Optical Differentiation of Quasi-periodic Patterns Using Talbot Interferometry

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

“…There are a number of oblique-type lattices that are to be self-imaged. An example of the oblique lattice is a hexagonal lattice of which the lattice constants are equal (i.e., a j j ¼ b j j) and the angle between the lattice vectors a and b is of y ¼ 120 : In this case the equations of constraints (8) and (9) are fulfilled for any integers s ¼ t ð Þ and n: Therefore, if we place a source of light at infinity on the left of the lattice and locate a plane of observation at z 0 ¼ 1=K on the right of the lattice, we can observe a self-imaged lattice of unit magnification (i.e., M ¼ 1). Other examples of oblique lattices, obeying the constraints (8) and (9), are the cases in which with equal lattice constants (i.e., a j j ¼ b j j) the angles between a and b are given by y ¼ 60 ; 90 for any integer s ¼ t …”

“…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].…”

Optical wave fields with lateral and longitudinal periodicity

“…In the cited literature, one finds reference to the Talbot effect; however, the aspect that the resonator also adds a longitudinal periodicity to the wave field has been neglected so far. Furthermore, the results may be useful to other situations that include self-imaging, for example, in interferometry [14], and in optical analog and quantum information processing [15,16]. These examples deal with stationary wave fields.…”

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].…”