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The conditions under which the information inside each subcell of a two-dimensional (2D) object, periodic in orthogonal directions, is replicated throughout all the subcells of the unit cell are obtained. Relative-phase relationship among all the subcells depends only on the number of subdivision but not the length-to-width ratio of the unit cell. From this relationship, the wave amplitude at all the subcells is calculated by superposition of the information from all the subcells in the orginal object. A 2D object periodic in nonorthogonal directions can be decomposed as a set of laterally shifted 2D objects which are periodic in orthogonal directions. Hence, the image formation problem for nonorthogonally periodic object can be solved directly from the superposition of results for the laterally shifted, orthogonally periodic ones.

The information inside each subcell of a two-dimensional periodic object is replicated throughout all the subcells of the unit cell at certain planes. An explicit expression describing the relative phase relationship among the replicated information is derived. From this expression, the wave amplitude at all the subcells caused by the interaction among the information coming from different subcells in the original object is obtained. A computer simulation of gray-level image synthesis using binary substructures and image differentiation is also given.

The natural modes of transverse vibration of circular saws containing radial slots are analyzed in this paper. Incision of equally-spaced asymmetry, equally sized, radial slots at the rim of a saw creates in some, but surprisingly not all, of the vibration modes of the circular saw. It causes the repeated natural frequencies in these asymmetric modes to split into two distinct values. These vibration modes are called the split modes. The vibration modes associated with the repeated natural frequencies, typical of the axisymmetric saw plate, are called the repeated modes. A relationship predicting which vibration modes are split and which are repeated for any configuration of slots on the saw is presented in this paper. Further, it is shown that parametric, transverse vibration instability can be excited in the split modes of the slotted saw by the saw guides and the workpiece. These parametric vibrations can not be excited in the repeated modes. The theoretical predictions of split and repeated vibration modes and the excitation of parametric instability are confirmed by experiments.