QUASI-SELF-IMAGING USING APERIODIC SEQUENCES

Fields with discrete, equally spaced longitudinal spatial frequencies are known to reproduce periodically on propagation. This self-imaging phenomenon is the result of an equalization of the phases acquired by the propagating plane-wave modes. I interpret the self-images as resulting from the presence of sharp peaks in the axial point-spread function and show that the formation of self-images and quasi-self-images does not require a longitudinal periodicity in the spectrum, The necessary condition for quasi-self-imaging is that the longitudinal frequencies form a discrete set resulting from the projection of a periodic lattice of a higher dimension. This leads to periodic, interlaced periodic, or aperiodic sequences that can be used to synthesize periodic self-imaging or aperiodic quasi-self-imaging fields. The effect is analyzed theoretically and demonstrated experimentally.