Ray aberrations of two-dimensional oblique lattices on the self-image plane

First-order aberration of a misfocused self-imaging system

“…In addition, the necessary condition for the diffracted pattern to replicate the grating pattern in phase is also given by [23][24][25] 1…”

“…The self-imaging effect is observed under appropriate conditions when a light (or matter) wave is transmitted through (or reflected from) a periodic pattern, and the observed results can be explained by using a scalar theory of diffraction with a parabolic approximation of the optical path length [17][18][19][20][21][22]. Recently, we have attempted a ray-optical approach to the self-imaging of periodic patterns, and then discussed the third-order (or fifth-order) aberrations of a self-imaging system with coherent illumination [23][24][25]. The derived aberration functions may become a measure of accuracy with which periodic patterns are reproduced on the self-image plane.…”

“…In our approach, we first derive the equations to trace the paths of several self-imaging rays of different orders which pass through the point of self-image. The procedure of derivation is based on the Fermat's principle and self-imaging conditions [23][24][25]. We next attempt to derive the functions of wavefront and ray aberrations (corresponding to several self-imaging rays of different orders), which are linear in a small longitudinal shift of focus of the image plane.…”