Characterization of Fresnel images of an elongated circular grating

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

“…(16), the path of the ray will deviate from that of the corresponding self-imaging ray as determined by Eq. (11). Therefore, the point at which the actual ray meets the image plane is displaced from an ideal point of image, so that the shape of the self-image may be aberrated.…”

“…In analogy with the case of a refracting lens system [25], the wavefront aberration W for a self-imaging system may be defined as the difference between the optical path lengths of the self-imaging ray in Eq. (11) and of the actual ray in Eq. (16)…”

“…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].…”

First-order aberration of a misfocused self-imaging system

“…Eversince the first discovery of self-imaging [1,2], various aspects of this phenomenon have been successfully applied in the fields of optical metrology [3][4][5][6][7][8][9][10][11][12], synthesis of mutiple images [13,14] and a regular array of illuminators [15,16]. 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].…”

A moiré method of visualizing electromagnetic force lines

“…In the past years the moire´fringes formed by overlapping simple structures such as line, radial, and circular gratings have been widely examined [4][5][6][7][8]. Also, complicated types of gratings such as Fresnel zones, skewed radial lines, spiral lines, matched radial-parallel lines and elongated circles have been studied for specific applications in moire´metrology [9][10][11][12][13][14]. If any two gratings are superimposed onto each other, optical moire´s readily appear even under the illumination of a white light source.…”