抄録
The matrix formulation for the intensity distribution of images obtained by a circular aperture is derived by using the circle sampling theorem obtained by the writer. By assuming that the amplitude distribution of the wave on a plane is limited within a circle and its Fourier-transform is also limited within another circle, it can be shown that the amplitude distribution mentioned above can be described by both Fourier-Bessel and circle sampling expansions. Then, by using these expansions two types of intensity matrices are derived for the intensity distribution of the above wave. The intensity matrix for the illumination upon the object plane is calculated by using H. H. Hopkins' phase-coherence factor, and intensity matrices for waves on the object plane after transmission of the object, on the planes of entrance and exit pupils and on the image plane are derived by the successive matrix-transformation from the above intensity matrix for the illumination. The elements of transformation matrices are generally obtained by considering the relation between a circle-sampling value (or Fourier-Bessel coefficient) of the waves on the first plane and the circle-sampling values (or Fourier-Bessel coefficients) of the waves on the second plane. The experimental methods determining the elements of an intensity matrix of a given image are discussed. Namely, concerning the circle-sampling type of intensity matrix, a matrix element Ams: nt can be obtained by measuring the intensity at the origin of the Fraunhofer diffraction pattern of waves produced after passing waves of a given image through the “circle sampling filter”, which is transparent on the circumferences of sampling circles having radii λms/ka and λnt/ka and has phase factors exp (-imθ) and exp (-inθ) respectively on these circumferences and intercepts the light outside of these circumferences. The Fourier-Bessel type of intensity matrix can be obtained in the same way-by inserting the circle-sampling filter mentioned above on the exit pupil of the image-forming system.
