Design of a circular Dammann grating

Abstract

A novel circular Dammann grating is proposed to generate uniform-intensity impulse rings corresponding to different diffraction orders in the far field. The intensities of the rings are determined by the coefficients of the circular sine series decomposition of the grating function. The definition of diffraction efficiency and uniformity for this novel device are described. Numerical solutions of binary phase circular Dammann gratings are presented. A binary phase three-order circular Dammann grating of pi phase depth is fabricated by an e-beam direct writing technique and is experimentally demonstrated.

Polarization-dependent circular Dammann grating made of azo-dye-doped liquid crystals

“…Circular Dammann gratings with periodic structures have been designed using the Hankel transform method [2,3] and the circular spot rotation method [4]. The phase modulation of the CDG can be binary [2][3][4], which is the simplest type, multilevel [5], or continuous. As a useful diffractive optical element, the CDG was reported to be a useful measurement tool for quick determination of the back focal length of a lens [6].…”

“…The number of the diffractive order with equal intensity in the spectral domain is defined as the order of a CDG. A radially periodic image gðrÞ with period T can be decomposed into a linear combination of circular sinusoid functions as [2] …”

Inverse symmetric Dammann gratings

“…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].…”

Quasi-Dammann grating with proportional intensity array spots

“…Modulation of the periodic structure of a binary diffraction grating to shape the intensity distributions of diffracted orders has attracted considerable interest in recent years [1][2][3][4]. Conventional Dammann gratings are binary-phase Fourier holograms capable of generating one-dimensional and two-dimensional array spots with high efficiency and high uniformity [5].…”

“…2). The phase delays of the cells are 1 (white cells) and 2 (black cells), respectively. L represents the number of cells, and the coordinate of the lth cell's nearest apex to the origin is ͑x l , y l ͒.…”