Self-imaging in polar coordinates

Fractional Montgomery effect: a self-imaging phenomenon

“…A few generalizations are postponed here: twodimensional objects, 25 especially those that benefit from polar coordinates; 26,27 the effect of partial coherence; 3,22,23 and temporal aspects of self-imaging. 15,24 Nevertheless, we hope to have shown that self-imaging is more than the classical Talbot effect.…”

First-order aberration of a misfocused self-imaging system

“…We may, therefore, understand the above results by comparing them with the theoretical estimation of irradiance of the aberrated image in Eq. (20). Fig.…”

“…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].…”

“…shows the irradiance distributions of self-images that are computed from Eq (20),. where we have chosen the aperture of y A ¼ 42p with s ¼ 1 and let other parameters be the same as the experimental conditions.…”

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

“…The image evaluation technique is useful in various applications related to the self-image formation of structures of linear or rectangular periodicity [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The self-imaging effect is not limited to the patterns of linear or rectangular periodicity but extended to the patterns of hexagonal periodicity [18][19][20][21][22]. In this paper, we attempt to extend the geometrical theory of aberration for a self-imaging system to the case of two-dimensional oblique lattices.…”