Symmetry property of a generalized Billet's N-split lens

This study examines the diffraction properties of a generalized split N-sector lens originating from Billet's split bi-sector lens. The intensity distributions vary dramatically as the number of split sectors increases, and especially compared with those of the classical Billet's split lens. Nevertheless, the type of lens splitting selected causes the interference pattern of equidistant straight lines in the original Billet's lens to form an N-fold angularly distributed pattern with an angle difference of 2π/N. For an odd number of splitting N, there is an additional angle shift of π/N for the azimuthally distributed patterns of equidistant straight lines. In other words, there are two kinds of symmetry even for simple splitting operations. On the other hand, the peak intensity distribution in the central portion resembles a concentric-circle-like pattern, when N is large as a result of N-beam interference.