Coherent Optical Generation and Inspection of Two-dimensional Periodic Structures

Uniform illumination by diffractive shaping of independent light beams

“…Thanks to the particu− lar diffractive element, called fan−out element or Dammann grating (DG) [5], each of the light sources creates an array of small spots which are uniformly distributed on the whole rectangular area. Those dots appear with defined distribution and each light source corresponds to the different subset of the spots.…”

Inverse symmetric Dammann gratings

“…Fig. 1a visualizes this typical binary phase (0, h) grating in a coordinate system normalized to a period length and all the transition points are in the range of [0, 1] [1,2]. Later, Killat et al found that this symmetry is not necessary for the generation of odd-numbered array illumination and improved their results [13].…”

“…This property makes them useful in the fields of optical computing, fiber-optic communications, and image processing which require an element or a system to convert a single input to several outputs. In 1970s, Dammann grating [1,2], a binary surface-relief grating for array illumination in the Fourier-transforming plane, was introduced to generate array illumination in the far field. Since then, the designs and applications of Dammann gratings have aroused continuous interest [3][4][5][6][7][8][9][10][11][12][13][14][15][16]: for example, multilevel-phase gratings [5,6] or continuous-phase gratings [7,8] are proposed and fabricated to improve light efficiency; translational symmetry combined with p phase shift is applied to obtain even-numbered array illuminators [3,4,14], circular Dammann gratings are introduced to generate the circular equal intensities in the different orders [9][10][11] and the even-numbered Dammann grating are used to achieve a dynamic optical coupled technology [12].…”

Ferroelectric Liquid Crystal Dammann Grating by Patterned Photoalignment

“…The Dammann grating is a kind of specially designed binary phase (0, π) grating that could create a diffraction pattern where the intensities of the diffracted spots are equal in some orders [20,21]. The idea of these kinds of grating was first proposed by Dammann and Gortler in 1971 to obtain multiple images from one input object for optical lithography [21].…”