A pupil function of aperture in image capturing systems is theoretically derived such that one can perfectly reconstruct all-in-focus image through linear filtering of the focal stack. The perfect reconstruction filters are also designed based on the derived pupil function. The designed filters are space-invariant; hence the presented method does not require region segmentation. Simulation results using synthetic scenes shows effectiveness of the derived pupil function and the filters.

The two-dimensional spatial image transmission characteristics of the optical graded-index fiber with a refractive index distribution including fourth and sixth order terms in the core region are investigated. Since the GRIN fiber for image transmission has a large core radius, the most field is tightly confined to the center of the core. The effect of the core-clad interface on the image transmission characteristics is approximately evaluated. Therefore the GRIN fiber is assumed to have an infinitely-extended index profile. The propagation constants and the electric field distributions in the core region are strongly affected by the coefficient of the fourth order term, D4, but, are only slightly affected by the sixth order term. The optimum value of D4 is found to be 0.8, because the deviation of the difference between the propagation constants of the two consecutive modes becomes minimum. For the graded-index fiber with D40.8, the on-axis and off-axis transmission characteristics show that the two dimensional image can be transmitted for a length of more than 50 m and the beam waist of the output image becomes 1.3 times of that of the input for spatial impulse image signal.

The purpose of the present note is to provide a necessary and sufficient condition in order that strongly connected group-matrix type automata, whose orders are prime, may be regular. Further, as an applications, a problem concerning factor automata of a strongly connected automaton will be discussed.

In the present paper, we introduce a new type of automata, called generalized group-matrix type automata, for representing general automata in connection with their automorphism groups. A family of subgroups of a given finite group, satisfying a certain condition, called the separation condition, will play a fundamental role.

Focal stacks (FS) have attracted attention as an alternative representation of light field (LF). However, the problem of reconstructing LF from its FS is considered ill-posed. Although many regularization methods have been discussed, no method has been proposed to solve this problem perfectly. This paper showed that the LF can be perfectly reconstructed from the FS through a filter bank in theory for Lambertian scenes without occlusion if the camera aperture for acquiring the FS is a Cauchy function. The numerical simulation demonstrated that the filter bank allows perfect reconstruction of the LF.