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

We extend the geometrical theory of aberration for a self-imaging system to the case of two-dimensional oblique lattices. In our approach, the fundamental translation vectors of the lattice are not restricted in both length and orientation. Evaluating the disturbance of light through the oblique lattice under coherent illumination, we find the conditions of constraint which limit the self-imaging of the oblique lattice. Various types of oblique lattices are shown to obey the self-imaging conditions. We derive the equations to trace the optical paths of self-imaging rays and then analyze the ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of the corresponding actual ray. The ray aberrations are shown to disappear when the periods of the lattice are large compared with the wavelength of light. We find that the ray aberrations carried by self-imaged oblique lattices are totally undercorrected and the aberrated image patches are displaced along the direction tangent vector of a chief ray.