplitude of diffraction image varies also sinusoidally with the same period as that of the pupil function. Accordingly, the intensity distribution of image has 2n bright leaves and 2n dark lines radiating from the center.
To make the experiment easier, the case when the amplitude varies as a rectangular wave form is treated instead of that of sinusoidal variation in the pupil. The pupil function is expanded as a Fourier series and the above discussion is applied to each terms. The diffraction patterns are shown theoretically as well as experimentally with the photographic illustration. The diffraction patterns in the case when the intensity varies in the same manner is obtained as the sum of the above mentioned diffraction pattern and the Airy disc. These patterns are also illustrated photographically.